id	sid	tid	token	lemma	pos
ma-99	1	1	2023	2023	NUM
ma-99	1	2	ada	ada	PROPN
ma-99	1	3	academica	academica	PROPN
ma-99	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-99	1	5	.	.	PUNCT
ma-99	2	1	j.	j.	PROPN
ma-99	2	2	math	math	PROPN
ma-99	2	3	.	.	PUNCT
ma-99	3	1	anal	anal	ADJ
ma-99	3	2	.	.	PUNCT
ma-99	4	1	3	3	NUM
ma-99	4	2	(	(	PUNCT
ma-99	4	3	2023	2023	NUM
ma-99	4	4	)	)	PUNCT
ma-99	5	1	4doi	4doi	NOUN
ma-99	5	2	:	:	PUNCT
ma-99	5	3	10.28924	10.28924	NUM
ma-99	5	4	/	/	SYM
ma-99	5	5	ada	ada	PROPN
ma-99	5	6	/	/	SYM
ma-99	5	7	ma.3.4	ma.3.4	PROPN
ma-99	5	8	parameter	parameter	PROPN
ma-99	5	9	estimation	estimation	NOUN
ma-99	5	10	for	for	ADP
ma-99	5	11	spdes	spde	NOUN
ma-99	5	12	driven	drive	VERB
ma-99	5	13	by	by	ADP
ma-99	5	14	cylindrical	cylindrical	ADJ
ma-99	5	15	stable	stable	ADJ
ma-99	5	16	processes	process	NOUN
ma-99	5	17	jaya	jaya	PROPN
ma-99	5	18	p.	p.	PROPN
ma-99	5	19	n.	n.	PROPN
ma-99	5	20	bishwal	bishwal	PROPN
ma-99	5	21	department	department	PROPN
ma-99	5	22	of	of	ADP
ma-99	5	23	mathematics	mathematics	PROPN
ma-99	5	24	and	and	CCONJ
ma-99	5	25	statistics	statistic	NOUN
ma-99	5	26	,	,	PUNCT
ma-99	5	27	university	university	PROPN
ma-99	5	28	of	of	ADP
ma-99	5	29	north	north	PROPN
ma-99	5	30	carolina	carolina	PROPN
ma-99	5	31	at	at	ADP
ma-99	5	32	charlotte,376	charlotte,376	PROPN
ma-99	5	33	fretwell	fretwell	NOUN
ma-99	5	34	bldg	bldg	PROPN
ma-99	5	35	,	,	PUNCT
ma-99	5	36	9201	9201	NUM
ma-99	5	37	university	university	NOUN
ma-99	5	38	city	city	NOUN
ma-99	5	39	blvd	blvd	PROPN
ma-99	5	40	.	.	PUNCT
ma-99	6	1	charlotte	charlotte	PROPN
ma-99	6	2	,	,	PUNCT
ma-99	6	3	nc	nc	PROPN
ma-99	6	4	28223	28223	NUM
ma-99	6	5	-	-	PUNCT
ma-99	6	6	0001	0001	NUM
ma-99	6	7	,	,	PUNCT
ma-99	6	8	usacorrespondence	usacorrespondence	NOUN
ma-99	6	9	:	:	PUNCT
ma-99	6	10	j.bishwal@uncc.edu	j.bishwal@uncc.edu	PROPN
ma-99	6	11	abstract	abstract	ADJ
ma-99	6	12	.	.	PUNCT
ma-99	7	1	we	we	PRON
ma-99	7	2	consider	consider	VERB
ma-99	7	3	infinite	infinite	ADJ
ma-99	7	4	dimensional	dimensional	ADJ
ma-99	7	5	extension	extension	NOUN
ma-99	7	6	of	of	ADP
ma-99	7	7	affine	affine	NOUN
ma-99	7	8	models	model	NOUN
ma-99	7	9	with	with	ADP
ma-99	7	10	heavy	heavy	ADJ
ma-99	7	11	tails	tail	NOUN
ma-99	7	12	in	in	ADP
ma-99	7	13	finance	finance	NOUN
ma-99	7	14	.	.	PUNCT
ma-99	8	1	westudy	westudy	VERB
ma-99	8	2	several	several	ADJ
ma-99	8	3	estimators	estimator	NOUN
ma-99	8	4	of	of	ADP
ma-99	8	5	the	the	DET
ma-99	8	6	drift	drift	NOUN
ma-99	8	7	parameter	parameter	NOUN
ma-99	8	8	in	in	ADP
ma-99	8	9	the	the	DET
ma-99	8	10	stochastic	stochastic	ADJ
ma-99	8	11	partial	partial	ADJ
ma-99	8	12	differential	differential	NOUN
ma-99	8	13	equation	equation	NOUN
ma-99	8	14	drivenby	drivenby	VERB
ma-99	8	15	cylindrical	cylindrical	ADJ
ma-99	8	16	stable	stable	ADJ
ma-99	8	17	processes	process	NOUN
ma-99	8	18	.	.	PUNCT
ma-99	9	1	we	we	PRON
ma-99	9	2	consider	consider	VERB
ma-99	9	3	several	several	ADJ
ma-99	9	4	sampling	sample	VERB
ma-99	9	5	schemes	scheme	NOUN
ma-99	9	6	.	.	PUNCT
ma-99	10	1	we	we	PRON
ma-99	10	2	also	also	ADV
ma-99	10	3	consider	consider	VERB
ma-99	10	4	randomsampling	randomsample	VERB
ma-99	10	5	scheme	scheme	NOUN
ma-99	10	6	,	,	PUNCT
ma-99	10	7	e.g	e.g	PROPN
ma-99	10	8	,	,	PUNCT
ma-99	10	9	when	when	SCONJ
ma-99	10	10	the	the	DET
ma-99	10	11	solution	solution	NOUN
ma-99	10	12	process	process	NOUN
ma-99	10	13	is	be	AUX
ma-99	10	14	observed	observe	VERB
ma-99	10	15	at	at	ADP
ma-99	10	16	the	the	DET
ma-99	10	17	arrival	arrival	NOUN
ma-99	10	18	times	time	NOUN
ma-99	10	19	of	of	ADP
ma-99	10	20	a	a	DET
ma-99	10	21	poisson	poisson	NOUN
ma-99	10	22	process.we	process.we	X
ma-99	10	23	obtain	obtain	VERB
ma-99	10	24	the	the	DET
ma-99	10	25	consistency	consistency	NOUN
ma-99	10	26	and	and	CCONJ
ma-99	10	27	the	the	DET
ma-99	10	28	asymptotic	asymptotic	ADJ
ma-99	10	29	normality	normality	NOUN
ma-99	10	30	of	of	ADP
ma-99	10	31	the	the	DET
ma-99	10	32	estimators	estimator	NOUN
ma-99	10	33	.	.	PUNCT
ma-99	11	1	1	1	X
ma-99	11	2	.	.	X
ma-99	11	3	introduction	introduction	NOUN
ma-99	11	4	parameter	parameter	NOUN
ma-99	11	5	estimation	estimation	NOUN
ma-99	11	6	in	in	ADP
ma-99	11	7	stochastic	stochastic	ADJ
ma-99	11	8	partial	partial	ADJ
ma-99	11	9	differential	differential	NOUN
ma-99	11	10	equations	equation	NOUN
ma-99	11	11	is	be	AUX
ma-99	11	12	a	a	DET
ma-99	11	13	very	very	ADV
ma-99	11	14	young	young	ADJ
ma-99	11	15	area	area	NOUN
ma-99	11	16	of	of	ADP
ma-99	11	17	researchin	researchin	NOUN
ma-99	11	18	view	view	NOUN
ma-99	11	19	of	of	ADP
ma-99	11	20	its	its	PRON
ma-99	11	21	applications	application	NOUN
ma-99	11	22	in	in	ADP
ma-99	11	23	finance	finance	NOUN
ma-99	11	24	,	,	PUNCT
ma-99	11	25	physics	physics	NOUN
ma-99	11	26	,	,	PUNCT
ma-99	11	27	biology	biology	NOUN
ma-99	11	28	and	and	CCONJ
ma-99	11	29	oceanography	oceanography	NOUN
ma-99	11	30	.	.	PUNCT
ma-99	12	1	loges	loges	PROPN
ma-99	13	1	[	[	X
ma-99	13	2	32	32	NUM
ma-99	13	3	]	]	PUNCT
ma-99	13	4	initiated	initiate	VERB
ma-99	13	5	thestudy	thestudy	NOUN
ma-99	13	6	of	of	ADP
ma-99	13	7	parameter	parameter	PROPN
ma-99	13	8	estimation	estimation	NOUN
ma-99	13	9	in	in	ADP
ma-99	13	10	infinite	infinite	ADJ
ma-99	13	11	dimensional	dimensional	ADJ
ma-99	13	12	stochastic	stochastic	ADJ
ma-99	13	13	differential	differential	ADJ
ma-99	13	14	equations	equation	NOUN
ma-99	13	15	.	.	PUNCT
ma-99	14	1	when	when	SCONJ
ma-99	14	2	thelength	thelength	NOUN
ma-99	14	3	of	of	ADP
ma-99	14	4	the	the	DET
ma-99	14	5	observation	observation	NOUN
ma-99	14	6	time	time	NOUN
ma-99	14	7	becomes	become	VERB
ma-99	14	8	large	large	ADJ
ma-99	14	9	,	,	PUNCT
ma-99	14	10	he	he	PRON
ma-99	14	11	obtained	obtain	VERB
ma-99	14	12	consistency	consistency	NOUN
ma-99	14	13	and	and	CCONJ
ma-99	14	14	asymptotic	asymptotic	ADJ
ma-99	14	15	normality	normality	NOUN
ma-99	14	16	ofthe	ofthe	PRON
ma-99	14	17	maximum	maximum	ADJ
ma-99	14	18	likelihood	likelihood	NOUN
ma-99	14	19	estimator	estimator	NOUN
ma-99	14	20	(	(	PUNCT
ma-99	14	21	mle	mle	PROPN
ma-99	14	22	)	)	PUNCT
ma-99	14	23	of	of	ADP
ma-99	14	24	a	a	DET
ma-99	14	25	real	real	ADV
ma-99	14	26	valued	value	VERB
ma-99	14	27	drift	drift	NOUN
ma-99	14	28	parameter	parameter	NOUN
ma-99	14	29	in	in	ADP
ma-99	14	30	a	a	DET
ma-99	14	31	hilbert	hilbert	NOUN
ma-99	14	32	space	space	NOUN
ma-99	14	33	valuedsde	valuedsde	NOUN
ma-99	14	34	.	.	PUNCT
ma-99	15	1	koski	koski	PROPN
ma-99	15	2	and	and	CCONJ
ma-99	15	3	loges	loge	NOUN
ma-99	16	1	[	[	X
ma-99	16	2	28	28	NUM
ma-99	16	3	]	]	PUNCT
ma-99	16	4	extended	extend	VERB
ma-99	16	5	the	the	DET
ma-99	16	6	work	work	NOUN
ma-99	16	7	of	of	ADP
ma-99	16	8	loges	loge	NOUN
ma-99	16	9	[	[	X
ma-99	16	10	32	32	NUM
ma-99	16	11	]	]	PUNCT
ma-99	16	12	to	to	ADP
ma-99	16	13	minimum	minimum	ADJ
ma-99	16	14	contrast	contrast	NOUN
ma-99	16	15	estimators	estimator	NOUN
ma-99	16	16	.	.	PUNCT
ma-99	17	1	koskiand	koskiand	PROPN
ma-99	17	2	loges	loges	PROPN
ma-99	18	1	[	[	X
ma-99	18	2	27	27	NUM
ma-99	18	3	]	]	PUNCT
ma-99	18	4	applied	apply	VERB
ma-99	18	5	the	the	DET
ma-99	18	6	work	work	NOUN
ma-99	18	7	to	to	ADP
ma-99	18	8	a	a	DET
ma-99	18	9	stochastic	stochastic	ADJ
ma-99	18	10	heat	heat	NOUN
ma-99	18	11	flow	flow	NOUN
ma-99	18	12	problem	problem	NOUN
ma-99	18	13	.	.	PUNCT
ma-99	19	1	martingale	martingale	PROPN
ma-99	19	2	estimation	estimation	NOUN
ma-99	19	3	functionfor	functionfor	NOUN
ma-99	19	4	discretely	discretely	ADV
ma-99	19	5	observed	observe	VERB
ma-99	19	6	diffusions	diffusion	NOUN
ma-99	19	7	was	be	AUX
ma-99	19	8	studied	study	VERB
ma-99	19	9	in	in	ADP
ma-99	19	10	bibby	bibby	PROPN
ma-99	19	11	and	and	CCONJ
ma-99	19	12	srensen	srensen	NOUN
ma-99	19	13	[	[	X
ma-99	19	14	2	2	NUM
ma-99	19	15	]	]	PUNCT
ma-99	19	16	.	.	PUNCT
ma-99	20	1	bishwal	bishwal	NOUN
ma-99	21	1	[	[	X
ma-99	21	2	6	6	NUM
ma-99	21	3	]	]	PUNCT
ma-99	21	4	studied	study	VERB
ma-99	21	5	a	a	DET
ma-99	21	6	newestimating	newestimating	NOUN
ma-99	21	7	function	function	NOUN
ma-99	21	8	for	for	ADP
ma-99	21	9	discretely	discretely	ADV
ma-99	21	10	sampled	sample	VERB
ma-99	21	11	diffusions	diffusion	NOUN
ma-99	21	12	by	by	ADP
ma-99	21	13	removing	remove	VERB
ma-99	21	14	the	the	DET
ma-99	21	15	stochastic	stochastic	ADJ
ma-99	21	16	integral	integral	NOUN
ma-99	21	17	in	in	ADP
ma-99	21	18	girsanovlikelihood	girsanovlikelihood	NOUN
ma-99	21	19	.	.	PUNCT
ma-99	22	1	bishwal	bishwal	NOUN
ma-99	23	1	[	[	X
ma-99	23	2	7	7	X
ma-99	23	3	]	]	PUNCT
ma-99	23	4	contains	contain	VERB
ma-99	23	5	asymptotic	asymptotic	ADJ
ma-99	23	6	theory	theory	NOUN
ma-99	23	7	on	on	ADP
ma-99	23	8	likelihood	likelihood	NOUN
ma-99	23	9	method	method	NOUN
ma-99	23	10	and	and	CCONJ
ma-99	23	11	bayesian	bayesian	NOUN
ma-99	23	12	method	method	NOUN
ma-99	23	13	fordrift	fordrift	NOUN
ma-99	23	14	estimation	estimation	NOUN
ma-99	23	15	of	of	ADP
ma-99	23	16	finite	finite	NOUN
ma-99	23	17	and	and	CCONJ
ma-99	23	18	infinite	infinite	ADJ
ma-99	23	19	dimensional	dimensional	ADJ
ma-99	23	20	stochastic	stochastic	ADJ
ma-99	23	21	differential	differential	ADJ
ma-99	23	22	equations	equation	NOUN
ma-99	23	23	.	.	PUNCT
ma-99	24	1	bishwal	bishwal	NOUN
ma-99	25	1	[	[	X
ma-99	25	2	12]studied	12]studied	NUM
ma-99	25	3	applications	application	NOUN
ma-99	25	4	of	of	ADP
ma-99	25	5	levy	levy	NOUN
ma-99	25	6	processes	process	NOUN
ma-99	25	7	in	in	ADP
ma-99	25	8	stochastic	stochastic	ADJ
ma-99	25	9	volatility	volatility	NOUN
ma-99	25	10	models	model	NOUN
ma-99	25	11	in	in	ADP
ma-99	25	12	finance.huebner	finance.huebner	PROPN
ma-99	25	13	,	,	PUNCT
ma-99	25	14	khasminskii	khasminskii	ADJ
ma-99	25	15	and	and	CCONJ
ma-99	25	16	rozovskii	rozovskii	PROPN
ma-99	25	17	[	[	X
ma-99	25	18	23	23	NUM
ma-99	25	19	]	]	PUNCT
ma-99	25	20	started	start	VERB
ma-99	25	21	statistical	statistical	ADJ
ma-99	25	22	investigation	investigation	NOUN
ma-99	25	23	in	in	ADP
ma-99	25	24	spdes	spde	NOUN
ma-99	25	25	.	.	PUNCT
ma-99	26	1	they	they	PRON
ma-99	26	2	gavetwo	gavetwo	VERB
ma-99	26	3	contrast	contrast	NOUN
ma-99	26	4	examples	example	NOUN
ma-99	26	5	of	of	ADP
ma-99	26	6	parabolic	parabolic	ADJ
ma-99	26	7	spdes	spde	NOUN
ma-99	26	8	in	in	ADP
ma-99	26	9	one	one	NUM
ma-99	26	10	of	of	ADP
ma-99	26	11	which	which	PRON
ma-99	26	12	they	they	PRON
ma-99	26	13	obtained	obtain	VERB
ma-99	26	14	consistency	consistency	NOUN
ma-99	26	15	,	,	PUNCT
ma-99	26	16	asymptoticnormality	asymptoticnormality	NOUN
ma-99	26	17	and	and	CCONJ
ma-99	26	18	asymptotic	asymptotic	ADJ
ma-99	26	19	efficiency	efficiency	NOUN
ma-99	26	20	of	of	ADP
ma-99	26	21	the	the	DET
ma-99	26	22	mle	mle	NOUN
ma-99	26	23	as	as	SCONJ
ma-99	26	24	noise	noise	NOUN
ma-99	26	25	intensity	intensity	NOUN
ma-99	26	26	decreases	decrease	VERB
ma-99	26	27	to	to	ADP
ma-99	26	28	zero	zero	NUM
ma-99	26	29	under	under	ADP
ma-99	26	30	thecondition	thecondition	NOUN
ma-99	26	31	of	of	ADP
ma-99	26	32	absolute	absolute	ADJ
ma-99	26	33	continuity	continuity	NOUN
ma-99	26	34	of	of	ADP
ma-99	26	35	measures	measure	NOUN
ma-99	26	36	generated	generate	VERB
ma-99	26	37	by	by	ADP
ma-99	26	38	the	the	DET
ma-99	26	39	process	process	NOUN
ma-99	26	40	for	for	ADP
ma-99	26	41	different	different	ADJ
ma-99	26	42	parameters	parameter	NOUN
ma-99	26	43	(	(	PUNCT
ma-99	26	44	the	the	DET
ma-99	26	45	received	receive	VERB
ma-99	26	46	:	:	PUNCT
ma-99	26	47	12	12	NUM
ma-99	26	48	apr	apr	NOUN
ma-99	26	49	2022	2022	NUM
ma-99	26	50	.	.	PUNCT
ma-99	27	1	key	key	ADJ
ma-99	27	2	words	word	NOUN
ma-99	27	3	and	and	CCONJ
ma-99	27	4	phrases	phrase	NOUN
ma-99	27	5	.	.	PUNCT
ma-99	28	1	stochastic	stochastic	ADJ
ma-99	28	2	partial	partial	ADJ
ma-99	28	3	differential	differential	NOUN
ma-99	28	4	equations	equation	NOUN
ma-99	28	5	;	;	PUNCT
ma-99	28	6	space	space	NOUN
ma-99	28	7	-	-	PUNCT
ma-99	28	8	time	time	NOUN
ma-99	28	9	colored	colored	ADJ
ma-99	28	10	noise	noise	NOUN
ma-99	28	11	;	;	PUNCT
ma-99	28	12	cylindrical	cylindrical	ADJ
ma-99	28	13	stable	stable	ADJ
ma-99	28	14	process;stable	process;stable	ADJ
ma-99	28	15	random	random	ADJ
ma-99	28	16	field	field	NOUN
ma-99	28	17	;	;	PUNCT
ma-99	28	18	super	super	ADJ
ma-99	28	19	levy	levy	NOUN
ma-99	28	20	process	process	NOUN
ma-99	28	21	;	;	PUNCT
ma-99	28	22	poisson	poisson	NOUN
ma-99	28	23	sampling	sampling	NOUN
ma-99	28	24	;	;	PUNCT
ma-99	28	25	martingale	martingale	NUM
ma-99	28	26	estimating	estimate	VERB
ma-99	28	27	function	function	NOUN
ma-99	28	28	;	;	PUNCT
ma-99	28	29	quasi	quasi	NOUN
ma-99	28	30	likelihood	likelihood	VERB
ma-99	28	31	estimator;stable	estimator;stable	PROPN
ma-99	28	32	ornstein	ornstein	PROPN
ma-99	28	33	-	-	PUNCT
ma-99	28	34	uhlenbeck	uhlenbeck	PROPN
ma-99	28	35	process	process	NOUN
ma-99	28	36	;	;	PUNCT
ma-99	28	37	stable	stable	ADJ
ma-99	28	38	black	black	ADJ
ma-99	28	39	-	-	PUNCT
ma-99	28	40	scholes	schole	NOUN
ma-99	28	41	model	model	NOUN
ma-99	28	42	;	;	PUNCT
ma-99	28	43	stable	stable	ADJ
ma-99	28	44	cox	cox	PROPN
ma-99	28	45	-	-	PUNCT
ma-99	28	46	ingersoll	ingersoll	PROPN
ma-99	28	47	-	-	PUNCT
ma-99	28	48	ross	ross	PROPN
ma-99	28	49	model	model	NOUN
ma-99	28	50	;	;	PUNCT
ma-99	28	51	consistency	consistency	NOUN
ma-99	28	52	;	;	PUNCT
ma-99	28	53	asymp	asymp	NOUN
ma-99	28	54	-	-	PUNCT
ma-99	28	55	totic	totic	ADJ
ma-99	28	56	normality	normality	NOUN
ma-99	28	57	.	.	PUNCT
ma-99	29	1	1	1	NUM
ma-99	29	2	https://adac.ee	https://adac.ee	PROPN
ma-99	29	3	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	29	4	eur	eur	NOUN
ma-99	29	5	.	.	PUNCT
ma-99	30	1	j.	j.	PROPN
ma-99	30	2	math	math	PROPN
ma-99	30	3	.	.	PUNCT
ma-99	31	1	anal	anal	PROPN
ma-99	31	2	.	.	PUNCT
ma-99	32	1	10.28924	10.28924	NUM
ma-99	32	2	/	/	SYM
ma-99	32	3	ada	ada	PROPN
ma-99	32	4	/	/	SYM
ma-99	32	5	ma.3.4	ma.3.4	PROPN
ma-99	32	6	2situation	2situation	PROPN
ma-99	32	7	is	be	AUX
ma-99	32	8	similar	similar	ADJ
ma-99	32	9	to	to	ADP
ma-99	32	10	the	the	DET
ma-99	32	11	classical	classical	ADJ
ma-99	32	12	finite	finite	ADJ
ma-99	32	13	dimensional	dimensional	ADJ
ma-99	32	14	case	case	NOUN
ma-99	32	15	)	)	PUNCT
ma-99	32	16	and	and	CCONJ
ma-99	32	17	in	in	ADP
ma-99	32	18	the	the	DET
ma-99	32	19	other	other	ADJ
ma-99	32	20	they	they	PRON
ma-99	32	21	obtained	obtain	VERB
ma-99	32	22	theseproperties	thesepropertie	NOUN
ma-99	32	23	as	as	SCONJ
ma-99	32	24	the	the	DET
ma-99	32	25	finite	finite	ADJ
ma-99	32	26	dimensional	dimensional	ADJ
ma-99	32	27	projection	projection	NOUN
ma-99	32	28	becomes	become	VERB
ma-99	32	29	large	large	ADJ
ma-99	32	30	under	under	ADP
ma-99	32	31	the	the	DET
ma-99	32	32	condition	condition	NOUN
ma-99	32	33	of	of	ADP
ma-99	32	34	singularity	singularity	NOUN
ma-99	32	35	ofthe	ofthe	NOUN
ma-99	32	36	measures	measure	NOUN
ma-99	32	37	generated	generate	VERB
ma-99	32	38	by	by	ADP
ma-99	32	39	the	the	DET
ma-99	32	40	process	process	NOUN
ma-99	32	41	for	for	ADP
ma-99	32	42	different	different	ADJ
ma-99	32	43	parameters	parameter	NOUN
ma-99	32	44	.	.	PUNCT
ma-99	33	1	the	the	DET
ma-99	33	2	second	second	ADJ
ma-99	33	3	example	example	NOUN
ma-99	33	4	was	be	AUX
ma-99	33	5	extendedby	extendedby	PROPN
ma-99	33	6	huebner	huebner	NOUN
ma-99	33	7	and	and	CCONJ
ma-99	33	8	rozovskii	rozovskii	PROPN
ma-99	33	9	[	[	X
ma-99	33	10	24	24	NUM
ma-99	33	11	]	]	PUNCT
ma-99	33	12	and	and	CCONJ
ma-99	33	13	the	the	DET
ma-99	33	14	first	first	ADJ
ma-99	33	15	example	example	NOUN
ma-99	33	16	was	be	AUX
ma-99	33	17	extended	extend	VERB
ma-99	33	18	by	by	ADP
ma-99	33	19	huebner	huebner	NOUN
ma-99	34	1	[	[	X
ma-99	34	2	22	22	NUM
ma-99	34	3	]	]	PUNCT
ma-99	34	4	to	to	ADP
ma-99	34	5	mle	mle	PROPN
ma-99	34	6	forgeneral	forgeneral	PROPN
ma-99	34	7	parabolic	parabolic	PROPN
ma-99	34	8	spdes	spde	NOUN
ma-99	34	9	where	where	SCONJ
ma-99	34	10	the	the	DET
ma-99	34	11	partial	partial	ADJ
ma-99	34	12	differential	differential	NOUN
ma-99	34	13	operators	operator	NOUN
ma-99	34	14	commute	commute	VERB
ma-99	34	15	and	and	CCONJ
ma-99	34	16	satisfy	satisfy	NOUN
ma-99	34	17	differentorder	differentorder	NOUN
ma-99	34	18	conditions	condition	NOUN
ma-99	34	19	in	in	ADP
ma-99	34	20	the	the	DET
ma-99	34	21	two	two	NUM
ma-99	34	22	cases.huebner	cases.huebner	NOUN
ma-99	35	1	[	[	X
ma-99	35	2	21	21	NUM
ma-99	35	3	]	]	PUNCT
ma-99	35	4	extended	extend	VERB
ma-99	35	5	the	the	DET
ma-99	35	6	problem	problem	NOUN
ma-99	35	7	to	to	ADP
ma-99	35	8	the	the	DET
ma-99	35	9	ml	ml	X
ma-99	35	10	estimation	estimation	NOUN
ma-99	35	11	of	of	ADP
ma-99	35	12	multidimensional	multidimensional	ADJ
ma-99	35	13	parameter	parameter	NOUN
ma-99	35	14	.	.	PUNCT
ma-99	36	1	lototskyand	lototskyand	NOUN
ma-99	36	2	rozovskii	rozovskii	PROPN
ma-99	37	1	[	[	X
ma-99	37	2	33	33	NUM
ma-99	37	3	]	]	PUNCT
ma-99	37	4	studied	study	VERB
ma-99	37	5	the	the	DET
ma-99	37	6	same	same	ADJ
ma-99	37	7	problem	problem	NOUN
ma-99	37	8	without	without	ADP
ma-99	37	9	the	the	DET
ma-99	37	10	commutativity	commutativity	NOUN
ma-99	37	11	condition	condition	NOUN
ma-99	37	12	.	.	PUNCT
ma-99	38	1	small	small	ADJ
ma-99	38	2	noiseasymptotics	noiseasymptotic	NOUN
ma-99	38	3	of	of	ADP
ma-99	38	4	the	the	DET
ma-99	38	5	nonparmetric	nonparmetric	ADJ
ma-99	38	6	estimation	estimation	NOUN
ma-99	38	7	of	of	ADP
ma-99	38	8	the	the	DET
ma-99	38	9	drift	drift	NOUN
ma-99	38	10	coefficient	coefficient	NOUN
ma-99	38	11	was	be	AUX
ma-99	38	12	studies	study	NOUN
ma-99	38	13	by	by	ADP
ma-99	38	14	ibragimov	ibragimov	ADJ
ma-99	38	15	andkhasminskii	andkhasminskii	NOUN
ma-99	39	1	[	[	X
ma-99	39	2	29].based	29].base	VERB
ma-99	39	3	on	on	ADP
ma-99	39	4	continuous	continuous	ADJ
ma-99	39	5	observations	observation	NOUN
ma-99	39	6	,	,	PUNCT
ma-99	39	7	usually	usually	ADV
ma-99	39	8	there	there	PRON
ma-99	39	9	can	can	AUX
ma-99	39	10	be	be	AUX
ma-99	39	11	two	two	NUM
ma-99	39	12	asymptotic	asymptotic	ADJ
ma-99	39	13	settings	setting	NOUN
ma-99	39	14	in	in	ADP
ma-99	39	15	spde	spde	NOUN
ma-99	39	16	:	:	PUNCT
ma-99	39	17	1	1	X
ma-99	39	18	)	)	PUNCT
ma-99	39	19	t	t	NOUN
ma-99	39	20	→	→	SYM
ma-99	39	21	∞	∞	PROPN
ma-99	39	22	2	2	NUM
ma-99	39	23	)	)	PUNCT
ma-99	39	24	n	n	NOUN
ma-99	39	25	→	→	SYM
ma-99	39	26	∞	∞	PROPN
ma-99	39	27	where	where	SCONJ
ma-99	39	28	t	t	PROPN
ma-99	39	29	is	be	AUX
ma-99	39	30	the	the	DET
ma-99	39	31	length	length	NOUN
ma-99	39	32	of	of	ADP
ma-99	39	33	the	the	DET
ma-99	39	34	observations	observation	NOUN
ma-99	39	35	and	and	CCONJ
ma-99	39	36	n	n	NOUN
ma-99	39	37	is	be	AUX
ma-99	39	38	the	the	DET
ma-99	39	39	number	number	NOUN
ma-99	39	40	of	of	ADP
ma-99	39	41	fouriercoefficients	fouriercoefficient	NOUN
ma-99	39	42	of	of	ADP
ma-99	39	43	the	the	DET
ma-99	39	44	spde	spde	NOUN
ma-99	39	45	solution.in	solution.in	PROPN
ma-99	39	46	a	a	DET
ma-99	39	47	bayesian	bayesian	NOUN
ma-99	39	48	approach	approach	NOUN
ma-99	39	49	,	,	PUNCT
ma-99	39	50	using	use	VERB
ma-99	39	51	the	the	DET
ma-99	39	52	first	first	ADJ
ma-99	39	53	setting	setting	NOUN
ma-99	39	54	,	,	PUNCT
ma-99	39	55	bishwal	bishwal	NOUN
ma-99	40	1	[	[	X
ma-99	40	2	3	3	NUM
ma-99	40	3	]	]	PUNCT
ma-99	40	4	proved	prove	VERB
ma-99	40	5	the	the	DET
ma-99	40	6	bernstein	bernstein	PROPN
ma-99	40	7	-	-	PUNCT
ma-99	40	8	von	von	PROPN
ma-99	40	9	misestheorem	misestheorem	PROPN
ma-99	40	10	and	and	CCONJ
ma-99	40	11	asymptotic	asymptotic	ADJ
ma-99	40	12	properties	property	NOUN
ma-99	40	13	of	of	ADP
ma-99	40	14	regular	regular	ADJ
ma-99	40	15	bayes	bayes	NOUN
ma-99	40	16	estimator	estimator	NOUN
ma-99	40	17	of	of	ADP
ma-99	40	18	the	the	DET
ma-99	40	19	drift	drift	NOUN
ma-99	40	20	parameter	parameter	NOUN
ma-99	40	21	in	in	ADP
ma-99	40	22	a	a	DET
ma-99	40	23	hilbertspace	hilbertspace	NOUN
ma-99	40	24	valued	value	VERB
ma-99	40	25	sde	sde	PROPN
ma-99	40	26	when	when	SCONJ
ma-99	40	27	the	the	DET
ma-99	40	28	corresponding	corresponding	ADJ
ma-99	40	29	ergodic	ergodic	ADJ
ma-99	40	30	diffusion	diffusion	NOUN
ma-99	40	31	process	process	NOUN
ma-99	40	32	is	be	AUX
ma-99	40	33	observed	observe	VERB
ma-99	40	34	continuously	continuously	ADV
ma-99	40	35	overa	overa	NOUN
ma-99	40	36	time	time	NOUN
ma-99	40	37	interval	interval	NOUN
ma-99	40	38	[	[	X
ma-99	40	39	0	0	NUM
ma-99	40	40	,	,	PUNCT
ma-99	40	41	t	t	X
ma-99	40	42	]	]	PUNCT
ma-99	40	43	.	.	PUNCT
ma-99	41	1	the	the	DET
ma-99	41	2	asymptotics	asymptotic	NOUN
ma-99	41	3	are	be	AUX
ma-99	41	4	studied	study	VERB
ma-99	41	5	as	as	ADP
ma-99	41	6	t	t	PROPN
ma-99	41	7	→	→	SYM
ma-99	41	8	∞	∞	PROPN
ma-99	41	9	under	under	ADP
ma-99	41	10	the	the	DET
ma-99	41	11	condition	condition	NOUN
ma-99	41	12	of	of	ADP
ma-99	41	13	absolutecontinuity	absolutecontinuity	NOUN
ma-99	41	14	of	of	ADP
ma-99	41	15	measures	measure	NOUN
ma-99	41	16	generated	generate	VERB
ma-99	41	17	by	by	ADP
ma-99	41	18	the	the	DET
ma-99	41	19	process	process	NOUN
ma-99	41	20	.	.	PUNCT
ma-99	42	1	results	result	NOUN
ma-99	42	2	are	be	AUX
ma-99	42	3	illustrated	illustrate	VERB
ma-99	42	4	for	for	ADP
ma-99	42	5	the	the	DET
ma-99	42	6	example	example	NOUN
ma-99	42	7	of	of	ADP
ma-99	42	8	anspde.using	anspde.use	VERB
ma-99	42	9	the	the	DET
ma-99	42	10	second	second	ADJ
ma-99	42	11	setting	setting	NOUN
ma-99	42	12	,	,	PUNCT
ma-99	42	13	bishwal	bishwal	NOUN
ma-99	43	1	[	[	X
ma-99	43	2	5	5	NUM
ma-99	43	3	]	]	PUNCT
ma-99	43	4	proved	prove	VERB
ma-99	43	5	the	the	DET
ma-99	43	6	bernstein	bernstein	PROPN
ma-99	43	7	-	-	PUNCT
ma-99	43	8	von	von	PROPN
ma-99	43	9	mises	mises	PROPN
ma-99	43	10	theorem	theorem	VERB
ma-99	43	11	and	and	CCONJ
ma-99	43	12	spectralasymptotics	spectralasymptotic	NOUN
ma-99	43	13	of	of	ADP
ma-99	43	14	bayes	bayes	NOUN
ma-99	43	15	estimators	estimator	NOUN
ma-99	43	16	for	for	ADP
ma-99	43	17	parabolic	parabolic	ADJ
ma-99	43	18	spdes	spde	NOUN
ma-99	43	19	when	when	SCONJ
ma-99	43	20	the	the	DET
ma-99	43	21	number	number	NOUN
ma-99	43	22	of	of	ADP
ma-99	43	23	fourier	fourier	NOUN
ma-99	43	24	coefficientsbecomes	coefficientsbecome	NOUN
ma-99	43	25	large	large	ADJ
ma-99	43	26	.	.	PUNCT
ma-99	44	1	in	in	ADP
ma-99	44	2	this	this	DET
ma-99	44	3	case	case	NOUN
ma-99	44	4	,	,	PUNCT
ma-99	44	5	the	the	DET
ma-99	44	6	measures	measure	NOUN
ma-99	44	7	generated	generate	VERB
ma-99	44	8	by	by	ADP
ma-99	44	9	the	the	DET
ma-99	44	10	process	process	NOUN
ma-99	44	11	for	for	ADP
ma-99	44	12	different	different	ADJ
ma-99	44	13	parameters	parameter	NOUN
ma-99	45	1	aresingular.bishwal	aresingular.bishwal	INTJ
ma-99	45	2	[	[	X
ma-99	45	3	10	10	NUM
ma-99	45	4	]	]	PUNCT
ma-99	45	5	studied	study	VERB
ma-99	45	6	bernstein	bernstein	PROPN
ma-99	45	7	-	-	PUNCT
ma-99	45	8	von	von	PROPN
ma-99	45	9	mises	mises	PROPN
ma-99	45	10	theorem	theorem	VERB
ma-99	45	11	and	and	CCONJ
ma-99	45	12	small	small	ADJ
ma-99	45	13	noise	noise	NOUN
ma-99	45	14	bayesian	bayesian	NOUN
ma-99	45	15	asymptotics	asymptotic	NOUN
ma-99	45	16	for	for	ADP
ma-99	45	17	par	par	ADJ
ma-99	45	18	-	-	PUNCT
ma-99	45	19	abolic	abolic	ADJ
ma-99	45	20	stochastic	stochastic	ADJ
ma-99	45	21	partial	partial	ADJ
ma-99	45	22	differential	differential	NOUN
ma-99	45	23	equations	equation	NOUN
ma-99	45	24	.	.	PUNCT
ma-99	46	1	bishwal	bishwal	NOUN
ma-99	47	1	[	[	X
ma-99	47	2	9	9	NUM
ma-99	47	3	]	]	PUNCT
ma-99	47	4	studied	study	VERB
ma-99	47	5	hypothesis	hypothesis	NOUN
ma-99	47	6	testing	testing	NOUN
ma-99	47	7	for	for	ADP
ma-99	47	8	fractionalstochastic	fractionalstochastic	ADJ
ma-99	47	9	partial	partial	ADJ
ma-99	47	10	differential	differential	NOUN
ma-99	47	11	equations	equation	NOUN
ma-99	47	12	with	with	ADP
ma-99	47	13	applications	application	NOUN
ma-99	47	14	to	to	ADP
ma-99	47	15	neurophysiology	neurophysiology	NOUN
ma-99	47	16	and	and	CCONJ
ma-99	47	17	finance.in	finance.in	PRON
ma-99	47	18	this	this	DET
ma-99	47	19	paper	paper	NOUN
ma-99	47	20	we	we	PRON
ma-99	47	21	study	study	VERB
ma-99	47	22	the	the	DET
ma-99	47	23	asymptotic	asymptotic	ADJ
ma-99	47	24	properties	property	NOUN
ma-99	47	25	of	of	ADP
ma-99	47	26	the	the	DET
ma-99	47	27	quasi	quasi	ADJ
ma-99	47	28	maximum	maximum	PROPN
ma-99	47	29	likelihood	likelihood	NOUN
ma-99	47	30	estimatorwhen	estimatorwhen	ADV
ma-99	47	31	we	we	PRON
ma-99	47	32	have	have	VERB
ma-99	47	33	observations	observation	NOUN
ma-99	47	34	of	of	ADP
ma-99	47	35	finite	finite	ADJ
ma-99	47	36	-	-	ADJ
ma-99	47	37	dimensional	dimensional	ADJ
ma-99	47	38	projections	projection	NOUN
ma-99	47	39	at	at	ADP
ma-99	47	40	poisson	poisson	PROPN
ma-99	47	41	arrival	arrival	PROPN
ma-99	47	42	time	time	NOUN
ma-99	47	43	points	point	NOUN
ma-99	47	44	.	.	PUNCT
ma-99	48	1	theasymptotic	theasymptotic	ADJ
ma-99	48	2	setting	setting	NOUN
ma-99	48	3	is	be	AUX
ma-99	48	4	only	only	ADV
ma-99	48	5	the	the	DET
ma-99	48	6	large	large	ADJ
ma-99	48	7	number	number	NOUN
ma-99	48	8	of	of	ADP
ma-99	48	9	observations	observation	NOUN
ma-99	48	10	at	at	ADP
ma-99	48	11	random	random	ADJ
ma-99	48	12	time	time	NOUN
ma-99	48	13	points	point	NOUN
ma-99	48	14	which	which	PRON
ma-99	48	15	are	be	AUX
ma-99	48	16	thearrivals	thearrival	NOUN
ma-99	48	17	of	of	ADP
ma-99	48	18	a	a	DET
ma-99	48	19	poisson	poisson	NOUN
ma-99	48	20	process.the	process.the	DET
ma-99	48	21	rest	rest	NOUN
ma-99	48	22	of	of	ADP
ma-99	48	23	the	the	DET
ma-99	48	24	paper	paper	NOUN
ma-99	48	25	is	be	AUX
ma-99	48	26	organized	organize	VERB
ma-99	48	27	as	as	SCONJ
ma-99	48	28	follows	follow	VERB
ma-99	48	29	:	:	PUNCT
ma-99	48	30	section	section	NOUN
ma-99	48	31	2	2	NUM
ma-99	48	32	contains	contain	VERB
ma-99	48	33	model	model	NOUN
ma-99	48	34	,	,	PUNCT
ma-99	48	35	assumptions	assumption	VERB
ma-99	48	36	andpreliminaries	andpreliminarie	NOUN
ma-99	48	37	.	.	PUNCT
ma-99	49	1	in	in	ADP
ma-99	49	2	section	section	NOUN
ma-99	49	3	3	3	NUM
ma-99	49	4	we	we	PRON
ma-99	49	5	prove	prove	VERB
ma-99	49	6	estimation	estimation	NOUN
ma-99	49	7	results	result	NOUN
ma-99	49	8	with	with	ADP
ma-99	49	9	additive	additive	ADJ
ma-99	49	10	noise	noise	NOUN
ma-99	49	11	.	.	PUNCT
ma-99	50	1	section	section	NOUN
ma-99	50	2	4	4	NUM
ma-99	50	3	and	and	CCONJ
ma-99	50	4	5	5	NUM
ma-99	50	5	,	,	PUNCT
ma-99	50	6	weprovide	weprovide	ADP
ma-99	50	7	estimation	estimation	NOUN
ma-99	50	8	results	result	NOUN
ma-99	50	9	with	with	ADP
ma-99	50	10	multiplicative	multiplicative	ADJ
ma-99	50	11	noise	noise	NOUN
ma-99	50	12	.	.	PUNCT
ma-99	51	1	in	in	ADP
ma-99	51	2	section	section	NOUN
ma-99	51	3	6	6	NUM
ma-99	51	4	,	,	PUNCT
ma-99	51	5	we	we	PRON
ma-99	51	6	give	give	VERB
ma-99	51	7	several	several	ADJ
ma-99	51	8	examples	example	NOUN
ma-99	51	9	.	.	PUNCT
ma-99	52	1	2	2	X
ma-99	52	2	.	.	X
ma-99	52	3	model	model	NOUN
ma-99	52	4	and	and	CCONJ
ma-99	52	5	preliminaries	preliminary	NOUN
ma-99	52	6	let	let	VERB
ma-99	52	7	h	h	NOUN
ma-99	52	8	be	be	AUX
ma-99	52	9	a	a	DET
ma-99	52	10	real	real	ADJ
ma-99	52	11	separable	separable	ADJ
ma-99	52	12	hilbert	hilbert	NOUN
ma-99	52	13	space	space	NOUN
ma-99	52	14	with	with	ADP
ma-99	52	15	inner	inner	ADJ
ma-99	52	16	product	product	NOUN
ma-99	52	17	〈	〈	PROPN
ma-99	52	18	·	·	SYM
ma-99	52	19	〉	〉	PROPN
ma-99	52	20	and	and	CCONJ
ma-99	52	21	norm	norm	NOUN
ma-99	52	22	|	|	ADV
ma-99	52	23	·	·	PUNCT
ma-99	52	24	|	|	INTJ
ma-99	52	25	.	.	PUNCT
ma-99	53	1	by	by	ADP
ma-99	53	2	l(h	l(h	PROPN
ma-99	53	3	)	)	PUNCT
ma-99	53	4	we	we	PRON
ma-99	53	5	denotethe	denotethe	VERB
ma-99	53	6	banach	banach	NOUN
ma-99	53	7	space	space	NOUN
ma-99	53	8	of	of	ADP
ma-99	53	9	bounded	bounded	ADJ
ma-99	53	10	linear	linear	PROPN
ma-99	53	11	operators	operator	NOUN
ma-99	53	12	from	from	ADP
ma-99	53	13	h	h	PROPN
ma-99	53	14	into	into	ADP
ma-99	53	15	h	h	NOUN
ma-99	53	16	endowded	endowde	VERB
ma-99	53	17	with	with	ADP
ma-99	53	18	the	the	DET
ma-99	53	19	operator	operator	NOUN
ma-99	53	20	norm	norm	NOUN
ma-99	53	21	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	53	22	eur	eur	PROPN
ma-99	53	23	.	.	PUNCT
ma-99	54	1	j.	j.	PROPN
ma-99	54	2	math	math	PROPN
ma-99	54	3	.	.	PUNCT
ma-99	55	1	anal	anal	PROPN
ma-99	55	2	.	.	PUNCT
ma-99	56	1	10.28924	10.28924	NUM
ma-99	56	2	/	/	SYM
ma-99	56	3	ada	ada	PROPN
ma-99	56	4	/	/	SYM
ma-99	56	5	ma.3.4	ma.3.4	PROPN
ma-99	56	6	3	3	NUM
ma-99	56	7	‖	‖	PROPN
ma-99	56	8	·	·	PUNCT
ma-99	56	9	‖l(h	‖l(h	NUM
ma-99	56	10	)	)	PUNCT
ma-99	56	11	.	.	PUNCT
ma-99	57	1	we	we	PRON
ma-99	57	2	fix	fix	VERB
ma-99	57	3	an	an	DET
ma-99	57	4	orthonormal	orthonormal	ADJ
ma-99	57	5	basis	basis	NOUN
ma-99	57	6	(	(	PUNCT
ma-99	57	7	en	en	X
ma-99	57	8	)	)	PUNCT
ma-99	57	9	in	in	ADP
ma-99	57	10	h.	h.	PROPN
ma-99	57	11	through	through	ADP
ma-99	57	12	the	the	DET
ma-99	57	13	basis	basis	NOUN
ma-99	57	14	(	(	PUNCT
ma-99	57	15	en	en	X
ma-99	57	16	)	)	PUNCT
ma-99	57	17	we	we	PRON
ma-99	57	18	will	will	AUX
ma-99	57	19	often	often	ADV
ma-99	57	20	identify	identify	VERB
ma-99	57	21	hin	hin	PRON
ma-99	57	22	l2	l2	NOUN
ma-99	57	23	.	.	PUNCT
ma-99	58	1	more	more	ADV
ma-99	58	2	generally	generally	ADV
ma-99	58	3	,	,	PUNCT
ma-99	58	4	for	for	ADP
ma-99	58	5	a	a	DET
ma-99	58	6	given	give	VERB
ma-99	58	7	sequence	sequence	NOUN
ma-99	58	8	ρ	ρ	NOUN
ma-99	58	9	=	=	SYM
ma-99	58	10	(	(	PUNCT
ma-99	58	11	ρn	ρn	INTJ
ma-99	58	12	)	)	PUNCT
ma-99	58	13	of	of	ADP
ma-99	58	14	real	real	ADJ
ma-99	58	15	numbers	number	NOUN
ma-99	58	16	we	we	PRON
ma-99	58	17	set	set	VERB
ma-99	58	18	l2ρ	l2ρ	PROPN
ma-99	58	19	=	=	SYM
ma-99	58	20	{	{	PUNCT
ma-99	58	21	(	(	PUNCT
ma-99	58	22	xn	xn	X
ma-99	58	23	)	)	PUNCT
ma-99	58	24	∈	∈	NOUN
ma-99	58	25	r∞	r∞	NOUN
ma-99	58	26	:	:	PUNCT
ma-99	58	27	∑	∑	PUNCT
ma-99	58	28	n≥1	n≥1	VERB
ma-99	58	29	x2	x2	PROPN
ma-99	58	30	nρ	nρ	PROPN
ma-99	58	31	2	2	NUM
ma-99	58	32	n	n	CCONJ
ma-99	58	33	<	<	X
ma-99	58	34	∞	∞	NUM
ma-99	58	35	}	}	PUNCT
ma-99	58	36	.	.	PUNCT
ma-99	59	1	where	where	SCONJ
ma-99	59	2	r∞	r∞	PROPN
ma-99	59	3	=	=	SYM
ma-99	59	4	rn	rn	PROPN
ma-99	59	5	.	.	PUNCT
ma-99	60	1	the	the	DET
ma-99	60	2	space	space	NOUN
ma-99	60	3	l2ρ	l2ρ	PROPN
ma-99	60	4	becomes	become	VERB
ma-99	60	5	a	a	DET
ma-99	60	6	separable	separable	ADJ
ma-99	60	7	hilbert	hilbert	NOUN
ma-99	60	8	space	space	NOUN
ma-99	60	9	with	with	ADP
ma-99	60	10	the	the	DET
ma-99	60	11	inner	inner	ADJ
ma-99	60	12	product	product	NOUN
ma-99	60	13	:	:	PUNCT
ma-99	60	14	〈	〈	PROPN
ma-99	60	15	x	x	X
ma-99	60	16	,	,	PUNCT
ma-99	60	17	y	y	PROPN
ma-99	60	18	〉	〉	NUM
ma-99	60	19	=	=	NOUN
ma-99	60	20	∑	∑	PROPN
ma-99	60	21	n≥1	n≥1	NOUN
ma-99	60	22	xnynρ	xnynρ	NOUN
ma-99	60	23	2	2	NUM
ma-99	60	24	n	n	NOUN
ma-99	60	25	for	for	ADP
ma-99	60	26	x	x	SYM
ma-99	60	27	=	=	SYM
ma-99	60	28	(	(	PUNCT
ma-99	60	29	xn	xn	PROPN
ma-99	60	30	)	)	PUNCT
ma-99	60	31	,	,	PUNCT
ma-99	60	32	y	y	PROPN
ma-99	60	33	=	=	SYM
ma-99	60	34	(	(	PUNCT
ma-99	60	35	yn	yn	NOUN
ma-99	60	36	)	)	PUNCT
ma-99	60	37	∈	∈	PROPN
ma-99	60	38	l2ρ	l2ρ	PROPN
ma-99	60	39	.	.	PUNCT
ma-99	61	1	let	let	VERB
ma-99	61	2	us	we	PRON
ma-99	61	3	fix	fix	VERB
ma-99	61	4	θ0	θ0	NOUN
ma-99	61	5	,	,	PUNCT
ma-99	61	6	the	the	DET
ma-99	61	7	unknown	unknown	ADJ
ma-99	61	8	true	true	ADJ
ma-99	61	9	value	value	NOUN
ma-99	61	10	of	of	ADP
ma-99	61	11	the	the	DET
ma-99	61	12	parameter	parameter	NOUN
ma-99	61	13	θ.let	θ.let	ADV
ma-99	61	14	(	(	PUNCT
ma-99	61	15	ω	ω	PROPN
ma-99	61	16	,	,	PUNCT
ma-99	61	17	f	f	PROPN
ma-99	61	18	,	,	PUNCT
ma-99	61	19	p	p	NOUN
ma-99	61	20	)	)	PUNCT
ma-99	61	21	be	be	AUX
ma-99	61	22	a	a	DET
ma-99	61	23	complete	complete	ADJ
ma-99	61	24	probability	probability	NOUN
ma-99	61	25	space	space	NOUN
ma-99	61	26	and	and	CCONJ
ma-99	61	27	z(t	z(t	NOUN
ma-99	61	28	,	,	PUNCT
ma-99	61	29	x	x	PRON
ma-99	61	30	)	)	PUNCT
ma-99	61	31	be	be	AUX
ma-99	61	32	a	a	DET
ma-99	61	33	process	process	NOUN
ma-99	61	34	on	on	ADP
ma-99	61	35	this	this	DET
ma-99	61	36	space	space	NOUN
ma-99	61	37	with	with	ADP
ma-99	61	38	valuesin	valuesin	NOUN
ma-99	61	39	the	the	DET
ma-99	61	40	schwarz	schwarz	PROPN
ma-99	61	41	space	space	NOUN
ma-99	61	42	of	of	ADP
ma-99	61	43	distributions	distribution	NOUN
ma-99	61	44	d′(g	d′(g	PROPN
ma-99	61	45	)	)	PUNCT
ma-99	61	46	such	such	ADJ
ma-99	61	47	that	that	PRON
ma-99	61	48	for	for	ADP
ma-99	61	49	φ	φ	PROPN
ma-99	61	50	,	,	PUNCT
ma-99	62	1	ψ	ψ	X
ma-99	62	2	∈	∈	ADP
ma-99	62	3	c∞0	c∞0	X
ma-99	62	4	(	(	PUNCT
ma-99	62	5	g	g	NOUN
ma-99	62	6	)	)	PUNCT
ma-99	62	7	,	,	PUNCT
ma-99	62	8	‖φ‖−1	‖φ‖−1	PROPN
ma-99	62	9	l2(g	l2(g	NOUN
ma-99	62	10	)	)	PUNCT
ma-99	62	11	〈	〈	PROPN
ma-99	62	12	w	w	PROPN
ma-99	62	13	(	(	PUNCT
ma-99	62	14	t	t	PROPN
ma-99	62	15	,	,	PUNCT
ma-99	62	16	·	·	PUNCT
ma-99	62	17	)	)	PUNCT
ma-99	62	18	,	,	PUNCT
ma-99	62	19	φ(·)〉is	φ(·)〉is	VERB
ma-99	62	20	a	a	DET
ma-99	62	21	one	one	NUM
ma-99	62	22	dimensional	dimensional	ADJ
ma-99	62	23	stable	stable	ADJ
ma-99	62	24	process.this	process.this	NOUN
ma-99	62	25	process	process	NOUN
ma-99	62	26	is	be	AUX
ma-99	62	27	usually	usually	ADV
ma-99	62	28	referred	refer	VERB
ma-99	62	29	to	to	ADP
ma-99	62	30	as	as	ADP
ma-99	62	31	the	the	DET
ma-99	62	32	cylindrical	cylindrical	ADJ
ma-99	62	33	α	α	ADJ
ma-99	62	34	-	-	ADJ
ma-99	62	35	stable	stable	ADJ
ma-99	62	36	process	process	NOUN
ma-99	62	37	(	(	PUNCT
ma-99	62	38	c.s.p	c.s.p	NOUN
ma-99	62	39	.	.	PUNCT
ma-99	62	40	)	)	PUNCT
ma-99	62	41	,	,	PUNCT
ma-99	62	42	α	α	PROPN
ma-99	62	43	∈	∈	PROPN
ma-99	62	44	(	(	PUNCT
ma-99	62	45	0	0	NUM
ma-99	62	46	,	,	PUNCT
ma-99	62	47	2).we	2).we	PROPN
ma-99	62	48	assume	assume	VERB
ma-99	62	49	that	that	SCONJ
ma-99	62	50	there	there	PRON
ma-99	62	51	exists	exist	VERB
ma-99	62	52	a	a	DET
ma-99	62	53	complete	complete	ADJ
ma-99	62	54	orthonormal	orthonormal	ADJ
ma-99	62	55	system	system	NOUN
ma-99	62	56	{	{	PUNCT
ma-99	62	57	hi}∞i=1	hi}∞i=1	X
ma-99	62	58	in	in	ADP
ma-99	62	59	l2(g	l2(g	NOUN
ma-99	62	60	)	)	PUNCT
ma-99	62	61	)	)	PUNCT
ma-99	62	62	such	such	ADJ
ma-99	62	63	that	that	DET
ma-99	62	64	forevery	forevery	NOUN
ma-99	62	65	i	i	NOUN
ma-99	62	66	=	=	NOUN
ma-99	62	67	1	1	NUM
ma-99	62	68	,	,	PUNCT
ma-99	62	69	2	2	NUM
ma-99	62	70	,	,	PUNCT
ma-99	62	71	.	.	PUNCT
ma-99	62	72	.	.	PUNCT
ma-99	63	1	.	.	PUNCT
ma-99	64	1	,	,	PUNCT
ma-99	64	2	hi	hi	INTJ
ma-99	64	3	∈	∈	PROPN
ma-99	64	4	zm,20	zm,20	PROPN
ma-99	64	5	(	(	PUNCT
ma-99	64	6	g	g	NOUN
ma-99	64	7	)	)	PUNCT
ma-99	64	8	∩	∩	NOUN
ma-99	64	9	c∞(g	c∞(g	PROPN
ma-99	64	10	)	)	PUNCT
ma-99	64	11	and	and	CCONJ
ma-99	64	12	λθhi	λθhi	NOUN
ma-99	64	13	=	=	SYM
ma-99	64	14	βi(θ)hi	βi(θ)hi	NOUN
ma-99	64	15	,	,	PUNCT
ma-99	64	16	and	and	CCONJ
ma-99	64	17	lθhi	lθhi	PROPN
ma-99	64	18	=	=	PUNCT
ma-99	64	19	µi(θ)hi	µi(θ)hi	PROPN
ma-99	64	20	for	for	ADP
ma-99	64	21	all	all	DET
ma-99	64	22	θ	θ	PRON
ma-99	64	23	∈	∈	NOUN
ma-99	64	24	θ	θ	NOUN
ma-99	64	25	where	where	SCONJ
ma-99	64	26	lθ	lθ	NOUN
ma-99	64	27	is	be	AUX
ma-99	64	28	a	a	DET
ma-99	64	29	closed	closed	ADJ
ma-99	64	30	self	self	NOUN
ma-99	64	31	adjoint	adjoint	NOUN
ma-99	64	32	extension	extension	NOUN
ma-99	64	33	of	of	ADP
ma-99	64	34	aθ	aθ	NOUN
ma-99	64	35	,	,	PUNCT
ma-99	64	36	λθ	λθ	X
ma-99	64	37	:	:	PUNCT
ma-99	64	38	=	=	SYM
ma-99	64	39	(	(	PUNCT
ma-99	64	40	k(θ)i	k(θ)i	PROPN
ma-99	64	41	−	−	PROPN
ma-99	64	42	lθ)1/2	lθ)1/2	PROPN
ma-99	64	43	m	m	PROPN
ma-99	64	44	,	,	PUNCT
ma-99	64	45	k(θ	k(θ	PROPN
ma-99	64	46	)	)	PUNCT
ma-99	64	47	is	be	AUX
ma-99	64	48	a	a	DET
ma-99	64	49	constant	constant	ADJ
ma-99	64	50	andand	andand	NOUN
ma-99	64	51	the	the	DET
ma-99	64	52	spectrum	spectrum	NOUN
ma-99	64	53	of	of	ADP
ma-99	64	54	the	the	DET
ma-99	64	55	operator	operator	NOUN
ma-99	64	56	λθ	λθ	ADP
ma-99	64	57	consists	consist	NOUN
ma-99	64	58	of	of	ADP
ma-99	64	59	eigenvalues	eigenvalue	NOUN
ma-99	64	60	{	{	PUNCT
ma-99	64	61	βi(θ)}∞i=1	βi(θ)}∞i=1	NUM
ma-99	64	62	of	of	ADP
ma-99	64	63	finite	finite	PROPN
ma-99	64	64	multiplicities	multiplicity	NOUN
ma-99	64	65	and	and	CCONJ
ma-99	65	1	µi	µi	PROPN
ma-99	65	2	=	=	PROPN
ma-99	65	3	−β2	−β2	PROPN
ma-99	65	4	m	m	VERB
ma-99	66	1	i	i	NOUN
ma-99	66	2	+	+	NUM
ma-99	66	3	k(θ).a	k(θ).a	NOUN
ma-99	66	4	levy	levy	NOUN
ma-99	66	5	process	process	NOUN
ma-99	66	6	(	(	PUNCT
ma-99	66	7	zt	zt	PROPN
ma-99	66	8	)	)	PUNCT
ma-99	66	9	with	with	ADP
ma-99	66	10	values	value	NOUN
ma-99	66	11	in	in	ADP
ma-99	66	12	h	h	NOUN
ma-99	66	13	is	be	AUX
ma-99	66	14	an	an	DET
ma-99	66	15	h	h	NOUN
ma-99	66	16	-	-	PUNCT
ma-99	66	17	valued	value	VERB
ma-99	66	18	process	process	NOUN
ma-99	66	19	defined	define	VERB
ma-99	66	20	on	on	ADP
ma-99	66	21	some	some	DET
ma-99	66	22	stochastic	stochastic	ADJ
ma-99	66	23	basis	basis	NOUN
ma-99	66	24	(	(	PUNCT
ma-99	66	25	ω	ω	NOUN
ma-99	66	26	,	,	PUNCT
ma-99	66	27	f	f	PROPN
ma-99	66	28	,	,	PUNCT
ma-99	66	29	(	(	PUNCT
ma-99	66	30	ft)t≥0	ft)t≥0	ADJ
ma-99	66	31	,	,	PUNCT
ma-99	66	32	p	p	NOUN
ma-99	66	33	)	)	PUNCT
ma-99	66	34	having	have	VERB
ma-99	66	35	stationary	stationary	ADJ
ma-99	66	36	independent	independent	ADJ
ma-99	66	37	increments	increment	NOUN
ma-99	66	38	,	,	PUNCT
ma-99	66	39	cadlag	cadlag	NOUN
ma-99	66	40	trajectories	trajectorie	VERB
ma-99	66	41	such	such	ADJ
ma-99	66	42	that	that	PRON
ma-99	66	43	z0	z0	PROPN
ma-99	66	44	=	=	SYM
ma-99	66	45	0,p	0,p	PROPN
ma-99	66	46	-	-	PUNCT
ma-99	66	47	a.s	a.s	PROPN
ma-99	66	48	.	.	PROPN
ma-99	66	49	one	one	NUM
ma-99	66	50	has	have	VERB
ma-99	66	51	that	that	SCONJ
ma-99	66	52	e[e	e[e	ADJ
ma-99	66	53	i〈zt	i〈zt	PROPN
ma-99	66	54	,	,	PUNCT
ma-99	66	55	s	s	PROPN
ma-99	66	56	〉	〉	NOUN
ma-99	66	57	]	]	PUNCT
ma-99	66	58	=	=	SYM
ma-99	66	59	exp(−tψ(s	exp(−tψ(s	PROPN
ma-99	66	60	)	)	PUNCT
ma-99	66	61	)	)	PUNCT
ma-99	66	62	,	,	PUNCT
ma-99	66	63	s	s	AUX
ma-99	66	64	∈	∈	PROPN
ma-99	66	65	hwhere	hwhere	ADV
ma-99	66	66	ψ	ψ	X
ma-99	66	67	:	:	PUNCT
ma-99	66	68	h	h	NOUN
ma-99	66	69	→	→	SYM
ma-99	66	70	c	c	NOUN
ma-99	66	71	is	be	AUX
ma-99	66	72	sazonov	sazonov	ADJ
ma-99	66	73	continuous	continuous	ADJ
ma-99	66	74	,	,	PUNCT
ma-99	66	75	negative	negative	ADJ
ma-99	66	76	definite	definite	ADJ
ma-99	66	77	function	function	NOUN
ma-99	66	78	such	such	ADJ
ma-99	66	79	that	that	DET
ma-99	66	80	ψ(0	ψ(0	NOUN
ma-99	66	81	)	)	PUNCT
ma-99	66	82	=	=	SYM
ma-99	67	1	0	0	X
ma-99	67	2	.	.	PUNCT
ma-99	68	1	thefunction	thefunction	NOUN
ma-99	68	2	ψ	ψ	PROPN
ma-99	68	3	is	be	AUX
ma-99	68	4	called	call	VERB
ma-99	68	5	the	the	DET
ma-99	68	6	exponent	exponent	NOUN
ma-99	68	7	of	of	ADP
ma-99	68	8	(	(	PUNCT
ma-99	68	9	zt).the	zt).the	PROPN
ma-99	68	10	exponent	exponent	NOUN
ma-99	68	11	ψ	ψ	X
ma-99	68	12	can	can	AUX
ma-99	68	13	be	be	AUX
ma-99	68	14	expressed	express	VERB
ma-99	68	15	by	by	ADP
ma-99	68	16	the	the	DET
ma-99	68	17	infinite	infinite	ADJ
ma-99	68	18	dimensional	dimensional	ADJ
ma-99	68	19	levy	levy	NOUN
ma-99	68	20	-	-	PUNCT
ma-99	68	21	khintchine	khintchine	NOUN
ma-99	68	22	formula	formula	NOUN
ma-99	69	1	ψ(s	ψ(s	PROPN
ma-99	69	2	)	)	PUNCT
ma-99	69	3	=	=	SYM
ma-99	69	4	1	1	NUM
ma-99	69	5	2	2	NUM
ma-99	69	6	〈	〈	NOUN
ma-99	69	7	qs	qs	X
ma-99	69	8	,	,	PUNCT
ma-99	69	9	s	s	PROPN
ma-99	69	10	〉	〉	NOUN
ma-99	69	11	−	−	PROPN
ma-99	69	12	i〈a	i〈a	X
ma-99	69	13	,	,	PUNCT
ma-99	69	14	s	s	PROPN
ma-99	69	15	〉	〉	NUM
ma-99	69	16	−	−	PROPN
ma-99	69	17	∫	∫	PROPN
ma-99	69	18	h	h	PROPN
ma-99	69	19	(	(	PUNCT
ma-99	69	20	e	e	NOUN
ma-99	69	21	i〈s	i〈s	PROPN
ma-99	69	22	,	,	PUNCT
ma-99	69	23	y	y	PROPN
ma-99	69	24	〉	〉	PROPN
ma-99	69	25	−	−	PROPN
ma-99	69	26	1−	1−	NUM
ma-99	69	27	i〈s	i〈s	ADP
ma-99	69	28	,	,	PUNCT
ma-99	69	29	y	y	PROPN
ma-99	69	30	〉	〉	PROPN
ma-99	69	31	1	1	NUM
ma-99	69	32	+	+	CCONJ
ma-99	69	33	|y	|y	NOUN
ma-99	69	34	|2	|2	X
ma-99	69	35	)	)	PUNCT
ma-99	69	36	ν(dy	ν(dy	NUM
ma-99	69	37	)	)	PUNCT
ma-99	69	38	,	,	PUNCT
ma-99	69	39	s	s	VERB
ma-99	69	40	∈	∈	PROPN
ma-99	69	41	h	h	NOUN
ma-99	69	42	where	where	SCONJ
ma-99	69	43	q	q	NOUN
ma-99	69	44	is	be	AUX
ma-99	69	45	the	the	DET
ma-99	69	46	non	non	ADJ
ma-99	69	47	-	-	ADJ
ma-99	69	48	negative	negative	ADJ
ma-99	69	49	trace	trace	NOUN
ma-99	69	50	class	class	NOUN
ma-99	69	51	operator	operator	NOUN
ma-99	69	52	on	on	ADP
ma-99	69	53	h	h	NOUN
ma-99	69	54	,	,	PUNCT
ma-99	69	55	a	a	DET
ma-99	69	56	∈	∈	PROPN
ma-99	69	57	h	h	NOUN
ma-99	69	58	and	and	CCONJ
ma-99	69	59	ν	ν	NOUN
ma-99	69	60	is	be	AUX
ma-99	69	61	the	the	DET
ma-99	69	62	levy	levy	NOUN
ma-99	69	63	measure	measure	NOUN
ma-99	69	64	or	or	CCONJ
ma-99	69	65	thejump	thejump	NOUN
ma-99	69	66	intensity	intensity	NOUN
ma-99	69	67	measure	measure	NOUN
ma-99	69	68	associated	associate	VERB
ma-99	69	69	to	to	ADP
ma-99	69	70	(	(	PUNCT
ma-99	69	71	zt).cylindrical	zt).cylindrical	PROPN
ma-99	69	72	α	α	NOUN
ma-99	69	73	-	-	ADJ
ma-99	69	74	stable	stable	ADJ
ma-99	69	75	process	process	NOUN
ma-99	69	76	(	(	PUNCT
ma-99	69	77	c.s.p	c.s.p	NOUN
ma-99	69	78	.	.	PUNCT
ma-99	69	79	)	)	PUNCT
ma-99	69	80	is	be	AUX
ma-99	69	81	a	a	DET
ma-99	69	82	levy	levy	NOUN
ma-99	69	83	process	process	NOUN
ma-99	69	84	taking	take	VERB
ma-99	69	85	values	value	NOUN
ma-99	69	86	in	in	ADP
ma-99	69	87	the	the	DET
ma-99	69	88	hilbert	hilbert	PROPN
ma-99	69	89	space	space	NOUN
ma-99	69	90	u	u	NOUN
ma-99	69	91	=	=	X
ma-99	69	92	l2ρ	l2ρ	X
ma-99	69	93	,	,	PUNCT
ma-99	69	94	with	with	ADP
ma-99	69	95	a	a	DET
ma-99	69	96	properly	properly	ADV
ma-99	69	97	chosen	choose	VERB
ma-99	69	98	weight	weight	NOUN
ma-99	69	99	ρ.consider	ρ.consider	NOUN
ma-99	69	100	the	the	DET
ma-99	69	101	linear	linear	ADJ
ma-99	69	102	spde	spde	NOUN
ma-99	69	103	dxt	dxt	PROPN
ma-99	70	1	=	=	PUNCT
ma-99	70	2	θaxtdt	θaxtdt	NOUN
ma-99	70	3	+	+	CCONJ
ma-99	70	4	dzt	dzt	NOUN
ma-99	70	5	,	,	PUNCT
ma-99	70	6	x	x	PROPN
ma-99	70	7	∈	∈	PROPN
ma-99	70	8	hc.s.p	hc.s.p	PROPN
ma-99	70	9	.	.	PUNCT
ma-99	71	1	z(t	z(t	NOUN
ma-99	71	2	)	)	PUNCT
ma-99	71	3	is	be	AUX
ma-99	71	4	a	a	DET
ma-99	71	5	cylindrical	cylindrical	ADJ
ma-99	71	6	α	α	ADJ
ma-99	71	7	-	-	ADJ
ma-99	71	8	stable	stable	ADJ
ma-99	71	9	process	process	NOUN
ma-99	71	10	,	,	PUNCT
ma-99	71	11	α	α	PROPN
ma-99	71	12	∈	∈	PROPN
ma-99	71	13	(	(	PUNCT
ma-99	71	14	0	0	NUM
ma-99	71	15	,	,	PUNCT
ma-99	71	16	2	2	NUM
ma-99	71	17	)	)	PUNCT
ma-99	71	18	which	which	PRON
ma-99	71	19	can	can	AUX
ma-99	71	20	be	be	AUX
ma-99	71	21	expanded	expand	VERB
ma-99	71	22	in	in	ADP
ma-99	71	23	the	the	DET
ma-99	71	24	series	series	NOUN
ma-99	71	25	z(t	z(t	NOUN
ma-99	71	26	)	)	PUNCT
ma-99	71	27	=	=	PUNCT
ma-99	72	1	∞∑	∞∑	NOUN
ma-99	72	2	i=1	i=1	PRON
ma-99	72	3	γizi(t)hi	γizi(t)hi	INTJ
ma-99	72	4	where	where	SCONJ
ma-99	72	5	{	{	PUNCT
ma-99	72	6	zi(t)}∞i=1	zi(t)}∞i=1	NOUN
ma-99	72	7	are	be	AUX
ma-99	72	8	independent	independent	ADJ
ma-99	72	9	,	,	PUNCT
ma-99	72	10	real	real	ADV
ma-99	72	11	valued	value	VERB
ma-99	72	12	,	,	PUNCT
ma-99	72	13	one	one	NUM
ma-99	72	14	dimensional	dimensional	ADJ
ma-99	72	15	,	,	PUNCT
ma-99	72	16	normalized	normalize	VERB
ma-99	72	17	,	,	PUNCT
ma-99	72	18	symmetric	symmetric	ADJ
ma-99	72	19	,	,	PUNCT
ma-99	72	20	α	α	NOUN
ma-99	72	21	-	-	PUNCT
ma-99	72	22	stableprocesses	stableprocesse	NOUN
ma-99	72	23	and	and	CCONJ
ma-99	72	24	(	(	PUNCT
ma-99	72	25	γi	γi	INTJ
ma-99	72	26	)	)	PUNCT
ma-99	72	27	is	be	AUX
ma-99	72	28	a	a	DET
ma-99	72	29	given	give	VERB
ma-99	72	30	sequence	sequence	NOUN
ma-99	72	31	of	of	ADP
ma-99	72	32	,	,	PUNCT
ma-99	72	33	possibly	possibly	ADV
ma-99	72	34	unbounded	unbounded	ADJ
ma-99	72	35	,	,	PUNCT
ma-99	72	36	positive	positive	ADJ
ma-99	72	37	numbers	number	NOUN
ma-99	72	38	,	,	PUNCT
ma-99	72	39	and	and	CCONJ
ma-99	72	40	hi	hi	INTJ
ma-99	72	41	is	be	AUX
ma-99	72	42	a	a	DET
ma-99	72	43	fixed	fix	VERB
ma-99	72	44	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	72	45	eur	eur	NOUN
ma-99	72	46	.	.	PUNCT
ma-99	73	1	j.	j.	PROPN
ma-99	73	2	math	math	PROPN
ma-99	73	3	.	.	PUNCT
ma-99	74	1	anal	anal	PROPN
ma-99	74	2	.	.	PUNCT
ma-99	75	1	10.28924	10.28924	NUM
ma-99	75	2	/	/	SYM
ma-99	75	3	ada	ada	PROPN
ma-99	75	4	/	/	SYM
ma-99	75	5	ma.3.4	ma.3.4	PROPN
ma-99	75	6	4orthonormal	4orthonormal	NUM
ma-99	75	7	basis	basis	NOUN
ma-99	75	8	in	in	ADP
ma-99	75	9	h.	h.	PROPN
ma-99	75	10	the	the	DET
ma-99	75	11	latter	latter	ADJ
ma-99	75	12	series	series	NOUN
ma-99	75	13	converges	converge	VERB
ma-99	75	14	p	p	NOUN
ma-99	75	15	-a.s	-a.s	PUNCT
ma-99	75	16	.	.	PUNCT
ma-99	76	1	in	in	ADP
ma-99	76	2	h−α	h−α	NOUN
ma-99	76	3	for	for	ADP
ma-99	76	4	α	α	PROPN
ma-99	76	5	>	>	X
ma-99	76	6	d/2	d/2	PROPN
ma-99	76	7	.	.	PUNCT
ma-99	77	1	indeed	indeed	ADV
ma-99	77	2	‖z(t)‖2	‖z(t)‖2	VERB
ma-99	77	3	−α	−α	NOUN
ma-99	77	4	=	=	PUNCT
ma-99	78	1	∞∑	∞∑	NUM
ma-99	78	2	i=1	i=1	NOUN
ma-99	78	3	γ2	γ2	NOUN
ma-99	79	1	i	i	PRON
ma-99	79	2	z	z	PROPN
ma-99	79	3	2	2	NUM
ma-99	79	4	i	i	NOUN
ma-99	79	5	(	(	PUNCT
ma-99	79	6	t)‖hi‖2	t)‖hi‖2	PROPN
ma-99	79	7	−α	−α	NOUN
ma-99	79	8	=	=	PUNCT
ma-99	80	1	∞∑	∞∑	NUM
ma-99	80	2	i=1	i=1	PROPN
ma-99	80	3	z2	z2	NOUN
ma-99	80	4	i	i	PRON
ma-99	80	5	(	(	PUNCT
ma-99	80	6	t)β−2α	t)β−2α	PROPN
ma-99	80	7	i	i	PRON
ma-99	80	8	and	and	CCONJ
ma-99	80	9	the	the	DET
ma-99	80	10	later	later	ADJ
ma-99	80	11	series	series	NOUN
ma-99	80	12	converges	converge	VERB
ma-99	80	13	p	p	PRON
ma-99	80	14	-a.s.for	-a.s.for	ADP
ma-99	80	15	any	any	DET
ma-99	80	16	j	j	PROPN
ma-99	80	17	∈	∈	PROPN
ma-99	80	18	n	n	CCONJ
ma-99	80	19	,	,	PUNCT
ma-99	80	20	t	t	PROPN
ma-99	80	21	≥	≥	NUM
ma-99	80	22	0	0	NUM
ma-99	80	23	,	,	PUNCT
ma-99	80	24	e[e	e[e	ADJ
ma-99	80	25	izj	izj	ADJ
ma-99	80	26	(	(	PUNCT
ma-99	80	27	t)h	t)h	NOUN
ma-99	80	28	]	]	X
ma-99	80	29	=	=	SYM
ma-99	80	30	e−t|h|	e−t|h|	NOUN
ma-99	80	31	α	α	NOUN
ma-99	80	32	.	.	PUNCT
ma-99	81	1	stable	stable	ADJ
ma-99	81	2	one	one	NUM
ma-99	81	3	-	-	PUNCT
ma-99	81	4	dimensional	dimensional	ADJ
ma-99	81	5	density	density	NOUN
ma-99	81	6	:	:	PUNCT
ma-99	81	7	a	a	PRON
ma-99	81	8	one	one	NUM
ma-99	81	9	-	-	PUNCT
ma-99	81	10	dimensional	dimensional	ADJ
ma-99	81	11	,	,	PUNCT
ma-99	81	12	normalized	normalize	VERB
ma-99	81	13	,	,	PUNCT
ma-99	81	14	symmetric	symmetric	ADJ
ma-99	81	15	α	α	VERB
ma-99	81	16	-	-	ADJ
ma-99	81	17	stable	stable	ADJ
ma-99	81	18	distribution	distribution	NOUN
ma-99	81	19	µα	µα	ADP
ma-99	81	20	,	,	PUNCT
ma-99	81	21	α	α	PROPN
ma-99	81	22	∈	∈	PROPN
ma-99	81	23	(	(	PUNCT
ma-99	81	24	0	0	NUM
ma-99	81	25	,	,	PUNCT
ma-99	81	26	2	2	NUM
ma-99	81	27	]	]	PUNCT
ma-99	81	28	has	have	VERB
ma-99	81	29	characteristicfunction	characteristicfunction	NOUN
ma-99	81	30	µ̂α(s	µ̂α(s	NUM
ma-99	81	31	)	)	PUNCT
ma-99	82	1	=	=	PUNCT
ma-99	82	2	e−|s|	e−|s|	NUM
ma-99	82	3	α	α	PROPN
ma-99	82	4	,	,	PUNCT
ma-99	82	5	s	s	VERB
ma-99	82	6	∈	∈	PROPN
ma-99	82	7	r.the	r.the	DET
ma-99	82	8	density	density	NOUN
ma-99	82	9	of	of	ADP
ma-99	82	10	µα	µα	ADP
ma-99	82	11	with	with	ADP
ma-99	82	12	respect	respect	NOUN
ma-99	82	13	to	to	ADP
ma-99	82	14	lebesgue	lebesgue	NOUN
ma-99	82	15	measure	measure	NOUN
ma-99	82	16	will	will	AUX
ma-99	82	17	be	be	AUX
ma-99	82	18	denoted	denote	VERB
ma-99	82	19	by	by	ADP
ma-99	82	20	pα	pα	PROPN
ma-99	82	21	.	.	PUNCT
ma-99	83	1	this	this	DET
ma-99	83	2	even	even	ADV
ma-99	83	3	functionis	functionis	PROPN
ma-99	83	4	known	know	VERB
ma-99	83	5	in	in	ADP
ma-99	83	6	closed	closed	ADJ
ma-99	83	7	form	form	NOUN
ma-99	83	8	only	only	ADV
ma-99	83	9	if	if	SCONJ
ma-99	83	10	α	α	NOUN
ma-99	83	11	=	=	SYM
ma-99	83	12	1	1	NUM
ma-99	83	13	or	or	CCONJ
ma-99	83	14	2	2	NUM
ma-99	83	15	.	.	PUNCT
ma-99	84	1	the	the	DET
ma-99	84	2	precise	precise	ADJ
ma-99	84	3	asymptotic	asymptotic	ADJ
ma-99	84	4	behavior	behavior	NOUN
ma-99	84	5	of	of	ADP
ma-99	84	6	the	the	DET
ma-99	84	7	density	density	NOUN
ma-99	84	8	pα	pα	PROPN
ma-99	84	9	,	,	PUNCT
ma-99	84	10	α	α	PROPN
ma-99	84	11	∈	∈	PROPN
ma-99	84	12	(	(	PUNCT
ma-99	84	13	0	0	NUM
ma-99	84	14	,	,	PUNCT
ma-99	84	15	2	2	NUM
ma-99	84	16	)	)	PUNCT
ma-99	84	17	is	be	AUX
ma-99	84	18	as	as	SCONJ
ma-99	84	19	follows	follow	VERB
ma-99	84	20	:	:	PUNCT
ma-99	84	21	for	for	ADP
ma-99	84	22	any	any	DET
ma-99	84	23	α	α	NOUN
ma-99	84	24	∈	∈	PROPN
ma-99	84	25	(	(	PUNCT
ma-99	84	26	0	0	NUM
ma-99	84	27	,	,	PUNCT
ma-99	84	28	2	2	NUM
ma-99	84	29	)	)	PUNCT
ma-99	84	30	,	,	PUNCT
ma-99	84	31	there	there	PRON
ma-99	84	32	exists	exist	VERB
ma-99	84	33	cα	cα	ADP
ma-99	84	34	such	such	ADJ
ma-99	84	35	that	that	PRON
ma-99	84	36	pα(x	pα(x	PUNCT
ma-99	84	37	)	)	PUNCT
ma-99	84	38	∼	∼	NOUN
ma-99	84	39	cα	cα	ADP
ma-99	84	40	xα+1	xα+1	PRON
ma-99	84	41	as	as	ADP
ma-99	84	42	x	x	X
ma-99	84	43	→∞.	→∞.	X
ma-99	84	44	stable	stable	ADJ
ma-99	84	45	measures	measure	NOUN
ma-99	84	46	on	on	ADP
ma-99	84	47	hilbert	hilbert	NOUN
ma-99	84	48	space	space	NOUN
ma-99	84	49	:	:	PUNCT
ma-99	84	50	a	a	DET
ma-99	84	51	random	random	ADJ
ma-99	84	52	variable	variable	NOUN
ma-99	84	53	ξ	ξ	PROPN
ma-99	84	54	on	on	ADP
ma-99	84	55	h	h	NOUN
ma-99	84	56	is	be	AUX
ma-99	84	57	called	call	VERB
ma-99	84	58	α	α	PRON
ma-99	84	59	-	-	ADJ
ma-99	84	60	stable	stable	ADJ
ma-99	84	61	(	(	PUNCT
ma-99	84	62	α	α	NOUN
ma-99	84	63	∈	∈	PROPN
ma-99	84	64	(	(	PUNCT
ma-99	84	65	0	0	NUM
ma-99	84	66	,	,	PUNCT
ma-99	84	67	2	2	NUM
ma-99	84	68	]	]	PUNCT
ma-99	84	69	)	)	PUNCT
ma-99	84	70	if	if	SCONJ
ma-99	84	71	for	for	ADP
ma-99	84	72	any	any	DET
ma-99	84	73	n	n	NOUN
ma-99	84	74	there	there	ADV
ma-99	84	75	exists	exist	VERB
ma-99	84	76	avector	avector	NOUN
ma-99	84	77	an	an	DET
ma-99	84	78	∈	∈	PROPN
ma-99	84	79	h	h	NOUN
ma-99	84	80	such	such	ADJ
ma-99	84	81	that	that	PRON
ma-99	84	82	for	for	ADP
ma-99	84	83	any	any	DET
ma-99	84	84	independent	independent	ADJ
ma-99	84	85	copies	copy	NOUN
ma-99	84	86	ξ1	ξ1	NOUN
ma-99	84	87	,	,	PUNCT
ma-99	84	88	ξ2	ξ2	NOUN
ma-99	84	89	,	,	PUNCT
ma-99	84	90	.	.	PUNCT
ma-99	84	91	.	.	PUNCT
ma-99	85	1	.	.	PUNCT
ma-99	86	1	,	,	PUNCT
ma-99	86	2	ξn	ξn	PROPN
ma-99	86	3	of	of	ADP
ma-99	86	4	ξ	ξ	PROPN
ma-99	86	5	,	,	PUNCT
ma-99	86	6	the	the	DET
ma-99	86	7	random	random	ADJ
ma-99	86	8	variable	variable	NOUN
ma-99	86	9	n−1	n−1	PROPN
ma-99	86	10	/	/	SYM
ma-99	86	11	α(ξ1	α(ξ1	NOUN
ma-99	86	12	+	+	X
ma-99	86	13	ξ2	ξ2	ADJ
ma-99	86	14	,	,	PUNCT
ma-99	86	15	.	.	PUNCT
ma-99	86	16	.	.	PUNCT
ma-99	87	1	.+	.+	NOUN
ma-99	87	2	ξn)−	ξn)−	NOUN
ma-99	87	3	an	an	PRON
ma-99	87	4	has	have	VERB
ma-99	87	5	the	the	DET
ma-99	87	6	same	same	ADJ
ma-99	87	7	distribution	distribution	NOUN
ma-99	87	8	as	as	ADP
ma-99	87	9	ξ	ξ	X
ma-99	87	10	.	.	PUNCT
ma-99	88	1	a	a	DET
ma-99	88	2	borel	borel	NOUN
ma-99	88	3	probability	probability	NOUN
ma-99	88	4	measure	measure	NOUN
ma-99	88	5	µ	µ	X
ma-99	88	6	on	on	ADP
ma-99	88	7	his	his	PRON
ma-99	88	8	said	say	VERB
ma-99	88	9	to	to	PART
ma-99	88	10	be	be	AUX
ma-99	88	11	α	α	NOUN
ma-99	88	12	-	-	ADJ
ma-99	88	13	stable	stable	ADJ
ma-99	88	14	if	if	SCONJ
ma-99	88	15	it	it	PRON
ma-99	88	16	is	be	AUX
ma-99	88	17	the	the	DET
ma-99	88	18	distribution	distribution	NOUN
ma-99	88	19	of	of	ADP
ma-99	88	20	a	a	DET
ma-99	88	21	stable	stable	ADJ
ma-99	88	22	random	random	ADJ
ma-99	88	23	variable	variable	NOUN
ma-99	88	24	with	with	ADP
ma-99	88	25	vales	vale	NOUN
ma-99	88	26	in	in	ADP
ma-99	88	27	h.	h.	PROPN
ma-99	88	28	stable	stable	ADJ
ma-99	88	29	ou	ou	PROPN
ma-99	88	30	process	process	NOUN
ma-99	88	31	:	:	PUNCT
ma-99	89	1	dxt	dxt	PROPN
ma-99	89	2	=	=	PUNCT
ma-99	90	1	−θxtdt	−θxtdt	PROPN
ma-99	91	1	+	+	NUM
ma-99	91	2	σdzt	σdzt	NOUN
ma-99	91	3	,	,	PUNCT
ma-99	91	4	x0	x0	PROPN
ma-99	91	5	=	=	PUNCT
ma-99	92	1	x0the	x0the	DET
ma-99	92	2	solution	solution	NOUN
ma-99	92	3	is	be	AUX
ma-99	92	4	xt	xt	ADP
ma-99	92	5	=	=	PUNCT
ma-99	92	6	e−θtx0	e−θtx0	PROPN
ma-99	93	1	+	+	CCONJ
ma-99	94	1	∫	∫	PROPN
ma-99	94	2	t	t	PROPN
ma-99	94	3	0	0	NUM
ma-99	95	1	e−θ(t−s)σdzs	e−θ(t−s)σdzs	PROPN
ma-99	95	2	.the	.the	PUNCT
ma-99	96	1	stochastic	stochastic	ADJ
ma-99	96	2	integral	integral	ADJ
ma-99	96	3	can	can	AUX
ma-99	96	4	be	be	AUX
ma-99	96	5	defined	define	VERB
ma-99	96	6	as	as	ADP
ma-99	96	7	the	the	DET
ma-99	96	8	limit	limit	NOUN
ma-99	96	9	in	in	ADP
ma-99	96	10	probability	probability	NOUN
ma-99	96	11	of	of	ADP
ma-99	96	12	riemann	riemann	PROPN
ma-99	96	13	sums.let	sums.let	PROPN
ma-99	96	14	yt	yt	PROPN
ma-99	96	15	=	=	SYM
ma-99	96	16	∫	∫	PROPN
ma-99	96	17	t	t	PROPN
ma-99	96	18	0	0	NUM
ma-99	97	1	e−θ(t−s)σdzs	e−θ(t−s)σdzs	PROPN
ma-99	97	2	.then	.then	PUNCT
ma-99	97	3	e[e	e[e	ADJ
ma-99	97	4	ihyt	ihyt	NOUN
ma-99	97	5	]	]	X
ma-99	97	6	=	=	SYM
ma-99	97	7	exp	exp	X
ma-99	97	8	[	[	PUNCT
ma-99	97	9	−σα|h|α	−σα|h|α	PROPN
ma-99	97	10	∫	∫	PROPN
ma-99	97	11	t	t	PROPN
ma-99	97	12	0	0	NUM
ma-99	98	1	e−αθsds	e−αθsds	ADP
ma-99	98	2	]	]	PUNCT
ma-99	98	3	=	=	PUNCT
ma-99	98	4	e−|h|	e−|h|	NUM
ma-99	98	5	αcα(t	αcα(t	PROPN
ma-99	98	6	)	)	PUNCT
ma-99	98	7	where	where	SCONJ
ma-99	98	8	cα(t	cα(t	X
ma-99	98	9	)	)	PUNCT
ma-99	98	10	=	=	SYM
ma-99	98	11	σ	σ	PROPN
ma-99	98	12	(	(	PUNCT
ma-99	98	13	1−	1−	NUM
ma-99	98	14	e−αθt	e−αθt	NOUN
ma-99	98	15	αθ	αθ	PROPN
ma-99	98	16	)	)	PUNCT
ma-99	98	17	.we	.we	PUNCT
ma-99	99	1	show	show	VERB
ma-99	99	2	that	that	SCONJ
ma-99	99	3	the	the	DET
ma-99	99	4	process	process	NOUN
ma-99	99	5	x	x	PUNCT
ma-99	99	6	is	be	AUX
ma-99	99	7	stochastically	stochastically	ADV
ma-99	99	8	continuous.first	continuous.first	ADJ
ma-99	99	9	we	we	PRON
ma-99	99	10	show	show	VERB
ma-99	99	11	that	that	SCONJ
ma-99	99	12	y	y	PROPN
ma-99	99	13	is	be	AUX
ma-99	99	14	stochastically	stochastically	ADV
ma-99	99	15	continuous	continuous	ADJ
ma-99	99	16	,	,	PUNCT
ma-99	99	17	i.e.	i.e.	X
ma-99	99	18	,	,	PUNCT
ma-99	99	19	lim	lim	PROPN
ma-99	99	20	h→0	h→0	NOUN
ma-99	99	21	+	+	NUM
ma-99	99	22	sup	sup	NOUN
ma-99	99	23	t≥0	t≥0	PROPN
ma-99	99	24	p	p	NOUN
ma-99	99	25	(	(	PUNCT
ma-99	99	26	|yt+h	|yt+h	ADP
ma-99	99	27	−	−	PROPN
ma-99	99	28	yt	yt	VERB
ma-99	99	29	|	|	ADV
ma-99	99	30	>	>	X
ma-99	99	31	ε	ε	PROPN
ma-99	99	32	)	)	PUNCT
ma-99	99	33	=	=	NOUN
ma-99	99	34	0	0	NUM
ma-99	99	35	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	99	36	eur	eur	PROPN
ma-99	99	37	.	.	PUNCT
ma-99	100	1	j.	j.	PROPN
ma-99	100	2	math	math	PROPN
ma-99	100	3	.	.	PUNCT
ma-99	101	1	anal	anal	PROPN
ma-99	101	2	.	.	PUNCT
ma-99	102	1	10.28924	10.28924	NUM
ma-99	102	2	/	/	SYM
ma-99	102	3	ada	ada	PROPN
ma-99	102	4	/	/	SYM
ma-99	102	5	ma.3.4	ma.3.4	PROPN
ma-99	102	6	5note	5note	NUM
ma-99	103	1	that	that	PRON
ma-99	103	2	for	for	ADP
ma-99	103	3	any	any	DET
ma-99	103	4	t	t	PROPN
ma-99	103	5	≥	≥	NOUN
ma-99	103	6	0	0	NUM
ma-99	103	7	,	,	PUNCT
ma-99	103	8	h	h	PROPN
ma-99	103	9	≥	≥	NOUN
ma-99	103	10	0	0	NUM
ma-99	103	11	,	,	PUNCT
ma-99	103	12	yt+h	yt+h	NUM
ma-99	103	13	−	−	PROPN
ma-99	103	14	yt	yt	NOUN
ma-99	103	15	=	=	SYM
ma-99	103	16	∫	∫	PROPN
ma-99	103	17	t+h	t+h	X
ma-99	103	18	t	t	PROPN
ma-99	103	19	e(t+h−s)adzs	e(t+h−s)adzs	X
ma-99	103	20	+	+	CCONJ
ma-99	103	21	eha	eha	PROPN
ma-99	103	22	∫	∫	PROPN
ma-99	103	23	t	t	PROPN
ma-99	103	24	0	0	PUNCT
ma-99	104	1	e(t−s)adzs	e(t−s)adzs	PROPN
ma-99	105	1	−	−	PROPN
ma-99	106	1	∫	∫	PROPN
ma-99	107	1	t	t	NOUN
ma-99	107	2	0	0	PUNCT
ma-99	108	1	e(t−s)adzs	e(t−s)adzs	PROPN
ma-99	108	2	=	=	PUNCT
ma-99	108	3	ehayt	ehayt	VERB
ma-99	108	4	−	−	PROPN
ma-99	108	5	yt	yt	NOUN
ma-99	108	6	+	+	CCONJ
ma-99	108	7	∫	∫	PROPN
ma-99	108	8	t+h	t+h	X
ma-99	108	9	t	t	NOUN
ma-99	108	10	e(t+h−s)adzslet	e(t+h−s)adzslet	NOUN
ma-99	108	11	us	we	PRON
ma-99	108	12	choose	choose	VERB
ma-99	108	13	p	p	X
ma-99	108	14	∈	∈	PROPN
ma-99	108	15	(	(	PUNCT
ma-99	108	16	0	0	NUM
ma-99	108	17	,	,	PUNCT
ma-99	108	18	α	α	NOUN
ma-99	108	19	)	)	PUNCT
ma-99	108	20	.	.	PUNCT
ma-99	109	1	we	we	PRON
ma-99	109	2	have	have	VERB
ma-99	109	3	p	p	NOUN
ma-99	109	4	(	(	PUNCT
ma-99	109	5	|yt+h	|yt+h	ADP
ma-99	109	6	−	−	PROPN
ma-99	109	7	yt	yt	VERB
ma-99	109	8	|	|	ADV
ma-99	109	9	>	>	X
ma-99	109	10	ε	ε	PROPN
ma-99	109	11	)	)	PUNCT
ma-99	109	12	≤	≤	NOUN
ma-99	109	13	p	p	NOUN
ma-99	109	14	(	(	PUNCT
ma-99	109	15	|ehayt	|ehayt	NOUN
ma-99	109	16	−	−	PROPN
ma-99	109	17	yt	yt	NOUN
ma-99	110	1	|	|	ADV
ma-99	110	2	>	>	X
ma-99	110	3	ε	ε	PROPN
ma-99	110	4	2	2	NUM
ma-99	110	5	)	)	PUNCT
ma-99	111	1	+	+	CCONJ
ma-99	111	2	p	p	NOUN
ma-99	111	3	(	(	PUNCT
ma-99	111	4	∣∣∣∣∫	∣∣∣∣∫	NOUN
ma-99	111	5	t+h	t+h	X
ma-99	111	6	t	t	PROPN
ma-99	111	7	e(t+h−s)adzs	e(t+h−s)adzs	X
ma-99	111	8	∣∣∣∣	∣∣∣∣	PROPN
ma-99	111	9	>	>	X
ma-99	111	10	ε	ε	PROPN
ma-99	111	11	2	2	NUM
ma-99	111	12	)	)	PUNCT
ma-99	111	13	≤	≤	NOUN
ma-99	111	14	2p	2p	NUM
ma-99	111	15	e|ehayt	e|ehayt	NOUN
ma-99	111	16	−	−	PROPN
ma-99	111	17	yt	yt	PROPN
ma-99	111	18	|p	|p	PROPN
ma-99	111	19	εp	εp	ADP
ma-99	111	20	+	+	NUM
ma-99	111	21	2p	2p	NUM
ma-99	111	22	e|	e|	PROPN
ma-99	111	23	∫	∫	PROPN
ma-99	112	1	h	h	NOUN
ma-99	112	2	0	0	NUM
ma-99	112	3	e	e	NOUN
ma-99	112	4	sadzs	sadzs	PROPN
ma-99	112	5	|p	|p	PROPN
ma-99	112	6	εp	εp	ADP
ma-99	112	7	=	=	SYM
ma-99	112	8	i1(t	i1(t	PROPN
ma-99	112	9	,	,	PUNCT
ma-99	112	10	h	h	NOUN
ma-99	112	11	)	)	PUNCT
ma-99	112	12	+	+	CCONJ
ma-99	112	13	i2(h).but	i2(h).but	PROPN
ma-99	112	14	e|yt	e|yt	NOUN
ma-99	112	15	|p	|p	NOUN
ma-99	112	16	≤	≤	ADJ
ma-99	112	17	cp	cp	INTJ
ma-99	112	18	(	(	PUNCT
ma-99	112	19	∞∑	∞∑	NUM
ma-99	112	20	n=1	n=1	ADP
ma-99	112	21	1−	1−	NUM
ma-99	112	22	e−αθt	e−αθt	NOUN
ma-99	113	1	αθ	αθ	INTJ
ma-99	113	2	)	)	PUNCT
ma-99	113	3	p	p	X
ma-99	113	4	/	/	SYM
ma-99	113	5	α	α	NOUN
ma-99	114	1	and	and	CCONJ
ma-99	114	2	so	so	ADV
ma-99	114	3	[	[	X
ma-99	114	4	i2(h)]α	i2(h)]α	X
ma-99	114	5	/	/	SYM
ma-99	114	6	p	p	X
ma-99	114	7	→	→	SYM
ma-99	114	8	0	0	PROPN
ma-99	114	9	as	as	ADP
ma-99	114	10	h	h	NOUN
ma-99	114	11	→	→	SYM
ma-99	114	12	0	0	NUM
ma-99	114	13	.	.	PUNCT
ma-99	115	1	concerning	concern	VERB
ma-99	115	2	i1	i1	PROPN
ma-99	115	3	,	,	PUNCT
ma-99	115	4	by	by	ADP
ma-99	115	5	khintchine	khintchine	PROPN
ma-99	115	6	inequality	inequality	NOUN
ma-99	115	7	|ehayt	|ehayt	NOUN
ma-99	115	8	−	−	PROPN
ma-99	115	9	yt	yt	NOUN
ma-99	116	1	|	|	ADV
ma-99	116	2	=	=	PUNCT
ma-99	116	3	∑	∑	NOUN
ma-99	116	4	n≥1	n≥1	NOUN
ma-99	116	5	∣∣(e−θh	∣∣(e−θh	VERB
ma-99	116	6	−	−	PROPN
ma-99	116	7	1)y	1)y	NUM
ma-99	116	8	nt	not	PART
ma-99	116	9	∣∣21/2	∣∣21/2	NOUN
ma-99	116	10	≤	≤	ADJ
ma-99	116	11	cp	cp	PROPN
ma-99	116	12	ẽ	ẽ	NOUN
ma-99	116	13	∣∣∣∣∣∣∑n≥1	∣∣∣∣∣∣∑n≥1	NOUN
ma-99	117	1	rn(e−θh	rn(e−θh	NOUN
ma-99	117	2	−	−	PROPN
ma-99	117	3	1)y	1)y	NUM
ma-99	117	4	nt	not	PART
ma-99	117	5	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ma-99	117	6	p1	p1	PROPN
ma-99	117	7	/	/	SYM
ma-99	117	8	p	p	NOUN
ma-99	117	9	.	.	PUNCT
ma-99	118	1	where	where	SCONJ
ma-99	118	2	ẽ	ẽ	PROPN
ma-99	118	3	denotes	denote	NOUN
ma-99	118	4	expectation	expectation	NOUN
ma-99	118	5	w.r.t	w.r.t	VERB
ma-99	118	6	.	.	PUNCT
ma-99	119	1	to	to	ADP
ma-99	119	2	the	the	DET
ma-99	119	3	measure	measure	NOUN
ma-99	119	4	p̃	p̃	PROPN
ma-99	119	5	p̃	p̃	PROPN
ma-99	119	6	(	(	PUNCT
ma-99	119	7	rn	rn	NOUN
ma-99	119	8	=	=	NOUN
ma-99	119	9	1	1	NUM
ma-99	119	10	)	)	PUNCT
ma-99	119	11	=	=	SYM
ma-99	120	1	p̃	p̃	PROPN
ma-99	120	2	(	(	PUNCT
ma-99	120	3	rn	rn	NOUN
ma-99	120	4	=	=	NOUN
ma-99	120	5	1	1	NUM
ma-99	120	6	)	)	PUNCT
ma-99	120	7	=	=	NUM
ma-99	120	8	1/2	1/2	NUM
ma-99	120	9	where	where	SCONJ
ma-99	120	10	arademacher	arademacher	ADV
ma-99	120	11	sequence	sequence	NOUN
ma-99	120	12	(	(	PUNCT
ma-99	120	13	rn	rn	NOUN
ma-99	120	14	)	)	PUNCT
ma-99	120	15	with	with	ADP
ma-99	120	16	rn	rn	PROPN
ma-99	120	17	:	:	PUNCT
ma-99	120	18	ω̃	ω̃	NUM
ma-99	120	19	→	→	SYM
ma-99	120	20	{	{	PUNCT
ma-99	120	21	−1	−1	NOUN
ma-99	120	22	,	,	PUNCT
ma-99	120	23	1	1	NUM
ma-99	120	24	}	}	PUNCT
ma-99	120	25	is	be	AUX
ma-99	120	26	defined	define	VERB
ma-99	120	27	on	on	ADP
ma-99	120	28	the	the	DET
ma-99	120	29	probability	probability	NOUN
ma-99	120	30	space	space	NOUN
ma-99	120	31	(	(	PUNCT
ma-99	120	32	ω̃	ω̃	PROPN
ma-99	120	33	,	,	PUNCT
ma-99	120	34	f̃	f̃	PROPN
ma-99	120	35	,	,	PUNCT
ma-99	120	36	p̃	p̃	PROPN
ma-99	120	37	)	)	PUNCT
ma-99	120	38	.hence	.hence	ADP
ma-99	120	39	e|ehayt	e|ehayt	PROPN
ma-99	120	40	−	−	PROPN
ma-99	120	41	yt	yt	PROPN
ma-99	120	42	|p	|p	VERB
ma-99	121	1	≤	≤	ADJ
ma-99	121	2	cpp	cpp	PROPN
ma-99	121	3	ẽe	ẽe	PROPN
ma-99	121	4	∑	∑	NOUN
ma-99	121	5	n≥1	n≥1	NOUN
ma-99	121	6	∣∣(e−θh	∣∣(e−θh	VERB
ma-99	121	7	−	−	PROPN
ma-99	121	8	1)y	1)y	NUM
ma-99	121	9	nt	not	PART
ma-99	121	10	∣∣21/2	∣∣21/2	NOUN
ma-99	121	11	≤	≤	ADJ
ma-99	121	12	cp	cp	PROPN
ma-99	121	13	∑	∑	NOUN
ma-99	121	14	n≥1	n≥1	NOUN
ma-99	121	15	∣∣(1−	∣∣(1−	ADJ
ma-99	121	16	e−θht)βn	e−θht)βn	ADJ
ma-99	121	17	∣∣α	∣∣α	ADJ
ma-99	121	18	(	(	PUNCT
ma-99	121	19	1−	1−	NUM
ma-99	121	20	e−θht	e−θht	NOUN
ma-99	121	21	)	)	PUNCT
ma-99	121	22	αθ	αθ	PROPN
ma-99	121	23	p	p	NUM
ma-99	121	24	/	/	SYM
ma-99	121	25	α	α	PROPN
ma-99	121	26	≤	≤	NUM
ma-99	121	27	cp	cp	NUM
ma-99	121	28	αp	αp	PROPN
ma-99	121	29	/	/	SYM
ma-99	121	30	α	α	PROPN
ma-99	121	31	∑	∑	NOUN
ma-99	121	32	n≥1	n≥1	NOUN
ma-99	121	33	∣∣(1−	∣∣(1−	ADJ
ma-99	121	34	e−θht)βn	e−θht)βn	ADJ
ma-99	121	35	∣∣α	∣∣α	ADJ
ma-99	121	36	θ	θ	PROPN
ma-99	121	37	p	p	PROPN
ma-99	121	38	/	/	SYM
ma-99	121	39	α	α	PROPN
ma-99	121	40	since	since	SCONJ
ma-99	121	41	lim	lim	PROPN
ma-99	121	42	h→0	h→0	PROPN
ma-99	121	43	+	+	CCONJ
ma-99	121	44	∑	∑	NOUN
ma-99	121	45	n≥1	n≥1	NOUN
ma-99	121	46	∣∣(1−	∣∣(1−	ADJ
ma-99	121	47	e−θht)βn	e−θht)βn	ADJ
ma-99	121	48	∣∣α	∣∣α	ADJ
ma-99	121	49	θ	θ	PROPN
ma-99	121	50	p	p	PUNCT
ma-99	121	51	/	/	SYM
ma-99	121	52	α	α	PROPN
ma-99	121	53	=	=	SYM
ma-99	121	54	0	0	NUM
ma-99	121	55	,	,	PUNCT
ma-99	121	56	we	we	PRON
ma-99	121	57	get	get	VERB
ma-99	121	58	lim	lim	PROPN
ma-99	121	59	h→0	h→0	NOUN
ma-99	121	60	+	+	CCONJ
ma-99	121	61	sup	sup	NOUN
ma-99	121	62	t≥0	t≥0	ADJ
ma-99	121	63	2p	2p	NUM
ma-99	121	64	e|ehayt	e|ehayt	NOUN
ma-99	121	65	−	−	PROPN
ma-99	121	66	yt	yt	PROPN
ma-99	121	67	|p	|p	PROPN
ma-99	121	68	εp	εp	ADP
ma-99	121	69	=	=	NOUN
ma-99	121	70	0	0	PROPN
ma-99	121	71	.	.	PUNCT
ma-99	122	1	since	since	SCONJ
ma-99	122	2	e|yt	e|yt	NOUN
ma-99	122	3	|p	|p	PROPN
ma-99	122	4	≤	≤	ADV
ma-99	122	5	cp	cp	X
ma-99	122	6	∑	∑	NOUN
ma-99	122	7	n≥1	n≥1	PROPN
ma-99	122	8	|βn|α	|βn|α	PROPN
ma-99	122	9	(	(	PUNCT
ma-99	122	10	1−	1−	NUM
ma-99	122	11	e−θht	e−θht	NOUN
ma-99	122	12	)	)	PUNCT
ma-99	122	13	αθ	αθ	PROPN
ma-99	122	14	p	p	NOUN
ma-99	122	15	/	/	SYM
ma-99	122	16	α	α	NOUN
ma-99	122	17	,	,	PUNCT
ma-99	122	18	hence	hence	ADV
ma-99	122	19	lim	lim	PROPN
ma-99	122	20	h→0	h→0	ADV
ma-99	122	21	∑	∑	VERB
ma-99	122	22	n≥1	n≥1	PROPN
ma-99	122	23	|βn|α	|βn|α	PROPN
ma-99	122	24	(	(	PUNCT
ma-99	122	25	1−	1−	NUM
ma-99	122	26	e−θht	e−θht	NOUN
ma-99	122	27	)	)	PUNCT
ma-99	122	28	αθ	αθ	PROPN
ma-99	122	29	p	p	NOUN
ma-99	122	30	/	/	SYM
ma-99	122	31	α	α	NOUN
ma-99	122	32	=	=	SYM
ma-99	122	33	0	0	PROPN
ma-99	122	34	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	122	35	eur	eur	PROPN
ma-99	122	36	.	.	PUNCT
ma-99	123	1	j.	j.	PROPN
ma-99	123	2	math	math	PROPN
ma-99	123	3	.	.	PUNCT
ma-99	124	1	anal	anal	PROPN
ma-99	124	2	.	.	PUNCT
ma-99	125	1	10.28924	10.28924	NUM
ma-99	125	2	/	/	SYM
ma-99	125	3	ada	ada	PROPN
ma-99	125	4	/	/	SYM
ma-99	125	5	ma.3.4	ma.3.4	PROPN
ma-99	125	6	6hence	6hence	NUM
ma-99	125	7	lim	lim	PROPN
ma-99	125	8	h→0	h→0	NOUN
ma-99	125	9	+	+	CCONJ
ma-99	125	10	2p	2p	NUM
ma-99	125	11	e|	e|	PROPN
ma-99	125	12	∫	∫	PROPN
ma-99	125	13	h	h	NOUN
ma-99	125	14	0	0	NUM
ma-99	126	1	e	e	NOUN
ma-99	126	2	sadzs	sadzs	PROPN
ma-99	126	3	|p	|p	PROPN
ma-99	126	4	εp	εp	ADP
ma-99	126	5	→	→	SYM
ma-99	126	6	0.thus	0.thus	NUM
ma-99	126	7	lim	lim	NOUN
ma-99	126	8	h→0	h→0	NOUN
ma-99	126	9	+	+	NUM
ma-99	126	10	sup	sup	PROPN
ma-99	126	11	t≥0	t≥0	NOUN
ma-99	126	12	i1(t	i1(t	PROPN
ma-99	126	13	,	,	PUNCT
ma-99	126	14	h	h	NOUN
ma-99	126	15	)	)	PUNCT
ma-99	126	16	=	=	SYM
ma-99	126	17	0	0	NUM
ma-99	127	1	this	this	PRON
ma-99	127	2	proves	prove	VERB
ma-99	127	3	stochastic	stochastic	ADJ
ma-99	127	4	continuity	continuity	NOUN
ma-99	127	5	of	of	ADP
ma-99	127	6	yt	yt	PROPN
ma-99	127	7	.	.	PUNCT
ma-99	128	1	using	use	VERB
ma-99	128	2	the	the	DET
ma-99	128	3	stochastic	stochastic	ADJ
ma-99	128	4	continuity	continuity	NOUN
ma-99	128	5	and	and	CCONJ
ma-99	128	6	ft	ft	NOUN
ma-99	128	7	-	-	PUNCT
ma-99	128	8	adaptedness	adaptedness	NOUN
ma-99	128	9	of	of	ADP
ma-99	128	10	x	x	SYM
ma-99	128	11	,	,	PUNCT
ma-99	128	12	we	we	PRON
ma-99	128	13	conclude	conclude	VERB
ma-99	128	14	that	that	SCONJ
ma-99	128	15	the	the	DET
ma-99	128	16	process	process	NOUN
ma-99	128	17	x	x	INTJ
ma-99	128	18	hasa	hasa	VERB
ma-99	128	19	predictable	predictable	ADJ
ma-99	128	20	version	version	NOUN
ma-99	128	21	.	.	PUNCT
ma-99	129	1	time	time	NOUN
ma-99	129	2	change	change	NOUN
ma-99	129	3	:	:	PUNCT
ma-99	129	4	let	let	VERB
ma-99	129	5	l	l	NOUN
ma-99	129	6	be	be	AUX
ma-99	129	7	a	a	DET
ma-99	129	8	one	one	NUM
ma-99	129	9	dimensional	dimensional	ADJ
ma-99	129	10	α	α	NOUN
ma-99	129	11	-	-	ADJ
ma-99	129	12	stable	stable	ADJ
ma-99	129	13	process	process	NOUN
ma-99	129	14	,	,	PUNCT
ma-99	129	15	α	α	PROPN
ma-99	129	16	∈	∈	PROPN
ma-99	129	17	(	(	PUNCT
ma-99	129	18	0	0	NUM
ma-99	129	19	,	,	PUNCT
ma-99	129	20	2	2	NUM
ma-99	129	21	)	)	PUNCT
ma-99	129	22	.	.	PUNCT
ma-99	130	1	then	then	ADV
ma-99	130	2	there	there	PRON
ma-99	130	3	exists	exist	VERB
ma-99	130	4	an	an	DET
ma-99	130	5	α	α	NUM
ma-99	130	6	-	-	ADJ
ma-99	130	7	stable	stable	ADJ
ma-99	130	8	process	process	NOUN
ma-99	130	9	,	,	PUNCT
ma-99	130	10	α	α	PROPN
ma-99	130	11	∈	∈	PROPN
ma-99	130	12	(	(	PUNCT
ma-99	130	13	0	0	NUM
ma-99	130	14	,	,	PUNCT
ma-99	130	15	2	2	NUM
ma-99	130	16	)	)	PUNCT
ma-99	130	17	z	z	NOUN
ma-99	130	18	=	=	SYM
ma-99	130	19	(	(	PUNCT
ma-99	130	20	zt	zt	PROPN
ma-99	130	21	)	)	PUNCT
ma-99	130	22	such	such	ADJ
ma-99	130	23	that∫	that∫	NOUN
ma-99	130	24	t	t	NOUN
ma-99	130	25	0	0	PUNCT
ma-99	130	26	e−θsdls	e−θsdls	X
ma-99	131	1	=	=	SYM
ma-99	131	2	z(u(t	z(u(t	PROPN
ma-99	131	3	)	)	PUNCT
ma-99	131	4	)	)	PUNCT
ma-99	132	1	where	where	SCONJ
ma-99	132	2	u(t	u(t	NOUN
ma-99	132	3	)	)	PUNCT
ma-99	132	4	=	=	SYM
ma-99	132	5	1−	1−	NUM
ma-99	132	6	e−αθt	e−αθt	NOUN
ma-99	132	7	αθ	αθ	PROPN
ma-99	132	8	.	.	PUNCT
ma-99	133	1	recall	recall	VERB
ma-99	133	2	that	that	SCONJ
ma-99	133	3	u	u	PROPN
ma-99	133	4	∈	∈	PROPN
ma-99	133	5	c∞([0,∞	c∞([0,∞	NOUN
ma-99	133	6	]	]	PUNCT
ma-99	133	7	)	)	PUNCT
ma-99	133	8	with	with	ADP
ma-99	133	9	u′(t	u′(t	NOUN
ma-99	133	10	)	)	PUNCT
ma-99	133	11	6=	6=	ADP
ma-99	133	12	0	0	NUM
ma-99	133	13	,	,	PUNCT
ma-99	133	14	t	t	PROPN
ma-99	133	15	≥	≥	NOUN
ma-99	133	16	0.in	0.in	NUM
ma-99	133	17	the	the	DET
ma-99	133	18	limiting	limit	VERB
ma-99	133	19	gaussian	gaussian	ADJ
ma-99	133	20	case	case	NOUN
ma-99	133	21	of	of	ADP
ma-99	133	22	α	α	NOUN
ma-99	133	23	=	=	SYM
ma-99	133	24	2	2	NUM
ma-99	133	25	,	,	PUNCT
ma-99	133	26	it	it	PRON
ma-99	133	27	becomes	become	VERB
ma-99	133	28	time	time	NOUN
ma-99	133	29	change	change	NOUN
ma-99	133	30	for	for	ADP
ma-99	133	31	brownian	brownian	ADJ
ma-99	133	32	motion	motion	NOUN
ma-99	133	33	.	.	PUNCT
ma-99	134	1	infinite	infinite	ADJ
ma-99	134	2	dimensional	dimensional	ADJ
ma-99	134	3	stable	stable	ADJ
ma-99	134	4	ou	ou	NOUN
ma-99	134	5	process	process	NOUN
ma-99	134	6	dxnt	dxnt	NOUN
ma-99	134	7	=	=	NOUN
ma-99	134	8	−θxnt	−θxnt	NOUN
ma-99	134	9	dt	dt	NOUN
ma-99	135	1	+	+	CCONJ
ma-99	135	2	σdznt	σdznt	ADJ
ma-99	135	3	,	,	PUNCT
ma-99	135	4	x	x	NOUN
ma-99	135	5	n	n	NOUN
ma-99	135	6	0	0	NUM
ma-99	135	7	=	=	SYM
ma-99	135	8	xn	xn	PROPN
ma-99	135	9	,	,	PUNCT
ma-99	135	10	n	n	PROPN
ma-99	135	11	∈	∈	NOUN
ma-99	135	12	nwith	nwith	NOUN
ma-99	136	1	x	x	PUNCT
ma-99	136	2	=	=	SYM
ma-99	136	3	(	(	PUNCT
ma-99	136	4	xn	xn	X
ma-99	136	5	)	)	PUNCT
ma-99	136	6	∈	∈	NOUN
ma-99	136	7	l2	l2	NOUN
ma-99	136	8	=	=	SYM
ma-99	136	9	h.	h.	NOUN
ma-99	136	10	the	the	DET
ma-99	136	11	solution	solution	NOUN
ma-99	136	12	is	be	AUX
ma-99	136	13	a	a	DET
ma-99	136	14	stochastic	stochastic	ADJ
ma-99	136	15	process	process	NOUN
ma-99	136	16	x	x	PUNCT
ma-99	136	17	=	=	PUNCT
ma-99	136	18	xxt	xxt	NOUN
ma-99	136	19	with	with	ADP
ma-99	136	20	values	value	NOUN
ma-99	136	21	in	in	ADP
ma-99	136	22	r∞	r∞	PROPN
ma-99	136	23	withcomponents	withcomponent	NOUN
ma-99	136	24	xxt	xxt	X
ma-99	137	1	=	=	SYM
ma-99	137	2	e−θtxn	e−θtxn	X
ma-99	137	3	+	+	NUM
ma-99	137	4	∫	∫	PROPN
ma-99	137	5	t	t	PROPN
ma-99	137	6	0	0	NUM
ma-99	137	7	e−θ(t−s)σdzns	e−θ(t−s)σdzns	VERB
ma-99	137	8	.(the	.(the	PRON
ma-99	137	9	stochastic	stochastic	ADJ
ma-99	137	10	integral	integral	ADJ
ma-99	137	11	can	can	AUX
ma-99	137	12	be	be	AUX
ma-99	137	13	defined	define	VERB
ma-99	137	14	as	as	ADP
ma-99	137	15	the	the	DET
ma-99	137	16	limit	limit	NOUN
ma-99	137	17	in	in	ADP
ma-99	137	18	probability	probability	NOUN
ma-99	137	19	of	of	ADP
ma-99	137	20	riemann	riemann	PROPN
ma-99	137	21	sums	sum	NOUN
ma-99	137	22	.	.	PUNCT
ma-99	137	23	)	)	PUNCT
ma-99	138	1	xxt	xxt	PROPN
ma-99	139	1	=	=	PUNCT
ma-99	139	2	∞∑	∞∑	NUM
ma-99	139	3	n=1	n=1	ADP
ma-99	139	4	xnt	xnt	NOUN
ma-99	139	5	en	en	NOUN
ma-99	139	6	=	=	PUNCT
ma-99	139	7	etax	etax	PROPN
ma-99	139	8	+	+	CCONJ
ma-99	139	9	za(t	za(t	NUM
ma-99	139	10	)	)	PUNCT
ma-99	139	11	where	where	SCONJ
ma-99	139	12	za(t	za(t	NUM
ma-99	139	13	)	)	PUNCT
ma-99	139	14	=	=	SYM
ma-99	140	1	∫	∫	PROPN
ma-99	140	2	t	t	NOUN
ma-99	140	3	0	0	PUNCT
ma-99	141	1	e(t−s)adzs	e(t−s)adzs	PROPN
ma-99	141	2	=	=	PUNCT
ma-99	142	1	∞∑	∞∑	NUM
ma-99	142	2	n=1	n=1	PROPN
ma-99	142	3	(	(	PUNCT
ma-99	142	4	∫	∫	PROPN
ma-99	142	5	t	t	PROPN
ma-99	142	6	0	0	NUM
ma-99	142	7	e−θ(t−s)σdzns	e−θ(t−s)σdzns	PROPN
ma-99	142	8	)	)	PUNCT
ma-99	142	9	en	en	ADP
ma-99	142	10	.	.	PUNCT
ma-99	143	1	the	the	DET
ma-99	143	2	process	process	NOUN
ma-99	143	3	xxt	xxt	NOUN
ma-99	143	4	is	be	AUX
ma-99	143	5	an	an	DET
ma-99	143	6	ft	ft	NOUN
ma-99	143	7	-	-	PUNCT
ma-99	143	8	adapted	adapt	VERB
ma-99	143	9	irreducible	irreducible	ADJ
ma-99	143	10	markov	markov	NOUN
ma-99	143	11	process	process	NOUN
ma-99	143	12	and	and	CCONJ
ma-99	143	13	its	its	PRON
ma-99	143	14	transition	transition	NOUN
ma-99	143	15	semigroup	semigroup	NOUN
ma-99	143	16	isstrong	isstrong	NOUN
ma-99	143	17	feller.let	feller.let	PROPN
ma-99	143	18	y	y	PROPN
ma-99	143	19	nt	not	PART
ma-99	143	20	=	=	PUNCT
ma-99	143	21	zna(t	zna(t	NOUN
ma-99	143	22	)	)	PUNCT
ma-99	144	1	=	=	SYM
ma-99	144	2	∫	∫	PROPN
ma-99	144	3	t	t	PROPN
ma-99	144	4	0	0	NUM
ma-99	144	5	e−θ(t−s)σdzns	e−θ(t−s)σdzns	PROPN
ma-99	144	6	,	,	PUNCT
ma-99	144	7	n	n	PROPN
ma-99	144	8	∈	∈	PROPN
ma-99	144	9	n	n	CCONJ
ma-99	144	10	,	,	PUNCT
ma-99	144	11	t	t	PROPN
ma-99	144	12	≥	≥	NUM
ma-99	144	13	0.then	0.then	PUNCT
ma-99	145	1	e[e	e[e	ADJ
ma-99	145	2	ihy	ihy	PROPN
ma-99	145	3	n	n	PRON
ma-99	145	4	t	t	X
ma-99	145	5	]	]	PUNCT
ma-99	145	6	=	=	SYM
ma-99	145	7	exp	exp	X
ma-99	145	8	[	[	PUNCT
ma-99	145	9	−σα|h|α	−σα|h|α	PROPN
ma-99	145	10	∫	∫	PROPN
ma-99	145	11	t	t	PROPN
ma-99	145	12	0	0	NUM
ma-99	146	1	e−αθsds	e−αθsds	ADP
ma-99	146	2	]	]	PUNCT
ma-99	146	3	=	=	PUNCT
ma-99	147	1	e−|h|	e−|h|	NOUN
ma-99	147	2	αcαn	αcαn	NOUN
ma-99	147	3	(	(	PUNCT
ma-99	147	4	t	t	NOUN
ma-99	147	5	)	)	PUNCT
ma-99	147	6	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	147	7	eur	eur	PROPN
ma-99	147	8	.	.	PUNCT
ma-99	148	1	j.	j.	PROPN
ma-99	148	2	math	math	PROPN
ma-99	148	3	.	.	PUNCT
ma-99	149	1	anal	anal	PROPN
ma-99	149	2	.	.	PUNCT
ma-99	150	1	10.28924	10.28924	NUM
ma-99	150	2	/	/	SYM
ma-99	150	3	ada	ada	PROPN
ma-99	150	4	/	/	SYM
ma-99	150	5	ma.3.4	ma.3.4	PROPN
ma-99	150	6	7where	7where	PROPN
ma-99	150	7	cn(t	cn(t	PUNCT
ma-99	150	8	)	)	PUNCT
ma-99	151	1	=	=	SYM
ma-99	151	2	σ	σ	PROPN
ma-99	151	3	(	(	PUNCT
ma-99	151	4	1−	1−	NUM
ma-99	151	5	e−αθt	e−αθt	NOUN
ma-99	151	6	αθ	αθ	PROPN
ma-99	151	7	)	)	PUNCT
ma-99	151	8	1	1	NUM
ma-99	151	9	/	/	SYM
ma-99	151	10	α	α	NOUN
ma-99	151	11	.	.	PUNCT
ma-99	152	1	it	it	PRON
ma-99	152	2	follows	follow	VERB
ma-99	152	3	that	that	SCONJ
ma-99	152	4	e[e	e[e	ADJ
ma-99	152	5	ihy	ihy	NOUN
ma-99	152	6	n	n	PRON
ma-99	152	7	t	t	X
ma-99	152	8	]	]	PUNCT
ma-99	153	1	=	=	PUNCT
ma-99	153	2	e[e	e[e	ADJ
ma-99	153	3	ihcn(t)ln	ihcn(t)ln	NOUN
ma-99	153	4	]	]	PUNCT
ma-99	153	5	,	,	PUNCT
ma-99	153	6	h	h	NOUN
ma-99	153	7	∈	∈	PROPN
ma-99	153	8	r	r	NOUN
ma-99	153	9	where	where	SCONJ
ma-99	153	10	(	(	PUNCT
ma-99	153	11	ln	ln	ADJ
ma-99	153	12	)	)	PUNCT
ma-99	153	13	are	be	AUX
ma-99	153	14	independent	independent	ADJ
ma-99	153	15	α	α	PRON
ma-99	153	16	-	-	ADJ
ma-99	153	17	stable	stable	ADJ
ma-99	153	18	random	random	ADJ
ma-99	153	19	variables	variable	NOUN
ma-99	153	20	having	have	VERB
ma-99	153	21	the	the	DET
ma-99	153	22	same	same	ADJ
ma-99	153	23	law	law	NOUN
ma-99	153	24	µα	µα	NOUN
ma-99	153	25	.	.	PUNCT
ma-99	154	1	thus	thus	ADV
ma-99	154	2	xxt	xxt	PROPN
ma-99	154	3	is	be	AUX
ma-99	154	4	ft-adapted.the	ft-adapted.the	DET
ma-99	154	5	markov	markov	NOUN
ma-99	154	6	property	property	NOUN
ma-99	154	7	easily	easily	ADV
ma-99	154	8	follows	follow	VERB
ma-99	154	9	from	from	ADP
ma-99	154	10	the	the	DET
ma-99	154	11	identity	identity	NOUN
ma-99	154	12	za(t	za(t	NUM
ma-99	154	13	+	+	CCONJ
ma-99	154	14	h)−	h)−	PROPN
ma-99	154	15	ehaza(t	ehaza(t	PROPN
ma-99	154	16	)	)	PUNCT
ma-99	154	17	=	=	SYM
ma-99	155	1	∫	∫	PROPN
ma-99	155	2	t+h	t+h	X
ma-99	156	1	t	t	PROPN
ma-99	156	2	e(t+h−s)adzs	e(t+h−s)adzs	X
ma-99	156	3	,	,	PUNCT
ma-99	156	4	t	t	PROPN
ma-99	156	5	,	,	PUNCT
ma-99	156	6	h	h	PROPN
ma-99	156	7	≥	≥	NOUN
ma-99	156	8	0	0	NUM
ma-99	156	9	.	.	PUNCT
ma-99	157	1	if	if	SCONJ
ma-99	157	2	the	the	DET
ma-99	157	3	cylindrical	cylindrical	ADJ
ma-99	157	4	levy	levy	NOUN
ma-99	157	5	process	process	NOUN
ma-99	157	6	z	z	NOUN
ma-99	157	7	takes	take	VERB
ma-99	157	8	values	value	NOUN
ma-99	157	9	in	in	ADP
ma-99	157	10	hilbert	hilbert	PROPN
ma-99	157	11	space	space	NOUN
ma-99	157	12	h	h	PROPN
ma-99	157	13	,	,	PUNCT
ma-99	157	14	the	the	PRON
ma-99	157	15	by	by	ADP
ma-99	157	16	the	the	DET
ma-99	157	17	kotelenez	kotelenez	PROPN
ma-99	157	18	regularityresults	regularityresult	VERB
ma-99	157	19	trajectories	trajectory	NOUN
ma-99	157	20	of	of	ADP
ma-99	157	21	the	the	DET
ma-99	157	22	process	process	NOUN
ma-99	157	23	x	x	PRON
ma-99	157	24	are	be	AUX
ma-99	157	25	cadlag	cadlag	NOUN
ma-99	157	26	with	with	ADP
ma-99	157	27	values	value	NOUN
ma-99	157	28	in	in	ADP
ma-99	157	29	h.	h.	PROPN
ma-99	157	30	moments	moment	NOUN
ma-99	157	31	of	of	ADP
ma-99	157	32	the	the	DET
ma-99	157	33	process	process	NOUN
ma-99	157	34	the	the	DET
ma-99	157	35	ou	ou	NOUN
ma-99	157	36	process	process	NOUN
ma-99	157	37	is	be	AUX
ma-99	157	38	stochastically	stochastically	ADV
ma-99	157	39	continuous	continuous	ADJ
ma-99	157	40	and	and	CCONJ
ma-99	157	41	trajectories	trajectory	NOUN
ma-99	157	42	in	in	ADP
ma-99	157	43	lp([0	lp([0	NOUN
ma-99	157	44	,	,	PUNCT
ma-99	157	45	t	t	X
ma-99	157	46	]	]	PUNCT
ma-99	157	47	;	;	PUNCT
ma-99	157	48	h	h	X
ma-99	157	49	)	)	PUNCT
ma-99	157	50	for	for	ADP
ma-99	157	51	any	any	DET
ma-99	157	52	0	0	PUNCT
ma-99	157	53	<	<	X
ma-99	157	54	p	p	X
ma-99	157	55	<	<	X
ma-99	157	56	αa.s	αa.s	NUM
ma-99	157	57	.	.	PUNCT
ma-99	158	1	set	set	VERB
ma-99	158	2	yt	yt	NOUN
ma-99	158	3	:	:	PUNCT
ma-99	158	4	=	=	NOUN
ma-99	158	5	za(t	za(t	NUM
ma-99	158	6	)	)	PUNCT
ma-99	158	7	.	.	PUNCT
ma-99	159	1	then	then	ADV
ma-99	159	2	we	we	PRON
ma-99	159	3	have	have	VERB
ma-99	159	4	e|yt	e|yt	NOUN
ma-99	159	5	|p	|p	ADJ
ma-99	159	6	≤	≤	ADJ
ma-99	159	7	c̃pσp	c̃pσp	ADV
ma-99	159	8	(	(	PUNCT
ma-99	159	9	∞∑	∞∑	NUM
ma-99	159	10	n=1	n=1	NUM
ma-99	159	11	1−	1−	NUM
ma-99	159	12	e−αθt	e−αθt	NOUN
ma-99	160	1	αθ	αθ	INTJ
ma-99	161	1	)	)	PUNCT
ma-99	162	1	p	p	X
ma-99	162	2	/	/	SYM
ma-99	162	3	α	α	NOUN
ma-99	162	4	where	where	SCONJ
ma-99	162	5	c̃p	c̃p	PROPN
ma-99	162	6	depends	depend	VERB
ma-99	162	7	on	on	ADP
ma-99	162	8	p.	p.	PROPN
ma-99	162	9	moments	moment	NOUN
ma-99	162	10	of	of	ADP
ma-99	162	11	the	the	DET
ma-99	162	12	stochastic	stochastic	ADJ
ma-99	162	13	integral	integral	ADJ
ma-99	162	14	suppose	suppose	NOUN
ma-99	162	15	(	(	PUNCT
ma-99	162	16	zt	zt	PROPN
ma-99	162	17	)	)	PUNCT
ma-99	162	18	is	be	AUX
ma-99	162	19	an	an	DET
ma-99	162	20	α	α	NOUN
ma-99	162	21	-	-	ADJ
ma-99	162	22	stable	stable	ADJ
ma-99	162	23	levy	levy	NOUN
ma-99	162	24	process	process	NOUN
ma-99	162	25	with	with	ADP
ma-99	162	26	0	0	NUM
ma-99	162	27	≤	≤	NUM
ma-99	162	28	α	α	NOUN
ma-99	162	29	≤	≤	ADJ
ma-99	162	30	2	2	NUM
ma-99	162	31	and	and	CCONJ
ma-99	162	32	y(t	y(t	NUM
ma-99	162	33	)	)	PUNCT
ma-99	163	1	is	be	AUX
ma-99	163	2	a	a	DET
ma-99	163	3	predictable	predictable	ADJ
ma-99	163	4	processsatisfying	processsatisfye	VERB
ma-99	163	5	∫	∫	PROPN
ma-99	163	6	t0	t0	PROPN
ma-99	163	7	|y(t)|αdt	|y(t)|αdt	X
ma-99	163	8	<	<	X
ma-99	163	9	∞.	∞.	PROPN
ma-99	163	10	then	then	ADV
ma-99	163	11	for	for	ADP
ma-99	163	12	any	any	PRON
ma-99	163	13	0	0	PUNCT
ma-99	163	14	<	<	X
ma-99	163	15	r	r	X
ma-99	163	16	<	<	X
ma-99	163	17	α	α	NOUN
ma-99	163	18	,	,	PUNCT
ma-99	163	19	there	there	PRON
ma-99	163	20	exists	exist	VERB
ma-99	163	21	a	a	DET
ma-99	163	22	constant	constant	ADJ
ma-99	163	23	c	c	NOUN
ma-99	163	24	such	such	ADJ
ma-99	164	1	that	that	SCONJ
ma-99	164	2	e	e	NOUN
ma-99	164	3	[	[	PUNCT
ma-99	164	4	sup	sup	NOUN
ma-99	164	5	t≤t	t≤t	PROPN
ma-99	164	6	∣∣∣∣∫	∣∣∣∣∫	NOUN
ma-99	164	7	t	t	NOUN
ma-99	164	8	0	0	NUM
ma-99	164	9	y(s)dzs	y(s)dzs	PROPN
ma-99	164	10	∣∣∣∣r	∣∣∣∣r	NOUN
ma-99	164	11	]	]	PUNCT
ma-99	165	1	≤	≤	NUM
ma-99	165	2	e	e	X
ma-99	165	3	[	[	X
ma-99	165	4	(	(	PUNCT
ma-99	165	5	∫	∫	PROPN
ma-99	165	6	t	t	PROPN
ma-99	165	7	0	0	NUM
ma-99	165	8	|y(t)|αdt	|y(t)|αdt	X
ma-99	165	9	)	)	PUNCT
ma-99	165	10	r	r	X
ma-99	165	11	/	/	SYM
ma-99	165	12	α	α	NOUN
ma-99	165	13	]	]	PUNCT
ma-99	165	14	.	.	PUNCT
ma-99	166	1	equivalence	equivalence	NOUN
ma-99	166	2	of	of	ADP
ma-99	166	3	transition	transition	NOUN
ma-99	166	4	probabilities	probability	NOUN
ma-99	166	5	assume	assume	VERB
ma-99	166	6	sup	sup	NOUN
ma-99	166	7	n≥1	n≥1	NOUN
ma-99	166	8	e−γntγ	e−γntγ	PROPN
ma-99	166	9	1	1	NUM
ma-99	166	10	/	/	SYM
ma-99	166	11	α	α	NOUN
ma-99	166	12	n	n	NOUN
ma-99	166	13	βn	βn	VERB
ma-99	167	1	=	=	SYM
ma-99	167	2	ct	ct	X
ma-99	167	3	<	<	X
ma-99	167	4	∞	∞	PROPN
ma-99	167	5	,	,	PUNCT
ma-99	167	6	e	e	PROPN
ma-99	167	7	∫	∫	PROPN
ma-99	167	8	t	t	PROPN
ma-99	167	9	0	0	NUM
ma-99	167	10	∑	∑	NOUN
ma-99	167	11	n≥1	n≥1	NOUN
ma-99	167	12	|y	|y	NOUN
ma-99	167	13	nt	not	PART
ma-99	167	14	|2	|2	NUM
ma-99	167	15	p/2	p/2	NOUN
ma-99	167	16	dt	dt	NOUN
ma-99	168	1	<	<	X
ma-99	168	2	∞.	∞.	PROPN
ma-99	168	3	let	let	VERB
ma-99	168	4	pα	pα	INTJ
ma-99	168	5	be	be	AUX
ma-99	168	6	the	the	DET
ma-99	168	7	density	density	NOUN
ma-99	168	8	of	of	ADP
ma-99	168	9	the	the	DET
ma-99	168	10	one	one	NUM
ma-99	168	11	dimensional	dimensional	ADJ
ma-99	168	12	stable	stable	ADJ
ma-99	168	13	measure	measure	NOUN
ma-99	168	14	.	.	PUNCT
ma-99	169	1	then	then	ADV
ma-99	169	2	the	the	DET
ma-99	169	3	laws	law	NOUN
ma-99	169	4	µxt	µxt	PROPN
ma-99	169	5	and	and	CCONJ
ma-99	169	6	µyt	µyt	PROPN
ma-99	169	7	of	of	ADP
ma-99	169	8	xxt	xxt	PROPN
ma-99	169	9	and	and	CCONJ
ma-99	169	10	xyt	xyt	PROPN
ma-99	169	11	respectively	respectively	ADV
ma-99	169	12	are	be	AUX
ma-99	169	13	equivalent	equivalent	ADJ
ma-99	169	14	for	for	ADP
ma-99	169	15	any	any	DET
ma-99	169	16	t	t	PROPN
ma-99	169	17	>	>	X
ma-99	169	18	0	0	NUM
ma-99	169	19	,	,	PUNCT
ma-99	169	20	x	x	PRON
ma-99	169	21	,	,	PUNCT
ma-99	169	22	y	y	PROPN
ma-99	169	23	∈	∈	PROPN
ma-99	169	24	h	h	NOUN
ma-99	169	25	,	,	PUNCT
ma-99	169	26	α	α	PROPN
ma-99	169	27	∈	∈	PROPN
ma-99	169	28	(	(	PUNCT
ma-99	169	29	0	0	NUM
ma-99	169	30	,	,	PUNCT
ma-99	169	31	2	2	NUM
ma-99	169	32	)	)	PUNCT
ma-99	169	33	.	.	PUNCT
ma-99	170	1	moreover	moreover	ADV
ma-99	170	2	,	,	PUNCT
ma-99	170	3	the	the	DET
ma-99	170	4	density	density	NOUN
ma-99	170	5	dµxt	dµxt	VERB
ma-99	170	6	dµxt	dµxt	NOUN
ma-99	170	7	of	of	ADP
ma-99	170	8	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	170	9	eur	eur	NOUN
ma-99	170	10	.	.	PUNCT
ma-99	171	1	j.	j.	PROPN
ma-99	171	2	math	math	PROPN
ma-99	171	3	.	.	PUNCT
ma-99	172	1	anal	anal	PROPN
ma-99	172	2	.	.	PUNCT
ma-99	173	1	10.28924	10.28924	NUM
ma-99	173	2	/	/	SYM
ma-99	173	3	ada	ada	PROPN
ma-99	173	4	/	/	SYM
ma-99	173	5	ma.3.4	ma.3.4	PROPN
ma-99	173	6	8	8	NUM
ma-99	173	7	µxt	µxt	NOUN
ma-99	173	8	with	with	ADP
ma-99	173	9	respect	respect	NOUN
ma-99	173	10	to	to	ADP
ma-99	173	11	µyt	µyt	NOUN
ma-99	173	12	is	be	AUX
ma-99	173	13	given	give	VERB
ma-99	173	14	by	by	ADP
ma-99	173	15	dµxt	dµxt	NOUN
ma-99	173	16	dµyt	dµyt	NOUN
ma-99	173	17	=	=	PROPN
ma-99	173	18	lim	lim	PROPN
ma-99	173	19	n→∞	n→∞	X
ma-99	173	20	n∏	n∏	PROPN
ma-99	174	1	k=1	k=1	PROPN
ma-99	174	2	pα	pα	INTJ
ma-99	174	3	(	(	PUNCT
ma-99	174	4	zk−e−θtxk	zk−e−θtxk	PROPN
ma-99	174	5	c(t	c(t	PROPN
ma-99	174	6	)	)	PUNCT
ma-99	174	7	)	)	PUNCT
ma-99	175	1	pα	pα	INTJ
ma-99	175	2	(	(	PUNCT
ma-99	175	3	zk−e−θtyk	zk−e−θtyk	PROPN
ma-99	175	4	c(t	c(t	PROPN
ma-99	175	5	)	)	PUNCT
ma-99	175	6	)	)	PUNCT
ma-99	175	7	.	.	PUNCT
ma-99	176	1	the	the	DET
ma-99	176	2	corresponding	correspond	VERB
ma-99	176	3	mle	mle	PROPN
ma-99	176	4	is	be	AUX
ma-99	176	5	denoted	denote	VERB
ma-99	176	6	as	as	ADP
ma-99	176	7	θ̂n	θ̂n	PROPN
ma-99	176	8	.	.	PUNCT
ma-99	176	9	priola	priola	PROPN
ma-99	176	10	et	et	PROPN
ma-99	176	11	al	al	PROPN
ma-99	176	12	.	.	PUNCT
ma-99	177	1	[	[	X
ma-99	177	2	38	38	NUM
ma-99	177	3	]	]	PUNCT
ma-99	177	4	obtained	obtain	VERB
ma-99	177	5	exponential	exponential	ADJ
ma-99	177	6	convergence	convergence	NOUN
ma-99	177	7	to	to	ADP
ma-99	177	8	the	the	DET
ma-99	177	9	invariant	invariant	ADJ
ma-99	177	10	measure	measure	NOUN
ma-99	177	11	,	,	PUNCT
ma-99	177	12	in	in	ADP
ma-99	177	13	the	the	DET
ma-99	177	14	total	total	ADJ
ma-99	177	15	variationnorm	variationnorm	NOUN
ma-99	177	16	,	,	PUNCT
ma-99	177	17	for	for	ADP
ma-99	177	18	solutions	solution	NOUN
ma-99	177	19	to	to	ADP
ma-99	177	20	sdes	sde	NOUN
ma-99	177	21	driven	drive	VERB
ma-99	177	22	by	by	ADP
ma-99	177	23	α	α	NOUN
ma-99	177	24	-	-	ADJ
ma-99	177	25	stable	stable	ADJ
ma-99	177	26	noises	noise	NOUN
ma-99	177	27	in	in	ADP
ma-99	177	28	finite	finite	NOUN
ma-99	177	29	and	and	CCONJ
ma-99	177	30	infinite	infinite	ADJ
ma-99	177	31	dimensions	dimension	NOUN
ma-99	177	32	using	use	VERB
ma-99	177	33	twoapproaches	twoapproache	NOUN
ma-99	177	34	:	:	PUNCT
ma-99	177	35	lyapounov	lyapounov	PROPN
ma-99	177	36	’s	’s	PART
ma-99	177	37	function	function	NOUN
ma-99	177	38	approach	approach	NOUN
ma-99	177	39	by	by	ADP
ma-99	177	40	harris	harris	PROPN
ma-99	177	41	and	and	CCONJ
ma-99	177	42	doeblin	doeblin	PROPN
ma-99	177	43	’s	’s	PART
ma-99	177	44	coupling	coupling	NOUN
ma-99	177	45	argument	argument	NOUN
ma-99	177	46	.	.	PUNCT
ma-99	178	1	in	in	ADP
ma-99	178	2	bothapproaches	bothapproache	NOUN
ma-99	178	3	irreducibility	irreducibility	NOUN
ma-99	178	4	and	and	CCONJ
ma-99	178	5	uniform	uniform	ADJ
ma-99	178	6	strong	strong	ADJ
ma-99	178	7	feller	feller	NOUN
ma-99	178	8	property	property	NOUN
ma-99	178	9	play	play	NOUN
ma-99	178	10	crucial	crucial	ADJ
ma-99	178	11	role.first	role.first	PROPN
ma-99	178	12	we	we	PRON
ma-99	178	13	consider	consider	VERB
ma-99	178	14	the	the	DET
ma-99	178	15	method	method	NOUN
ma-99	178	16	of	of	ADP
ma-99	178	17	moments	moment	NOUN
ma-99	178	18	estimation	estimation	NOUN
ma-99	178	19	in	in	ADP
ma-99	178	20	modified	modify	VERB
ma-99	178	21	tempered	temper	VERB
ma-99	178	22	stable	stable	ADJ
ma-99	178	23	-	-	PUNCT
ma-99	178	24	ornstein	ornstein	ADJ
ma-99	178	25	-	-	PUNCT
ma-99	178	26	uhlenbeck	uhlenbeck	PROPN
ma-99	178	27	model	model	PROPN
ma-99	178	28	.	.	PUNCT
ma-99	179	1	masuda	masuda	PROPN
ma-99	179	2	and	and	CCONJ
ma-99	179	3	uehara	uehara	PROPN
ma-99	180	1	[	[	X
ma-99	180	2	36	36	NUM
ma-99	180	3	]	]	PUNCT
ma-99	180	4	studied	study	VERB
ma-99	180	5	two	two	NUM
ma-99	180	6	-	-	PUNCT
ma-99	180	7	step	step	NOUN
ma-99	180	8	estimation	estimation	NOUN
ma-99	180	9	in	in	ADP
ma-99	180	10	ergodic	ergodic	ADJ
ma-99	180	11	levy	levy	NOUN
ma-99	180	12	drivensde	drivensde	PROPN
ma-99	180	13	dxt	dxt	PROPN
ma-99	180	14	=	=	SYM
ma-99	180	15	a(θ	a(θ	PROPN
ma-99	180	16	,	,	PUNCT
ma-99	180	17	xt)dt	xt)dt	PUNCT
ma-99	181	1	+	+	CCONJ
ma-99	181	2	b(β	b(β	NOUN
ma-99	181	3	,	,	PUNCT
ma-99	181	4	xt−)dzt	xt−)dzt	PROPN
ma-99	181	5	,	,	PUNCT
ma-99	181	6	x0	x0	PROPN
ma-99	181	7	=	=	PUNCT
ma-99	181	8	x0.masuda	x0.masuda	PROPN
ma-99	182	1	[	[	X
ma-99	182	2	35	35	NUM
ma-99	182	3	]	]	PUNCT
ma-99	182	4	studied	study	VERB
ma-99	182	5	multi	multi	ADJ
ma-99	182	6	-	-	ADJ
ma-99	182	7	step	step	ADJ
ma-99	182	8	estimation	estimation	NOUN
ma-99	182	9	in	in	ADP
ma-99	182	10	stable	stable	ADJ
ma-99	182	11	ou	ou	X
ma-99	182	12	model	model	NOUN
ma-99	182	13	:	:	PUNCT
ma-99	182	14	dxt	dxt	PROPN
ma-99	182	15	=	=	PUNCT
ma-99	183	1	−θxtdt	−θxtdt	PROPN
ma-99	184	1	+	+	NUM
ma-99	184	2	σdzt	σdzt	NOUN
ma-99	184	3	,	,	PUNCT
ma-99	184	4	x0	x0	PROPN
ma-99	185	1	=	=	PUNCT
ma-99	185	2	x0.for	x0.for	ADP
ma-99	185	3	the	the	DET
ma-99	185	4	least	least	ADJ
ma-99	185	5	squares	square	NOUN
ma-99	185	6	estimator	estimator	NOUN
ma-99	185	7	(	(	PUNCT
ma-99	185	8	lse	lse	PROPN
ma-99	185	9	)	)	PUNCT
ma-99	185	10	θ̃n	θ̃n	NOUN
ma-99	185	11	of	of	ADP
ma-99	185	12	θ	θ	PROPN
ma-99	185	13	,	,	PUNCT
ma-99	185	14	hu	hu	PROPN
ma-99	185	15	and	and	CCONJ
ma-99	185	16	long	long	ADJ
ma-99	186	1	[	[	X
ma-99	186	2	20	20	NUM
ma-99	186	3	]	]	PUNCT
ma-99	186	4	obtained	obtain	VERB
ma-99	186	5	(	(	PUNCT
ma-99	186	6	t	t	PROPN
ma-99	186	7	log	log	NOUN
ma-99	186	8	n	n	PROPN
ma-99	186	9	)	)	PUNCT
ma-99	186	10	1	1	NUM
ma-99	186	11	/	/	SYM
ma-99	186	12	α	α	PROPN
ma-99	186	13	(	(	PUNCT
ma-99	186	14	θ̃n	θ̃n	VERB
ma-99	186	15	−	−	NOUN
ma-99	186	16	θ0)→d	θ0)→d	ADP
ma-99	186	17	s′α	s′α	PROPN
ma-99	186	18	s′′+	s′′+	NOUN
ma-99	186	19	α/2where	α/2where	NOUN
ma-99	187	1	sα	sα	ADJ
ma-99	187	2	is	be	AUX
ma-99	187	3	stable	stable	ADJ
ma-99	187	4	distribution	distribution	NOUN
ma-99	187	5	of	of	ADP
ma-99	187	6	order	order	NOUN
ma-99	187	7	β.while	β.while	VERB
ma-99	187	8	in	in	ADP
ma-99	187	9	gaussian	gaussian	ADJ
ma-99	187	10	ou	ou	ADP
ma-99	187	11	case	case	NOUN
ma-99	187	12	,	,	PUNCT
ma-99	187	13	for	for	ADP
ma-99	187	14	different	different	ADJ
ma-99	187	15	parts	part	NOUN
ma-99	187	16	θ	θ	X
ma-99	187	17	>	>	PUNCT
ma-99	187	18	0	0	PROPN
ma-99	187	19	,	,	PUNCT
ma-99	187	20	θ	θ	PROPN
ma-99	187	21	<	<	X
ma-99	187	22	0	0	NUM
ma-99	187	23	and	and	CCONJ
ma-99	187	24	θ	θ	PROPN
ma-99	187	25	=	=	SYM
ma-99	187	26	0	0	NUM
ma-99	187	27	,	,	PUNCT
ma-99	187	28	lan	lan	PROPN
ma-99	187	29	,	,	PUNCT
ma-99	187	30	lamn	lamn	ADV
ma-99	187	31	and	and	CCONJ
ma-99	187	32	labfhold	labfhold	VERB
ma-99	187	33	respectively	respectively	ADV
ma-99	187	34	(	(	PUNCT
ma-99	187	35	see	see	VERB
ma-99	187	36	bishwal	bishwal	NOUN
ma-99	187	37	[	[	X
ma-99	187	38	11	11	NUM
ma-99	187	39	]	]	NUM
ma-99	187	40	)	)	PUNCT
ma-99	187	41	,	,	PUNCT
ma-99	187	42	in	in	ADP
ma-99	187	43	stable	stable	ADJ
ma-99	187	44	case	case	NOUN
ma-99	187	45	entirely	entirely	ADV
ma-99	187	46	different	different	ADJ
ma-99	187	47	phenomena	phenomena	NOUN
ma-99	187	48	occur.the	occur.the	DET
ma-99	187	49	solution	solution	NOUN
ma-99	187	50	of	of	ADP
ma-99	187	51	the	the	DET
ma-99	187	52	sde	sde	PROPN
ma-99	187	53	is	be	AUX
ma-99	187	54	given	give	VERB
ma-99	187	55	by	by	ADP
ma-99	187	56	xt	xt	PROPN
ma-99	187	57	=	=	PUNCT
ma-99	187	58	e−θ(t−s)xs	e−θ(t−s)xs	PROPN
ma-99	188	1	+	+	SYM
ma-99	188	2	σ	σ	NUM
ma-99	188	3	∫	∫	PROPN
ma-99	188	4	t	t	PROPN
ma-99	188	5	s	s	PROPN
ma-99	188	6	e−θ(t−s)dzu	e−θ(t−s)dzu	PROPN
ma-99	188	7	,	,	PUNCT
ma-99	188	8	t	t	PROPN
ma-99	188	9	≥	≥	NOUN
ma-99	188	10	0	0	NUM
ma-99	188	11	.	.	PUNCT
ma-99	189	1	due	due	ADP
ma-99	189	2	to	to	ADP
ma-99	189	3	the	the	DET
ma-99	189	4	stable	stable	ADJ
ma-99	189	5	integral	integral	ADJ
ma-99	189	6	property	property	NOUN
ma-99	189	7	,	,	PUNCT
ma-99	189	8	l	l	PROPN
ma-99	189	9	(	(	PUNCT
ma-99	189	10	∫	∫	PROPN
ma-99	189	11	t	t	PROPN
ma-99	189	12	s	s	PROPN
ma-99	189	13	e−θ(t−s)dzu	e−θ(t−s)dzu	NOUN
ma-99	189	14	)	)	PUNCT
ma-99	189	15	=	=	SYM
ma-99	189	16	sα(κ∆(θ	sα(κ∆(θ	PROPN
ma-99	189	17	)	)	PUNCT
ma-99	189	18	)	)	PUNCT
ma-99	190	1	where	where	SCONJ
ma-99	190	2	κ∆(θ	κ∆(θ	X
ma-99	190	3	)	)	PUNCT
ma-99	190	4	=	=	PRON
ma-99	190	5	{	{	PUNCT
ma-99	190	6	1−	1−	NUM
ma-99	190	7	e−θ∆	e−θ∆	NOUN
ma-99	190	8	θα	θα	NOUN
ma-99	190	9	}	}	SYM
ma-99	190	10	1	1	NUM
ma-99	190	11	/	/	SYM
ma-99	190	12	α	α	PRON
ma-99	190	13	∼	∼	NOUN
ma-99	190	14	∆1	∆1	NOUN
ma-99	190	15	/	/	SYM
ma-99	190	16	α	α	NOUN
ma-99	190	17	.	.	PUNCT
ma-99	190	18	for	for	ADP
ma-99	190	19	each	each	DET
ma-99	190	20	j	j	PROPN
ma-99	190	21	≤	≤	NUM
ma-99	190	22	n	n	CCONJ
ma-99	190	23	,	,	PUNCT
ma-99	190	24	the	the	DET
ma-99	190	25	transition	transition	NOUN
ma-99	190	26	probability	probability	NOUN
ma-99	190	27	is	be	AUX
ma-99	190	28	given	give	VERB
ma-99	190	29	by	by	ADP
ma-99	190	30	l(xtj	l(xtj	NOUN
ma-99	190	31	|xtj−1	|xtj−1	NUM
ma-99	190	32	=	=	SYM
ma-99	190	33	x	x	X
ma-99	190	34	)	)	PUNCT
ma-99	190	35	=	=	SYM
ma-99	190	36	δx	δx	ADP
ma-99	190	37	exp(−θ∆	exp(−θ∆	PROPN
ma-99	190	38	)	)	PUNCT
ma-99	190	39	?	?	PUNCT
ma-99	191	1	sα(κ∆(θ	sα(κ∆(θ	PROPN
ma-99	191	2	)	)	PUNCT
ma-99	191	3	)	)	PUNCT
ma-99	191	4	.	.	PUNCT
ma-99	192	1	lamn	lamn	PROPN
ma-99	192	2	holds	hold	VERB
ma-99	192	3	for	for	ADP
ma-99	192	4	θ	θ	PROPN
ma-99	192	5	∈	∈	PROPN
ma-99	192	6	r	r	NOUN
ma-99	192	7	when	when	SCONJ
ma-99	192	8	t	t	PROPN
ma-99	192	9	is	be	AUX
ma-99	192	10	fixed	fix	VERB
ma-99	192	11	.	.	PUNCT
ma-99	193	1	n1	n1	PROPN
ma-99	193	2	/	/	SYM
ma-99	193	3	α−1/2(θ̂n	α−1/2(θ̂n	NUM
ma-99	193	4	−	−	PROPN
ma-99	193	5	θ)→d	θ)→d	NOUN
ma-99	193	6	mn(0	mn(0	NOUN
ma-99	193	7	,	,	PUNCT
ma-99	193	8	iθ(t	iθ(t	NOUN
ma-99	193	9	)	)	PUNCT
ma-99	193	10	−1	−1	NOUN
ma-99	193	11	)	)	PUNCT
ma-99	193	12	.	.	PUNCT
ma-99	194	1	where	where	SCONJ
ma-99	194	2	iθ(t	iθ(t	NOUN
ma-99	194	3	)	)	PUNCT
ma-99	194	4	is	be	AUX
ma-99	194	5	the	the	DET
ma-99	194	6	fisher	fisher	PROPN
ma-99	194	7	information	information	NOUN
ma-99	194	8	of	of	ADP
ma-99	194	9	the	the	DET
ma-99	194	10	process	process	NOUN
ma-99	194	11	.	.	PUNCT
ma-99	195	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	195	2	eur	eur	PROPN
ma-99	195	3	.	.	PUNCT
ma-99	196	1	j.	j.	PROPN
ma-99	196	2	math	math	PROPN
ma-99	196	3	.	.	PUNCT
ma-99	197	1	anal	anal	PROPN
ma-99	197	2	.	.	PUNCT
ma-99	198	1	10.28924	10.28924	NUM
ma-99	198	2	/	/	SYM
ma-99	198	3	ada	ada	PROPN
ma-99	198	4	/	/	SYM
ma-99	198	5	ma.3.4	ma.3.4	PROPN
ma-99	198	6	9we	9we	PROPN
ma-99	198	7	study	study	NOUN
ma-99	198	8	estimation	estimation	NOUN
ma-99	198	9	in	in	ADP
ma-99	198	10	mts	mts	PROPN
ma-99	198	11	-	-	PUNCT
ma-99	198	12	ou	ou	NOUN
ma-99	198	13	sv	sv	PROPN
ma-99	198	14	model	model	PROPN
ma-99	198	15	.	.	PUNCT
ma-99	199	1	the	the	DET
ma-99	199	2	inverse	inverse	ADJ
ma-99	199	3	gaussian	gaussian	NOUN
ma-99	199	4	-	-	PUNCT
ma-99	199	5	ou	ou	NOUN
ma-99	199	6	and	and	CCONJ
ma-99	199	7	gamma	gamma	NOUN
ma-99	199	8	-	-	PUNCT
ma-99	199	9	ou	ou	NOUN
ma-99	199	10	modelsare	modelsare	PROPN
ma-99	199	11	special	special	ADJ
ma-99	199	12	cases.an	cases.an	ADP
ma-99	199	13	infinitely	infinitely	ADV
ma-99	199	14	divisible	divisible	ADJ
ma-99	199	15	distribution	distribution	NOUN
ma-99	199	16	is	be	AUX
ma-99	199	17	said	say	VERB
ma-99	199	18	to	to	PART
ma-99	199	19	be	be	AUX
ma-99	199	20	α	α	PRON
ma-99	199	21	-	-	PUNCT
ma-99	199	22	modified	modify	VERB
ma-99	199	23	tampered	tamper	VERB
ma-99	199	24	stable	stable	ADJ
ma-99	199	25	distribution	distribution	NOUN
ma-99	199	26	(	(	PUNCT
ma-99	199	27	α	α	NOUN
ma-99	199	28	-	-	PUNCT
ma-99	199	29	mts)distribution	mts)distribution	NOUN
ma-99	199	30	if	if	SCONJ
ma-99	199	31	its	its	PRON
ma-99	199	32	levy	levy	NOUN
ma-99	199	33	triplet	triplet	NOUN
ma-99	199	34	is	be	AUX
ma-99	199	35	given	give	VERB
ma-99	199	36	by	by	ADP
ma-99	199	37	σ2	σ2	PROPN
ma-99	199	38	=	=	SYM
ma-99	199	39	0	0	NUM
ma-99	199	40	,	,	PUNCT
ma-99	199	41	ν(dx	ν(dx	PROPN
ma-99	199	42	)	)	PUNCT
ma-99	199	43	=	=	SYM
ma-99	200	1	c	c	NOUN
ma-99	200	2	λα+	λα+	PROPN
ma-99	200	3	1	1	NUM
ma-99	200	4	2	2	NUM
ma-99	200	5	+	+	NUM
ma-99	200	6	kα+	kα+	NOUN
ma-99	200	7	1	1	NUM
ma-99	200	8	2	2	NUM
ma-99	200	9	λ+x	λ+x	NUM
ma-99	201	1	xα+	xα+	NOUN
ma-99	201	2	1	1	NUM
ma-99	201	3	2	2	X
ma-99	201	4	ix>0	ix>0	NOUN
ma-99	201	5	+	+	NOUN
ma-99	201	6	λ	λ	X
ma-99	201	7	α+	α+	PUNCT
ma-99	201	8	1	1	NUM
ma-99	201	9	2	2	NUM
ma-99	201	10	+	+	NUM
ma-99	201	11	kα+	kα+	NOUN
ma-99	201	12	1	1	NUM
ma-99	201	13	2	2	NUM
ma-99	201	14	λ−x	λ−x	NOUN
ma-99	201	15	xα+	xα+	NOUN
ma-99	201	16	1	1	NUM
ma-99	201	17	2	2	NUM
ma-99	201	18	ix<0	ix<0	PROPN
ma-99	201	19			PROPN
ma-99	201	20	dx	dx	PROPN
ma-99	201	21	,	,	PUNCT
ma-99	201	22	γ	γ	X
ma-99	201	23	=	=	X
ma-99	201	24	µ+	µ+	PROPN
ma-99	201	25	c	c	X
ma-99	201	26	(	(	PUNCT
ma-99	201	27	γ	γ	X
ma-99	201	28	(	(	PUNCT
ma-99	201	29	1	1	NUM
ma-99	201	30	2	2	NUM
ma-99	201	31	−	−	PROPN
ma-99	201	32	α	α	X
ma-99	201	33	)	)	PUNCT
ma-99	201	34	2α+	2α+	NUM
ma-99	201	35	1	1	NUM
ma-99	201	36	2	2	NUM
ma-99	201	37	(	(	PUNCT
ma-99	201	38	λ2α−1	λ2α−1	NOUN
ma-99	201	39	+	+	CCONJ
ma-99	201	40	−	−	PROPN
ma-99	201	41	λ2α−1	λ2α−1	NOUN
ma-99	201	42	−	−	PROPN
ma-99	201	43	)	)	PUNCT
ma-99	201	44	−	−	PROPN
ma-99	202	1	λα−	λα−	SYM
ma-99	202	2	1	1	NUM
ma-99	202	3	2	2	NUM
ma-99	202	4	+	+	CCONJ
ma-99	202	5	kα−	kα−	X
ma-99	202	6	1	1	NUM
ma-99	202	7	2	2	NUM
ma-99	202	8	(	(	PUNCT
ma-99	202	9	λ+	λ+	X
ma-99	202	10	)	)	PUNCT
ma-99	202	11	+	+	CCONJ
ma-99	202	12	λ	λ	X
ma-99	202	13	α−	α−	ADP
ma-99	202	14	1	1	NUM
ma-99	202	15	2	2	NUM
ma-99	202	16	−	−	NOUN
ma-99	202	17	kα−	kα−	PUNCT
ma-99	202	18	1	1	NUM
ma-99	202	19	2	2	NUM
ma-99	202	20	(	(	PUNCT
ma-99	202	21	λ−	λ−	PROPN
ma-99	202	22	)	)	PUNCT
ma-99	202	23	)	)	PUNCT
ma-99	202	24	where	where	SCONJ
ma-99	202	25	c	c	AUX
ma-99	202	26	>	>	X
ma-99	202	27	0	0	NUM
ma-99	202	28	,	,	PUNCT
ma-99	202	29	λ+	λ+	ADP
ma-99	202	30	,	,	PUNCT
ma-99	202	31	λ−	λ−	PROPN
ma-99	202	32	>	>	X
ma-99	202	33	0	0	PROPN
ma-99	202	34	,	,	PUNCT
ma-99	202	35	µ	µ	X
ma-99	202	36	∈	∈	PROPN
ma-99	202	37	r	r	NOUN
ma-99	202	38	,	,	PUNCT
ma-99	202	39	α	α	NOUN
ma-99	202	40	∈	∈	PROPN
ma-99	202	41	(	(	PUNCT
ma-99	202	42	−∞	−∞	NOUN
ma-99	202	43	,	,	PUNCT
ma-99	202	44	1)\{1	1)\{1	NUM
ma-99	202	45	2	2	NUM
ma-99	202	46	}	}	PUNCT
ma-99	202	47	and	and	CCONJ
ma-99	202	48	kp(x	kp(x	NUM
ma-99	202	49	)	)	PUNCT
ma-99	202	50	is	be	AUX
ma-99	202	51	the	the	DET
ma-99	202	52	modified	modify	VERB
ma-99	202	53	bessel	bessel	NOUN
ma-99	202	54	functionof	functionof	PROPN
ma-99	202	55	second	second	ADJ
ma-99	202	56	kind	kind	NOUN
ma-99	202	57	.	.	PUNCT
ma-99	203	1	we	we	PRON
ma-99	203	2	denote	denote	VERB
ma-99	203	3	the	the	DET
ma-99	203	4	mts	mts	NOUN
ma-99	203	5	random	random	ADJ
ma-99	203	6	variable	variable	NOUN
ma-99	203	7	by	by	ADP
ma-99	203	8	x	x	PUNCT
ma-99	203	9	∼	∼	NOUN
ma-99	203	10	mts(α	mts(α	NOUN
ma-99	203	11	,	,	PUNCT
ma-99	203	12	c	c	NOUN
ma-99	203	13	,	,	PUNCT
ma-99	203	14	λ+	λ+	ADP
ma-99	203	15	,	,	PUNCT
ma-99	203	16	λ−	λ−	PROPN
ma-99	203	17	,	,	PUNCT
ma-99	203	18	µ	µ	NOUN
ma-99	203	19	)	)	PUNCT
ma-99	203	20	.	.	PUNCT
ma-99	204	1	the	the	DET
ma-99	204	2	levymeasure	levymeasure	NOUN
ma-99	204	3	ν(dx	ν(dx	NOUN
ma-99	204	4	)	)	PUNCT
ma-99	204	5	is	be	AUX
ma-99	204	6	called	call	VERB
ma-99	204	7	the	the	DET
ma-99	204	8	mts	mts	NOUN
ma-99	204	9	levy	levy	NOUN
ma-99	204	10	measure	measure	NOUN
ma-99	204	11	with	with	ADP
ma-99	204	12	parameter	parameter	NOUN
ma-99	204	13	(	(	PUNCT
ma-99	204	14	α	α	NOUN
ma-99	204	15	,	,	PUNCT
ma-99	204	16	c	c	NOUN
ma-99	204	17	,	,	PUNCT
ma-99	204	18	λ+	λ+	ADP
ma-99	204	19	,	,	PUNCT
ma-99	204	20	λ−).the	λ−).the	ADJ
ma-99	204	21	mts	mts	NOUN
ma-99	204	22	distribution	distribution	NOUN
ma-99	204	23	is	be	AUX
ma-99	204	24	obtained	obtain	VERB
ma-99	204	25	by	by	ADP
ma-99	204	26	taking	take	VERB
ma-99	204	27	a	a	DET
ma-99	204	28	symmetric	symmetric	ADJ
ma-99	204	29	α	α	ADJ
ma-99	204	30	-	-	ADJ
ma-99	204	31	stable	stable	ADJ
ma-99	204	32	distribution	distribution	NOUN
ma-99	204	33	with	with	ADP
ma-99	204	34	α	α	PROPN
ma-99	204	35	∈	∈	PROPN
ma-99	204	36	(	(	PUNCT
ma-99	204	37	0	0	NUM
ma-99	204	38	,	,	PUNCT
ma-99	204	39	1)and	1)and	NUM
ma-99	204	40	multiplying	multiply	VERB
ma-99	204	41	by	by	ADP
ma-99	204	42	a	a	DET
ma-99	204	43	levy	levy	NOUN
ma-99	204	44	measure	measure	NOUN
ma-99	204	45	with	with	ADP
ma-99	204	46	√|x	√|x	ADJ
ma-99	204	47	|λα+	|λα+	NOUN
ma-99	204	48	1	1	NUM
ma-99	204	49	2kα+	2kα+	NUM
ma-99	204	50	1	1	NUM
ma-99	204	51	2	2	NUM
ma-99	204	52	(	(	PUNCT
ma-99	204	53	λ|x	λ|x	NOUN
ma-99	204	54	|	|	ADV
ma-99	204	55	)	)	PUNCT
ma-99	204	56	on	on	ADP
ma-99	204	57	each	each	DET
ma-99	204	58	half	half	NOUN
ma-99	204	59	of	of	ADP
ma-99	204	60	the	the	DET
ma-99	204	61	real	real	ADJ
ma-99	204	62	axis	axis	NOUN
ma-99	204	63	.	.	PUNCT
ma-99	205	1	themeasure	themeasure	NOUN
ma-99	205	2	can	can	AUX
ma-99	205	3	be	be	AUX
ma-99	205	4	extended	extend	VERB
ma-99	205	5	to	to	ADP
ma-99	205	6	the	the	DET
ma-99	205	7	case	case	NOUN
ma-99	205	8	α	α	NOUN
ma-99	205	9	≤	≤	NOUN
ma-99	205	10	0	0	NUM
ma-99	205	11	.	.	PUNCT
ma-99	206	1	if	if	SCONJ
ma-99	206	2	α	α	PRON
ma-99	206	3	=	=	NOUN
ma-99	206	4	1	1	NUM
ma-99	206	5	2	2	NUM
ma-99	206	6	,	,	PUNCT
ma-99	206	7	then	then	ADV
ma-99	206	8	γ	γ	PROPN
ma-99	206	9	may	may	AUX
ma-99	206	10	not	not	PART
ma-99	206	11	be	be	AUX
ma-99	206	12	defined	define	VERB
ma-99	206	13	,	,	PUNCT
ma-99	206	14	so	so	CCONJ
ma-99	206	15	it	it	PRON
ma-99	206	16	is	be	AUX
ma-99	206	17	removed.the	removed.the	PRON
ma-99	206	18	mts	mts	NOUN
ma-99	206	19	distribution	distribution	NOUN
ma-99	206	20	was	be	AUX
ma-99	206	21	introduced	introduce	VERB
ma-99	206	22	by	by	ADP
ma-99	206	23	kim	kim	PROPN
ma-99	206	24	,	,	PUNCT
ma-99	206	25	rachev	rachev	VERB
ma-99	206	26	and	and	CCONJ
ma-99	206	27	chung	chung	VERB
ma-99	207	1	[	[	X
ma-99	207	2	25].the	25].the	DET
ma-99	207	3	tails	tail	NOUN
ma-99	207	4	of	of	ADP
ma-99	207	5	the	the	DET
ma-99	207	6	α	α	NOUN
ma-99	207	7	-	-	PUNCT
ma-99	207	8	mts	mts	NOUN
ma-99	207	9	distribution	distribution	NOUN
ma-99	207	10	are	be	AUX
ma-99	207	11	thinner	thin	ADJ
ma-99	207	12	than	than	ADP
ma-99	207	13	those	those	PRON
ma-99	207	14	of	of	ADP
ma-99	207	15	the	the	DET
ma-99	207	16	2α	2α	NOUN
ma-99	207	17	-	-	PUNCT
ma-99	207	18	stable	stable	ADJ
ma-99	207	19	and	and	CCONJ
ma-99	207	20	fatter	fat	ADJ
ma-99	207	21	(	(	PUNCT
ma-99	207	22	heavier)than	heavier)than	ADP
ma-99	207	23	those	those	PRON
ma-99	207	24	of	of	ADP
ma-99	207	25	the	the	DET
ma-99	207	26	2α	2α	NOUN
ma-99	207	27	-	-	PUNCT
ma-99	207	28	ts	ts	ADP
ma-99	207	29	distribution	distribution	NOUN
ma-99	207	30	.	.	PUNCT
ma-99	208	1	at	at	ADP
ma-99	208	2	the	the	DET
ma-99	208	3	zero	zero	NUM
ma-99	208	4	neighborhood	neighborhood	NOUN
ma-99	208	5	,	,	PUNCT
ma-99	208	6	all	all	DET
ma-99	208	7	three	three	NUM
ma-99	208	8	have	have	VERB
ma-99	208	9	the	the	DET
ma-99	208	10	same	same	ADJ
ma-99	208	11	asymptoticbehavior.if	asymptoticbehavior.if	PROPN
ma-99	208	12	λ+	λ+	PUNCT
ma-99	208	13	>	>	X
ma-99	208	14	λ−	λ−	PROPN
ma-99	208	15	,	,	PUNCT
ma-99	208	16	then	then	ADV
ma-99	208	17	the	the	DET
ma-99	208	18	distribution	distribution	NOUN
ma-99	208	19	is	be	AUX
ma-99	208	20	skewed	skew	VERB
ma-99	208	21	to	to	ADP
ma-99	208	22	the	the	DET
ma-99	208	23	left	left	NOUN
ma-99	208	24	.	.	PUNCT
ma-99	209	1	if	if	SCONJ
ma-99	209	2	λ+	λ+	ADP
ma-99	209	3	<	<	X
ma-99	209	4	λ−	λ−	PROPN
ma-99	209	5	,	,	PUNCT
ma-99	209	6	then	then	ADV
ma-99	209	7	the	the	DET
ma-99	209	8	distribution	distribution	NOUN
ma-99	209	9	is	be	AUX
ma-99	209	10	skewed	skew	VERB
ma-99	209	11	to	to	ADP
ma-99	209	12	the	the	DET
ma-99	209	13	right	right	NOUN
ma-99	209	14	.	.	PUNCT
ma-99	210	1	if	if	SCONJ
ma-99	210	2	λ+	λ+	NUM
ma-99	210	3	=	=	SYM
ma-99	210	4	λ−	λ−	PROPN
ma-99	210	5	,	,	PUNCT
ma-99	210	6	then	then	ADV
ma-99	210	7	the	the	DET
ma-99	210	8	distribution	distribution	NOUN
ma-99	210	9	is	be	AUX
ma-99	210	10	symmetric	symmetric	ADJ
ma-99	210	11	.	.	PUNCT
ma-99	211	1	c	c	NOUN
ma-99	211	2	controls	control	VERB
ma-99	211	3	the	the	DET
ma-99	211	4	kurtosis	kurtosis	NOUN
ma-99	211	5	of	of	ADP
ma-99	211	6	the	the	DET
ma-99	211	7	distribution	distribution	NOUN
ma-99	211	8	.	.	PUNCT
ma-99	212	1	if	if	SCONJ
ma-99	212	2	c	c	NOUN
ma-99	212	3	increases	increase	VERB
ma-99	212	4	,	,	PUNCT
ma-99	212	5	the	the	DET
ma-99	212	6	peakedness	peakedness	NOUN
ma-99	212	7	of	of	ADP
ma-99	212	8	the	the	DET
ma-99	212	9	distributionincreases.as	distributionincreases.as	PROPN
ma-99	212	10	α	α	PROPN
ma-99	212	11	decreases	decrease	VERB
ma-99	212	12	,	,	PUNCT
ma-99	212	13	the	the	DET
ma-99	212	14	distribution	distribution	NOUN
ma-99	212	15	has	have	VERB
ma-99	212	16	fatter	fat	ADJ
ma-99	212	17	tails	tail	NOUN
ma-99	212	18	and	and	CCONJ
ma-99	212	19	increased	increase	VERB
ma-99	212	20	peakedness	peakedness	NOUN
ma-99	212	21	.	.	PUNCT
ma-99	213	1	the	the	DET
ma-99	213	2	levy	levy	NOUN
ma-99	213	3	processcorresponding	processcorresponde	VERB
ma-99	213	4	to	to	ADP
ma-99	213	5	the	the	DET
ma-99	213	6	mts	mts	NOUN
ma-99	213	7	distribution	distribution	NOUN
ma-99	213	8	has	have	VERB
ma-99	213	9	finite	finite	ADJ
ma-99	213	10	activity	activity	NOUN
ma-99	213	11	if	if	SCONJ
ma-99	213	12	α	α	PRON
ma-99	213	13	<	<	X
ma-99	213	14	0	0	NUM
ma-99	213	15	and	and	CCONJ
ma-99	213	16	infinite	infinite	ADJ
ma-99	213	17	activity	activity	NOUN
ma-99	213	18	if	if	SCONJ
ma-99	213	19	α	α	PROPN
ma-99	213	20	>	>	X
ma-99	213	21	0	0	X
ma-99	213	22	.	.	PUNCT
ma-99	214	1	ithas	ithas	PROPN
ma-99	214	2	finite	finite	VERB
ma-99	214	3	variation	variation	NOUN
ma-99	214	4	if	if	SCONJ
ma-99	214	5	α	α	PRON
ma-99	214	6	<	<	X
ma-99	214	7	1	1	NUM
ma-99	214	8	2	2	NUM
ma-99	214	9	and	and	CCONJ
ma-99	214	10	infinite	infinite	ADJ
ma-99	214	11	variation	variation	NOUN
ma-99	214	12	if	if	SCONJ
ma-99	214	13	α	α	PROPN
ma-99	214	14	>	>	X
ma-99	214	15	1	1	NUM
ma-99	214	16	2	2	NUM
ma-99	214	17	.with	.with	ADP
ma-99	214	18	proper	proper	ADJ
ma-99	214	19	choice	choice	NOUN
ma-99	214	20	of	of	ADP
ma-99	214	21	c	c	PROPN
ma-99	214	22	and	and	CCONJ
ma-99	214	23	µ	µ	NOUN
ma-99	214	24	,	,	PUNCT
ma-99	214	25	mts	mts	NOUN
ma-99	214	26	distribution	distribution	NOUN
ma-99	214	27	has	have	VERB
ma-99	214	28	zero	zero	NUM
ma-99	214	29	mean	mean	NOUN
ma-99	214	30	and	and	CCONJ
ma-99	214	31	unit	unit	NOUN
ma-99	214	32	variance	variance	NOUN
ma-99	214	33	,	,	PUNCT
ma-99	214	34	and	and	CCONJ
ma-99	214	35	thedistribution	thedistribution	NOUN
ma-99	214	36	is	be	AUX
ma-99	214	37	called	call	VERB
ma-99	214	38	standard	standard	ADJ
ma-99	214	39	mts	mts	NOUN
ma-99	214	40	distribution	distribution	NOUN
ma-99	214	41	and	and	CCONJ
ma-99	214	42	denoted	denote	VERB
ma-99	214	43	x	x	PUNCT
ma-99	214	44	∼	∼	NOUN
ma-99	214	45	stdmts(α	stdmts(α	NOUN
ma-99	214	46	,	,	PUNCT
ma-99	214	47	λ+	λ+	ADP
ma-99	214	48	,	,	PUNCT
ma-99	214	49	λ−).cgmy	λ−).cgmy	NUM
ma-99	214	50	process	process	NOUN
ma-99	214	51	proposed	propose	VERB
ma-99	214	52	in	in	ADP
ma-99	214	53	carr	carr	PROPN
ma-99	214	54	et	et	PROPN
ma-99	214	55	al	al	PROPN
ma-99	214	56	.	.	PUNCT
ma-99	215	1	[	[	X
ma-99	215	2	14	14	NUM
ma-99	215	3	]	]	PUNCT
ma-99	215	4	is	be	AUX
ma-99	215	5	a	a	DET
ma-99	215	6	tempered	temper	VERB
ma-99	215	7	stable	stable	ADJ
ma-99	215	8	process	process	NOUN
ma-99	215	9	.	.	PUNCT
ma-99	216	1	in	in	ADP
ma-99	216	2	order	order	NOUN
ma-99	216	3	to	to	PART
ma-99	216	4	obtain	obtain	VERB
ma-99	216	5	aclosed	aclose	VERB
ma-99	216	6	form	form	NOUN
ma-99	216	7	solution	solution	NOUN
ma-99	216	8	of	of	ADP
ma-99	216	9	the	the	DET
ma-99	216	10	european	european	ADJ
ma-99	216	11	option	option	NOUN
ma-99	216	12	price	price	NOUN
ma-99	216	13	,	,	PUNCT
ma-99	216	14	cgmy	cgmy	NOUN
ma-99	216	15	used	use	VERB
ma-99	216	16	the	the	DET
ma-99	216	17	generalised	generalise	VERB
ma-99	216	18	fourier	fourier	NOUN
ma-99	216	19	transformof	transformof	ADP
ma-99	216	20	the	the	DET
ma-99	216	21	distribution	distribution	NOUN
ma-99	216	22	of	of	ADP
ma-99	216	23	the	the	DET
ma-99	216	24	stock	stock	NOUN
ma-99	216	25	price	price	NOUN
ma-99	216	26	under	under	ADP
ma-99	216	27	the	the	DET
ma-99	216	28	assumption	assumption	NOUN
ma-99	216	29	of	of	ADP
ma-99	216	30	markov	markov	NOUN
ma-99	216	31	property.the	property.the	DET
ma-99	216	32	stochastic	stochastic	ADJ
ma-99	216	33	volatility	volatility	NOUN
ma-99	216	34	model	model	NOUN
ma-99	216	35	is	be	AUX
ma-99	216	36	given	give	VERB
ma-99	216	37	by	by	ADP
ma-99	216	38	d	d	PROPN
ma-99	216	39	yt	yt	NOUN
ma-99	216	40	=	=	SYM
ma-99	216	41	(	(	PUNCT
ma-99	216	42	µ+	µ+	X
ma-99	216	43	βxt	βxt	NOUN
ma-99	216	44	)	)	PUNCT
ma-99	216	45	dt	dt	NOUN
ma-99	217	1	+	+	CCONJ
ma-99	217	2	√	√	PROPN
ma-99	217	3	xt	xt	ADP
ma-99	218	1	dwt	dwt	PROPN
ma-99	219	1	+	+	CCONJ
ma-99	219	2	ρ	ρ	PROPN
ma-99	219	3	dzt	dzt	NOUN
ma-99	219	4	dxt	dxt	NOUN
ma-99	219	5	=	=	PUNCT
ma-99	219	6	−θ	−θ	PROPN
ma-99	219	7	xt	xt	PUNCT
ma-99	220	1	dt	dt	X
ma-99	221	1	+	+	CCONJ
ma-99	221	2	dztwhere	dztwhere	X
ma-99	221	3	µ	µ	X
ma-99	221	4	is	be	AUX
ma-99	221	5	the	the	DET
ma-99	221	6	drift	drift	NOUN
ma-99	221	7	parameter	parameter	NOUN
ma-99	221	8	,	,	PUNCT
ma-99	221	9	β	β	X
ma-99	221	10	is	be	AUX
ma-99	221	11	the	the	DET
ma-99	221	12	risk	risk	NOUN
ma-99	221	13	premium	premium	NOUN
ma-99	221	14	,	,	PUNCT
ma-99	221	15	θ	θ	X
ma-99	221	16	>	>	X
ma-99	221	17	0	0	PUNCT
ma-99	221	18	is	be	AUX
ma-99	221	19	the	the	DET
ma-99	221	20	drift	drift	NOUN
ma-99	221	21	of	of	ADP
ma-99	221	22	the	the	DET
ma-99	221	23	volatility	volatility	NOUN
ma-99	221	24	and	and	CCONJ
ma-99	221	25	zt	zt	PROPN
ma-99	221	26	isa	isa	PROPN
ma-99	221	27	mts	mts	NOUN
ma-99	221	28	process	process	NOUN
ma-99	221	29	.	.	PUNCT
ma-99	222	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	222	2	eur	eur	PROPN
ma-99	222	3	.	.	PUNCT
ma-99	223	1	j.	j.	PROPN
ma-99	223	2	math	math	PROPN
ma-99	223	3	.	.	PUNCT
ma-99	224	1	anal	anal	PROPN
ma-99	224	2	.	.	PUNCT
ma-99	225	1	10.28924	10.28924	NUM
ma-99	225	2	/	/	SYM
ma-99	225	3	ada	ada	PROPN
ma-99	225	4	/	/	SYM
ma-99	225	5	ma.3.4	ma.3.4	PROPN
ma-99	225	6	10we	10we	NOUN
ma-99	225	7	estimate	estimate	VERB
ma-99	225	8	θ	θ	PROPN
ma-99	225	9	from	from	ADP
ma-99	225	10	the	the	DET
ma-99	225	11	observations	observation	NOUN
ma-99	225	12	of	of	ADP
ma-99	225	13	{	{	PUNCT
ma-99	225	14	yt	yt	NOUN
ma-99	225	15	}	}	PUNCT
ma-99	225	16	at	at	ADP
ma-99	225	17	the	the	DET
ma-99	225	18	time	time	NOUN
ma-99	225	19	points	point	NOUN
ma-99	225	20	tk	tk	PROPN
ma-99	225	21	=	=	SYM
ma-99	225	22	k∆	k∆	PROPN
ma-99	225	23	,	,	PUNCT
ma-99	225	24	k	k	PROPN
ma-99	225	25	=	=	SYM
ma-99	225	26	0	0	NUM
ma-99	225	27	,	,	PUNCT
ma-99	225	28	1	1	NUM
ma-99	225	29	,	,	PUNCT
ma-99	225	30	2	2	NUM
ma-99	225	31	,	,	PUNCT
ma-99	225	32	.	.	PUNCT
ma-99	225	33	.	.	PUNCT
ma-99	226	1	.	.	PUNCT
ma-99	227	1	,	,	PUNCT
ma-99	227	2	n	n	CCONJ
ma-99	227	3	,	,	PUNCT
ma-99	227	4	∆	∆	PROPN
ma-99	227	5	>	>	X
ma-99	227	6	0	0	X
ma-99	227	7	.	.	PUNCT
ma-99	228	1	cm(z	cm(z	PUNCT
ma-99	228	2	)	)	PUNCT
ma-99	229	1	:	:	PUNCT
ma-99	229	2	=	=	PUNCT
ma-99	229	3	dm	dm	PRON
ma-99	229	4	dum	dum	NOUN
ma-99	229	5	logφts(u)|u=0for	logφts(u)|u=0for	ADP
ma-99	229	6	the	the	DET
ma-99	229	7	tempered	temper	VERB
ma-99	229	8	stable	stable	ADJ
ma-99	229	9	distribution	distribution	NOUN
ma-99	229	10	ts(b	ts(b	PUNCT
ma-99	229	11	,	,	PUNCT
ma-99	229	12	δ	δ	PROPN
ma-99	229	13	,	,	PUNCT
ma-99	229	14	γ	γ	PROPN
ma-99	229	15	)	)	PUNCT
ma-99	229	16	where	where	SCONJ
ma-99	229	17	0	0	NUM
ma-99	229	18	<	<	X
ma-99	229	19	b	b	X
ma-99	229	20	<	<	X
ma-99	229	21	1	1	NUM
ma-99	229	22	,	,	PUNCT
ma-99	229	23	δ	δ	PROPN
ma-99	229	24	>	>	X
ma-99	229	25	0	0	PROPN
ma-99	229	26	,	,	PUNCT
ma-99	229	27	γ	γ	X
ma-99	229	28	≥	≥	NUM
ma-99	229	29	0	0	NUM
ma-99	229	30	,	,	PUNCT
ma-99	229	31	the	the	DET
ma-99	229	32	m	m	PROPN
ma-99	229	33	-	-	PUNCT
ma-99	229	34	th	th	VERB
ma-99	229	35	cumulantis	cumulantis	NOUN
ma-99	229	36	given	give	VERB
ma-99	229	37	by	by	ADP
ma-99	229	38	cm(z	cm(z	NOUN
ma-99	229	39	)	)	PUNCT
ma-99	229	40	=	=	PUNCT
ma-99	230	1	−δ(−2)mγ(b−m)/bb(b	−δ(−2)mγ(b−m)/bb(b	ADP
ma-99	230	2	−	−	NOUN
ma-99	230	3	1	1	NUM
ma-99	230	4	)	)	PUNCT
ma-99	230	5	.	.	PUNCT
ma-99	230	6	.	.	PUNCT
ma-99	230	7	.	.	PUNCT
ma-99	231	1	(	(	PUNCT
ma-99	231	2	b	b	X
ma-99	231	3	−	−	PROPN
ma-99	231	4	(	(	PUNCT
ma-99	231	5	m	m	NOUN
ma-99	231	6	−	−	PROPN
ma-99	231	7	1))for	1))for	NUM
ma-99	231	8	γ	γ	X
ma-99	231	9	>	>	X
ma-99	231	10	0	0	PROPN
ma-99	231	11	.	.	PUNCT
ma-99	232	1	when	when	SCONJ
ma-99	232	2	γ	γ	X
ma-99	232	3	=	=	SYM
ma-99	232	4	0	0	NUM
ma-99	232	5	,	,	PUNCT
ma-99	232	6	it	it	PRON
ma-99	232	7	is	be	AUX
ma-99	232	8	positive	positive	ADJ
ma-99	232	9	b	b	ADJ
ma-99	232	10	-	-	PUNCT
ma-99	232	11	stable	stable	ADJ
ma-99	232	12	distribution	distribution	NOUN
ma-99	232	13	for	for	ADP
ma-99	232	14	which	which	PRON
ma-99	232	15	the	the	DET
ma-99	232	16	moments	moment	NOUN
ma-99	232	17	of	of	ADP
ma-99	232	18	only	only	ADJ
ma-99	232	19	order	order	NOUN
ma-99	232	20	k	k	X
ma-99	232	21	<	<	X
ma-99	232	22	b	b	X
ma-99	232	23	exist	exist	VERB
ma-99	232	24	.	.	PUNCT
ma-99	233	1	for	for	ADP
ma-99	233	2	b	b	NOUN
ma-99	233	3	=	=	SYM
ma-99	233	4	1/2	1/2	NUM
ma-99	233	5	,	,	PUNCT
ma-99	233	6	ts	ts	ADP
ma-99	233	7	distribution	distribution	NOUN
ma-99	233	8	reduces	reduce	VERB
ma-99	233	9	to	to	PART
ma-99	233	10	inverse	inverse	NOUN
ma-99	233	11	gaussian	gaussian	NOUN
ma-99	233	12	(	(	PUNCT
ma-99	233	13	ig	ig	PROPN
ma-99	233	14	)	)	PUNCT
ma-99	233	15	distribution.the	distribution.the	DET
ma-99	233	16	infinite	infinite	ADJ
ma-99	233	17	divisibility	divisibility	NOUN
ma-99	233	18	of	of	ADP
ma-99	233	19	this	this	DET
ma-99	233	20	distribution	distribution	NOUN
ma-99	233	21	allows	allow	VERB
ma-99	233	22	one	one	NUM
ma-99	233	23	to	to	PART
ma-99	233	24	construct	construct	VERB
ma-99	233	25	the	the	DET
ma-99	233	26	corresponding	correspond	VERB
ma-99	233	27	levy	levy	NOUN
ma-99	233	28	process.a	process.a	NOUN
ma-99	233	29	levy	levy	NOUN
ma-99	233	30	process	process	NOUN
ma-99	233	31	z	z	NOUN
ma-99	233	32	=	=	PUNCT
ma-99	233	33	(	(	PUNCT
ma-99	233	34	zt)t≥0	zt)t≥0	PROPN
ma-99	233	35	is	be	AUX
ma-99	233	36	said	say	VERB
ma-99	233	37	to	to	PART
ma-99	233	38	be	be	AUX
ma-99	233	39	a	a	DET
ma-99	233	40	tempered	temper	VERB
ma-99	233	41	stable	stable	ADJ
ma-99	233	42	process	process	NOUN
ma-99	233	43	if	if	SCONJ
ma-99	233	44	z1	z1	PROPN
ma-99	233	45	follows	follow	VERB
ma-99	233	46	a	a	DET
ma-99	233	47	temperedstable	temperedstable	ADJ
ma-99	233	48	distribution	distribution	NOUN
ma-99	233	49	.	.	PUNCT
ma-99	234	1	the	the	DET
ma-99	234	2	tempered	temper	VERB
ma-99	234	3	stable	stable	ADJ
ma-99	234	4	process	process	NOUN
ma-99	234	5	is	be	AUX
ma-99	234	6	of	of	ADP
ma-99	234	7	finite	finite	ADJ
ma-99	234	8	activity	activity	NOUN
ma-99	234	9	if	if	SCONJ
ma-99	234	10	α	α	PRON
ma-99	234	11	<	<	X
ma-99	234	12	0	0	NUM
ma-99	234	13	and	and	CCONJ
ma-99	234	14	infinite	infinite	ADJ
ma-99	234	15	activity	activity	NOUN
ma-99	234	16	if	if	SCONJ
ma-99	234	17	0	0	NUM
ma-99	234	18	<	<	X
ma-99	234	19	α	α	X
ma-99	234	20	<	<	X
ma-99	234	21	2	2	NUM
ma-99	234	22	.	.	PUNCT
ma-99	235	1	the	the	DET
ma-99	235	2	tempered	temper	VERB
ma-99	235	3	stable	stable	ADJ
ma-99	235	4	process	process	NOUN
ma-99	235	5	is	be	AUX
ma-99	235	6	of	of	ADP
ma-99	235	7	finite	finite	ADJ
ma-99	235	8	variation	variation	NOUN
ma-99	235	9	if	if	SCONJ
ma-99	235	10	0	0	NUM
ma-99	235	11	<	<	X
ma-99	235	12	α	α	X
ma-99	235	13	<	<	X
ma-99	235	14	1	1	NUM
ma-99	235	15	and	and	CCONJ
ma-99	235	16	infinite	infinite	ADJ
ma-99	235	17	variation	variation	NOUN
ma-99	235	18	if	if	SCONJ
ma-99	235	19	1	1	NUM
ma-99	235	20	<	<	X
ma-99	235	21	α	α	X
ma-99	235	22	<	<	X
ma-99	235	23	2.the	2.the	DET
ma-99	235	24	mts	mts	PROPN
ma-99	235	25	-	-	PUNCT
ma-99	235	26	garch	garch	NOUN
ma-99	235	27	model	model	NOUN
ma-99	235	28	is	be	AUX
ma-99	235	29	given	give	VERB
ma-99	235	30	by	by	ADP
ma-99	235	31	log	log	PROPN
ma-99	235	32	st	st	PROPN
ma-99	235	33	st−1	st−1	PROPN
ma-99	235	34	=	=	PROPN
ma-99	235	35	rt	rt	PROPN
ma-99	236	1	−	−	PROPN
ma-99	236	2	dt	dt	X
ma-99	236	3	+	+	CCONJ
ma-99	236	4	λtσt	λtσt	NOUN
ma-99	236	5	−	−	PROPN
ma-99	236	6	g(σt	g(σt	PROPN
ma-99	236	7	;	;	PUNCT
ma-99	236	8	α	α	PROPN
ma-99	236	9	,	,	PUNCT
ma-99	236	10	λ+	λ+	ADP
ma-99	236	11	,	,	PUNCT
ma-99	236	12	λ−	λ−	PROPN
ma-99	236	13	)	)	PUNCT
ma-99	237	1	+	+	NUM
ma-99	237	2	σtεt	σtεt	PROPN
ma-99	237	3	σ2	σ2	PROPN
ma-99	237	4	t	t	PROPN
ma-99	237	5	=	=	PUNCT
ma-99	237	6	(	(	PUNCT
ma-99	237	7	α0	α0	ADJ
ma-99	237	8	+	+	NUM
ma-99	237	9	α1σ	α1σ	NOUN
ma-99	237	10	2	2	NUM
ma-99	237	11	t−1ε	t−1ε	VERB
ma-99	237	12	2	2	NUM
ma-99	237	13	t−1	t−1	NOUN
ma-99	237	14	+	+	CCONJ
ma-99	237	15	β1σ	β1σ	SYM
ma-99	237	16	2	2	NUM
ma-99	237	17	t−1	t−1	NOUN
ma-99	237	18	)	)	PUNCT
ma-99	237	19	∧	∧	PROPN
ma-99	237	20	ρ	ρ	PROPN
ma-99	237	21	,	,	PUNCT
ma-99	237	22	ε0	ε0	NOUN
ma-99	237	23	=	=	SYM
ma-99	237	24	0	0	NUM
ma-99	238	1	α0	α0	ADJ
ma-99	238	2	,	,	PUNCT
ma-99	238	3	α1	α1	PROPN
ma-99	238	4	,	,	PUNCT
ma-99	238	5	β1	β1	PROPN
ma-99	238	6	≥	≥	NUM
ma-99	238	7	0	0	NUM
ma-99	238	8	,	,	PUNCT
ma-99	238	9	α1	α1	PROPN
ma-99	238	10	+	+	CCONJ
ma-99	238	11	β1	β1	PROPN
ma-99	238	12	<	<	X
ma-99	238	13	1	1	NUM
ma-99	238	14	,	,	PUNCT
ma-99	238	15	0	0	NUM
ma-99	238	16	<	<	X
ma-99	238	17	ρ	ρ	X
ma-99	238	18	<	<	X
ma-99	238	19	λ2	λ2	NOUN
ma-99	239	1	+	+	PROPN
ma-99	239	2	,	,	PUNCT
ma-99	239	3	εt	εt	PROPN
ma-99	239	4	∼	∼	NOUN
ma-99	239	5	stdmts(α	stdmts(α	PROPN
ma-99	239	6	,	,	PUNCT
ma-99	239	7	λ+	λ+	ADP
ma-99	239	8	,	,	PUNCT
ma-99	239	9	λ−	λ−	PROPN
ma-99	239	10	)	)	PUNCT
ma-99	239	11	,	,	PUNCT
ma-99	239	12	rt	rt	PROPN
ma-99	239	13	is	be	AUX
ma-99	239	14	the	the	DET
ma-99	239	15	risk	risk	NOUN
ma-99	239	16	-	-	PUNCT
ma-99	239	17	free	free	ADJ
ma-99	239	18	rate	rate	NOUN
ma-99	239	19	,	,	PUNCT
ma-99	239	20	dtis	dtis	NOUN
ma-99	239	21	the	the	DET
ma-99	239	22	dividend	dividend	NOUN
ma-99	239	23	rate	rate	NOUN
ma-99	239	24	,	,	PUNCT
ma-99	239	25	λt	λt	X
ma-99	239	26	is	be	AUX
ma-99	239	27	the	the	DET
ma-99	239	28	market	market	NOUN
ma-99	239	29	price	price	NOUN
ma-99	239	30	of	of	ADP
ma-99	239	31	risk	risk	NOUN
ma-99	239	32	,	,	PUNCT
ma-99	239	33	g	g	PROPN
ma-99	239	34	is	be	AUX
ma-99	239	35	the	the	DET
ma-99	239	36	characteristic	characteristic	ADJ
ma-99	239	37	exponent	exponent	NOUN
ma-99	239	38	of	of	ADP
ma-99	239	39	the	the	DET
ma-99	239	40	laplacetransform	laplacetransform	NOUN
ma-99	239	41	for	for	ADP
ma-99	239	42	the	the	DET
ma-99	239	43	distribution	distribution	NOUN
ma-99	239	44	stdmts(α	stdmts(α	NOUN
ma-99	239	45	,	,	PUNCT
ma-99	239	46	λ+	λ+	ADP
ma-99	239	47	,	,	PUNCT
ma-99	239	48	λ−	λ−	PROPN
ma-99	239	49	)	)	PUNCT
ma-99	239	50	,	,	PUNCT
ma-99	239	51	i.e.	i.e.	X
ma-99	239	52	,	,	PUNCT
ma-99	239	53	g(x	g(x	NOUN
ma-99	239	54	;	;	PUNCT
ma-99	239	55	α	α	NOUN
ma-99	239	56	,	,	PUNCT
ma-99	239	57	λ+	λ+	ADP
ma-99	239	58	,	,	PUNCT
ma-99	239	59	λ−	λ−	PROPN
ma-99	239	60	)	)	PUNCT
ma-99	239	61	=	=	PUNCT
ma-99	240	1	log(e(exp(xεt)).the	log(e(exp(xεt)).the	DET
ma-99	240	2	characteristic	characteristic	ADJ
ma-99	240	3	function	function	NOUN
ma-99	240	4	of	of	ADP
ma-99	240	5	z	z	PROPN
ma-99	240	6	is	be	AUX
ma-99	240	7	given	give	VERB
ma-99	240	8	by	by	ADP
ma-99	240	9	φz(u	φz(u	NOUN
ma-99	240	10	)	)	PUNCT
ma-99	240	11	=	=	SYM
ma-99	240	12	exp(iuµ+	exp(iuµ+	PROPN
ma-99	240	13	gr(u;α	gr(u;α	PROPN
ma-99	240	14	,	,	PUNCT
ma-99	240	15	c	c	NOUN
ma-99	240	16	,	,	PUNCT
ma-99	240	17	λ+	λ+	ADP
ma-99	240	18	,	,	PUNCT
ma-99	240	19	λ−	λ−	PROPN
ma-99	240	20	)	)	PUNCT
ma-99	241	1	+	+	CCONJ
ma-99	241	2	gi(u;α	gi(u;α	ADJ
ma-99	241	3	,	,	PUNCT
ma-99	241	4	c	c	NOUN
ma-99	241	5	,	,	PUNCT
ma-99	241	6	λ+	λ+	ADP
ma-99	241	7	,	,	PUNCT
ma-99	241	8	λ−	λ−	PROPN
ma-99	241	9	)	)	PUNCT
ma-99	241	10	)	)	PUNCT
ma-99	242	1	where	where	SCONJ
ma-99	242	2	for	for	ADP
ma-99	242	3	u	u	PROPN
ma-99	242	4	∈	∈	PROPN
ma-99	242	5	r	r	PROPN
ma-99	242	6	,	,	PUNCT
ma-99	242	7	gr(u;α	gr(u;α	PROPN
ma-99	242	8	,	,	PUNCT
ma-99	242	9	c	c	NOUN
ma-99	242	10	,	,	PUNCT
ma-99	242	11	λ+	λ+	ADP
ma-99	242	12	,	,	PUNCT
ma-99	242	13	λ−	λ−	PROPN
ma-99	242	14	)	)	PUNCT
ma-99	242	15	=	=	PUNCT
ma-99	242	16	2−	2−	NUM
ma-99	242	17	α+3	α+3	NUM
ma-99	242	18	2	2	NUM
ma-99	242	19	√	√	NOUN
ma-99	242	20	πcγ	πcγ	NOUN
ma-99	242	21	(	(	PUNCT
ma-99	242	22	1−	1−	NUM
ma-99	242	23	α	α	NOUN
ma-99	242	24	2	2	NUM
ma-99	242	25	)	)	PUNCT
ma-99	242	26	[	[	PUNCT
ma-99	242	27	(	(	PUNCT
ma-99	242	28	λ2	λ2	NOUN
ma-99	242	29	+	+	CCONJ
ma-99	242	30	+	+	NUM
ma-99	242	31	u2	u2	NOUN
ma-99	242	32	)	)	PUNCT
ma-99	242	33	α	α	NOUN
ma-99	242	34	2	2	NUM
ma-99	242	35	−	−	NOUN
ma-99	242	36	λα+	λα+	NOUN
ma-99	242	37	+	+	CCONJ
ma-99	242	38	(	(	PUNCT
ma-99	242	39	λ2	λ2	NOUN
ma-99	242	40	−	−	PROPN
ma-99	242	41	+	+	CCONJ
ma-99	242	42	u2	u2	NOUN
ma-99	242	43	)	)	PUNCT
ma-99	242	44	α	α	NOUN
ma-99	242	45	2	2	NUM
ma-99	242	46	−	−	PROPN
ma-99	242	47	λα−	λα−	SYM
ma-99	242	48	]	]	PUNCT
ma-99	242	49	,	,	PUNCT
ma-99	242	50	gi(u;α	gi(u;α	PROPN
ma-99	242	51	,	,	PUNCT
ma-99	242	52	c	c	NOUN
ma-99	242	53	,	,	PUNCT
ma-99	242	54	λ+	λ+	ADP
ma-99	242	55	,	,	PUNCT
ma-99	242	56	λ−	λ−	PROPN
ma-99	242	57	)	)	PUNCT
ma-99	242	58	=	=	VERB
ma-99	242	59	iuc2−	iuc2−	VERB
ma-99	242	60	α+1	α+1	SYM
ma-99	242	61	2	2	NUM
ma-99	242	62	γ	γ	X
ma-99	242	63	(	(	PUNCT
ma-99	242	64	1−	1−	NUM
ma-99	242	65	α	α	NOUN
ma-99	242	66	2	2	NUM
ma-99	242	67	)	)	PUNCT
ma-99	242	68	[	[	PUNCT
ma-99	243	1	λα−1	λα−1	PROPN
ma-99	243	2	+	+	CCONJ
ma-99	243	3	f	f	X
ma-99	243	4	(	(	PUNCT
ma-99	243	5	1	1	NUM
ma-99	243	6	,	,	PUNCT
ma-99	243	7	1−	1−	NUM
ma-99	243	8	α	α	NOUN
ma-99	243	9	2	2	NUM
ma-99	243	10	;	;	PUNCT
ma-99	243	11	3	3	NUM
ma-99	243	12	2	2	NUM
ma-99	243	13	,	,	PUNCT
ma-99	243	14	;	;	PUNCT
ma-99	243	15	−	−	PROPN
ma-99	243	16	u2	u2	PROPN
ma-99	243	17	λ2	λ2	PROPN
ma-99	243	18	+	+	CCONJ
ma-99	243	19	)	)	PUNCT
ma-99	243	20	−	−	PROPN
ma-99	244	1	λα−1	λα−1	INTJ
ma-99	244	2	−	−	PROPN
ma-99	244	3	f	f	NOUN
ma-99	244	4	(	(	PUNCT
ma-99	244	5	1	1	NUM
ma-99	244	6	,	,	PUNCT
ma-99	244	7	1−	1−	NUM
ma-99	244	8	α	α	NOUN
ma-99	244	9	2	2	NUM
ma-99	244	10	;	;	PUNCT
ma-99	244	11	3	3	NUM
ma-99	244	12	2	2	NUM
ma-99	244	13	,	,	PUNCT
ma-99	244	14	;	;	PUNCT
ma-99	244	15	−	−	PROPN
ma-99	244	16	u2	u2	PROPN
ma-99	244	17	λ2	λ2	PROPN
ma-99	244	18	−	−	PROPN
ma-99	244	19	)	)	PUNCT
ma-99	244	20	]	]	PUNCT
ma-99	244	21	where	where	SCONJ
ma-99	244	22	f	f	PROPN
ma-99	244	23	is	be	AUX
ma-99	244	24	the	the	DET
ma-99	244	25	hyper	hyper	ADJ
ma-99	244	26	-	-	ADJ
ma-99	244	27	geometric	geometric	ADJ
ma-99	244	28	function	function	NOUN
ma-99	244	29	.	.	PUNCT
ma-99	245	1	the	the	DET
ma-99	245	2	value	value	NOUN
ma-99	245	3	of	of	ADP
ma-99	245	4	gi	gi	NOUN
ma-99	245	5	for	for	ADP
ma-99	245	6	symmetric	symmetric	ADJ
ma-99	245	7	mts	mts	NOUN
ma-99	245	8	distribution	distribution	NOUN
ma-99	245	9	is	be	AUX
ma-99	245	10	alwayszero.the	alwayszero.the	DET
ma-99	245	11	m	m	PROPN
ma-99	245	12	-	-	PUNCT
ma-99	245	13	th	th	VERB
ma-99	245	14	cumulant	cumulant	NOUN
ma-99	245	15	is	be	AUX
ma-99	245	16	given	give	VERB
ma-99	245	17	by	by	ADP
ma-99	245	18	cm(z	cm(z	NOUN
ma-99	245	19	)	)	PUNCT
ma-99	245	20	=	=	SYM
ma-99	246	1	µ	µ	NOUN
ma-99	246	2	if	if	SCONJ
ma-99	246	3	m	m	VERB
ma-99	246	4	=	=	SYM
ma-99	246	5	1	1	NUM
ma-99	246	6	,	,	PUNCT
ma-99	246	7	cm(z	cm(z	X
ma-99	246	8	)	)	PUNCT
ma-99	246	9	=	=	SYM
ma-99	247	1	2m−	2m−	NUM
ma-99	247	2	α+3	α+3	ADP
ma-99	247	3	2	2	NUM
ma-99	247	4	(	(	PUNCT
ma-99	247	5	m	m	NOUN
ma-99	247	6	−	−	NUM
ma-99	247	7	1	1	NUM
ma-99	247	8	2	2	NUM
ma-99	247	9	)	)	PUNCT
ma-99	247	10	!	!	PUNCT
ma-99	248	1	cγ	cγ	INTJ
ma-99	248	2	(	(	PUNCT
ma-99	248	3	m	m	VERB
ma-99	248	4	−	−	NOUN
ma-99	248	5	α	α	NOUN
ma-99	248	6	2	2	NUM
ma-99	248	7	)	)	PUNCT
ma-99	248	8	(	(	PUNCT
ma-99	248	9	λα−m+	λα−m+	X
ma-99	248	10	−	−	PROPN
ma-99	248	11	λα−m−	λα−m−	NOUN
ma-99	248	12	)	)	PUNCT
ma-99	249	1	i	i	PRON
ma-99	249	2	f	f	X
ma-99	249	3	m	m	VERB
ma-99	249	4	=	=	NOUN
ma-99	249	5	3	3	NUM
ma-99	249	6	,	,	PUNCT
ma-99	249	7	5	5	NUM
ma-99	249	8	,	,	PUNCT
ma-99	249	9	7	7	NUM
ma-99	249	10	,	,	PUNCT
ma-99	249	11	.	.	PUNCT
ma-99	249	12	.	.	PUNCT
ma-99	249	13	.	.	PUNCT
ma-99	250	1	cm(z	cm(z	PUNCT
ma-99	250	2	)	)	PUNCT
ma-99	251	1	=	=	PUNCT
ma-99	251	2	2−	2−	NUM
ma-99	252	1	α+3	α+3	NUM
ma-99	252	2	2	2	NUM
ma-99	252	3	√	√	PROPN
ma-99	252	4	π	π	PROPN
ma-99	252	5	(	(	PUNCT
ma-99	252	6	m	m	PROPN
ma-99	252	7	!	!	PUNCT
ma-99	252	8	m	m	VERB
ma-99	252	9	2	2	NUM
ma-99	252	10	!	!	PUNCT
ma-99	252	11	)	)	PUNCT
ma-99	253	1	cγ	cγ	NOUN
ma-99	253	2	(	(	PUNCT
ma-99	253	3	m	m	VERB
ma-99	253	4	−	−	NOUN
ma-99	253	5	α	α	NOUN
ma-99	253	6	2	2	NUM
ma-99	253	7	)	)	PUNCT
ma-99	253	8	(	(	PUNCT
ma-99	253	9	λα−m+	λα−m+	X
ma-99	253	10	+	+	CCONJ
ma-99	253	11	λα−m−	λα−m−	NOUN
ma-99	253	12	)	)	PUNCT
ma-99	254	1	i	i	PRON
ma-99	254	2	f	f	VERB
ma-99	254	3	m	m	VERB
ma-99	254	4	=	=	ADJ
ma-99	254	5	2	2	NUM
ma-99	254	6	,	,	PUNCT
ma-99	254	7	4	4	NUM
ma-99	254	8	,	,	PUNCT
ma-99	254	9	6	6	NUM
ma-99	254	10	,	,	PUNCT
ma-99	254	11	.	.	PUNCT
ma-99	254	12	.	.	PUNCT
ma-99	254	13	.	.	PUNCT
ma-99	255	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	255	2	eur	eur	PROPN
ma-99	255	3	.	.	PUNCT
ma-99	256	1	j.	j.	PROPN
ma-99	256	2	math	math	PROPN
ma-99	256	3	.	.	PUNCT
ma-99	257	1	anal	anal	PROPN
ma-99	257	2	.	.	PUNCT
ma-99	258	1	10.28924	10.28924	NUM
ma-99	258	2	/	/	SYM
ma-99	258	3	ada	ada	PROPN
ma-99	258	4	/	/	SYM
ma-99	258	5	ma.3.4	ma.3.4	PROPN
ma-99	258	6	11the	11the	NOUN
ma-99	258	7	mean	mean	VERB
ma-99	258	8	,	,	PUNCT
ma-99	258	9	variance	variance	NOUN
ma-99	258	10	,	,	PUNCT
ma-99	258	11	skewness	skewness	NOUN
ma-99	258	12	and	and	CCONJ
ma-99	258	13	excess	excess	ADJ
ma-99	258	14	kurtosis	kurtosis	NOUN
ma-99	258	15	are	be	AUX
ma-99	258	16	given	give	VERB
ma-99	258	17	by	by	ADP
ma-99	258	18	e(z	e(z	PROPN
ma-99	258	19	)	)	PUNCT
ma-99	258	20	=	=	PUNCT
ma-99	259	1	c1(z	c1(z	PROPN
ma-99	259	2	)	)	PUNCT
ma-99	259	3	=	=	NOUN
ma-99	259	4	µ+	µ+	PUNCT
ma-99	259	5	2−	2−	NUM
ma-99	259	6	α+1	α+1	NUM
ma-99	259	7	2	2	NUM
ma-99	259	8	cγ	cγ	NOUN
ma-99	259	9	(	(	PUNCT
ma-99	259	10	1−	1−	NUM
ma-99	259	11	α	α	NOUN
ma-99	259	12	2	2	NUM
ma-99	259	13	)	)	PUNCT
ma-99	259	14	(	(	PUNCT
ma-99	259	15	λα−1	λα−1	PROPN
ma-99	259	16	+	+	CCONJ
ma-99	259	17	−	−	PROPN
ma-99	259	18	λα−1	λα−1	PROPN
ma-99	259	19	−	−	PROPN
ma-99	259	20	)	)	PUNCT
ma-99	259	21	,	,	PUNCT
ma-99	259	22	v	v	X
ma-99	259	23	(	(	PUNCT
ma-99	259	24	z	z	NOUN
ma-99	259	25	)	)	PUNCT
ma-99	259	26	=	=	SYM
ma-99	259	27	c2(z	c2(z	NOUN
ma-99	259	28	)	)	PUNCT
ma-99	259	29	=	=	PUNCT
ma-99	259	30	2−	2−	NUM
ma-99	259	31	α+1	α+1	NUM
ma-99	259	32	2	2	NUM
ma-99	259	33	√	√	NUM
ma-99	259	34	πcγ	πcγ	NOUN
ma-99	259	35	(	(	PUNCT
ma-99	259	36	1−	1−	NUM
ma-99	259	37	α	α	NOUN
ma-99	259	38	2	2	NUM
ma-99	259	39	)	)	PUNCT
ma-99	259	40	(	(	PUNCT
ma-99	259	41	λα−2	λα−2	VERB
ma-99	259	42	+	+	CCONJ
ma-99	259	43	+	+	CCONJ
ma-99	259	44	λα−2	λα−2	NOUN
ma-99	259	45	−	−	PROPN
ma-99	259	46	)	)	PUNCT
ma-99	259	47	,	,	PUNCT
ma-99	259	48	s(z	s(z	PROPN
ma-99	259	49	)	)	PUNCT
ma-99	259	50	=	=	SYM
ma-99	260	1	c3(z	c3(z	X
ma-99	260	2	)	)	PUNCT
ma-99	260	3	c2(z)3/2	c2(z)3/2	PUNCT
ma-99	261	1	=	=	SYM
ma-99	261	2	2	2	NUM
ma-99	261	3	α+9	α+9	NUM
ma-99	261	4	4	4	NUM
ma-99	261	5	γ	γ	X
ma-99	261	6	(	(	PUNCT
ma-99	261	7	3−α	3−α	NUM
ma-99	261	8	2	2	NUM
ma-99	261	9	)	)	PUNCT
ma-99	261	10	(	(	PUNCT
ma-99	261	11	λα−3	λα−3	ADJ
ma-99	261	12	+	+	NOUN
ma-99	261	13	−	−	PROPN
ma-99	261	14	λα−3	λα−3	ADJ
ma-99	261	15	−	−	NOUN
ma-99	261	16	)	)	PUNCT
ma-99	261	17	π3/4c1/2(γ	π3/4c1/2(γ	PROPN
ma-99	261	18	(	(	PUNCT
ma-99	261	19	1−α	1−α	NUM
ma-99	261	20	2	2	NUM
ma-99	261	21	)	)	PUNCT
ma-99	261	22	(	(	PUNCT
ma-99	261	23	λα−2	λα−2	VERB
ma-99	261	24	+	+	CCONJ
ma-99	261	25	+	+	CCONJ
ma-99	261	26	λα−2	λα−2	NOUN
ma-99	261	27	−	−	PROPN
ma-99	261	28	)	)	PUNCT
ma-99	261	29	)	)	PUNCT
ma-99	261	30	3/2	3/2	NUM
ma-99	261	31	,	,	PUNCT
ma-99	261	32	κ(z	κ(z	PROPN
ma-99	261	33	)	)	PUNCT
ma-99	261	34	=	=	SYM
ma-99	262	1	c4(z	c4(z	X
ma-99	262	2	)	)	PUNCT
ma-99	262	3	c2(z)2	c2(z)2	NOUN
ma-99	262	4	=	=	SYM
ma-99	262	5	3	3	NUM
ma-99	262	6	·	·	SYM
ma-99	262	7	2	2	NUM
ma-99	262	8	α+3	α+3	NUM
ma-99	262	9	2	2	NUM
ma-99	262	10	cγ	cγ	NOUN
ma-99	262	11	(	(	PUNCT
ma-99	262	12	2−	2−	NUM
ma-99	262	13	α	α	NOUN
ma-99	262	14	2	2	NUM
ma-99	262	15	)	)	PUNCT
ma-99	262	16	(	(	PUNCT
ma-99	262	17	λα−4	λα−4	X
ma-99	262	18	+	+	CCONJ
ma-99	262	19	+	+	CCONJ
ma-99	262	20	λα−4	λα−4	PROPN
ma-99	262	21	−	−	NOUN
ma-99	262	22	)	)	PUNCT
ma-99	262	23	√	√	PROPN
ma-99	262	24	πc(γ	πc(γ	PUNCT
ma-99	262	25	(	(	PUNCT
ma-99	262	26	1−α	1−α	NUM
ma-99	262	27	2	2	NUM
ma-99	262	28	)	)	PUNCT
ma-99	262	29	(	(	PUNCT
ma-99	262	30	λα−2	λα−2	VERB
ma-99	262	31	+	+	CCONJ
ma-99	262	32	+	+	CCONJ
ma-99	262	33	λα−2	λα−2	NOUN
ma-99	262	34	−	−	PROPN
ma-99	262	35	)	)	PUNCT
ma-99	262	36	)	)	PUNCT
ma-99	262	37	2	2	X
ma-99	262	38	.	.	PUNCT
ma-99	263	1	if	if	SCONJ
ma-99	263	2	α	α	PRON
ma-99	263	3	∈	∈	PROPN
ma-99	263	4	(	(	PUNCT
ma-99	263	5	0	0	NUM
ma-99	263	6	,	,	PUNCT
ma-99	263	7	2)\{1	2)\{1	NUM
ma-99	263	8	}	}	PUNCT
ma-99	263	9	,	,	PUNCT
ma-99	263	10	the	the	DET
ma-99	263	11	levy	levy	NOUN
ma-99	263	12	measure	measure	NOUN
ma-99	263	13	of	of	ADP
ma-99	263	14	α	α	NOUN
ma-99	263	15	-	-	ADJ
ma-99	263	16	stable	stable	ADJ
ma-99	263	17	,	,	PUNCT
ma-99	263	18	α	α	NOUN
ma-99	263	19	-	-	PUNCT
ma-99	263	20	ts	ts	NOUN
ma-99	263	21	and	and	CCONJ
ma-99	263	22	α	α	X
ma-99	263	23	-	-	PUNCT
ma-99	263	24	mts	mts	NOUN
ma-99	263	25	have	have	VERB
ma-99	263	26	the	the	DET
ma-99	263	27	same	same	ADJ
ma-99	263	28	asymptotic	asymptotic	ADJ
ma-99	263	29	behav	behav	NOUN
ma-99	263	30	-	-	PUNCT
ma-99	263	31	ior	ior	NOUN
ma-99	263	32	at	at	ADP
ma-99	263	33	the	the	DET
ma-99	263	34	zero	zero	NUM
ma-99	263	35	neighborhood	neighborhood	NOUN
ma-99	263	36	.	.	PUNCT
ma-99	264	1	however	however	ADV
ma-99	264	2	,	,	PUNCT
ma-99	264	3	the	the	DET
ma-99	264	4	tails	tail	NOUN
ma-99	264	5	of	of	ADP
ma-99	264	6	the	the	DET
ma-99	264	7	levy	levy	NOUN
ma-99	264	8	measures	measure	NOUN
ma-99	264	9	for	for	ADP
ma-99	264	10	the	the	DET
ma-99	264	11	α	α	NOUN
ma-99	264	12	-	-	PUNCT
ma-99	264	13	mts	mts	NOUN
ma-99	264	14	distributionare	distributionare	NOUN
ma-99	264	15	thinner	thin	ADJ
ma-99	264	16	than	than	ADP
ma-99	264	17	those	those	PRON
ma-99	264	18	of	of	ADP
ma-99	264	19	α	α	NOUN
ma-99	264	20	-	-	ADJ
ma-99	264	21	stable	stable	ADJ
ma-99	264	22	and	and	CCONJ
ma-99	264	23	heavier	heavy	ADJ
ma-99	264	24	than	than	ADP
ma-99	264	25	those	those	PRON
ma-99	264	26	of	of	ADP
ma-99	264	27	α	α	NOUN
ma-99	264	28	-	-	PUNCT
ma-99	264	29	ts	ts	ADP
ma-99	264	30	distribution.when	distribution.when	PROPN
ma-99	264	31	z	z	NOUN
ma-99	264	32	is	be	AUX
ma-99	264	33	a	a	DET
ma-99	264	34	ig	ig	PROPN
ma-99	264	35	process	process	NOUN
ma-99	264	36	,	,	PUNCT
ma-99	264	37	the	the	DET
ma-99	264	38	moment	moment	NOUN
ma-99	264	39	estimators	estimator	NOUN
ma-99	264	40	of	of	ADP
ma-99	264	41	ρ	ρ	PROPN
ma-99	264	42	and	and	CCONJ
ma-99	264	43	θ	θ	PROPN
ma-99	264	44	are	be	AUX
ma-99	264	45	given	give	VERB
ma-99	264	46	by	by	ADP
ma-99	264	47	θ̂n	θ̂n	ADP
ma-99	264	48	:	:	PUNCT
ma-99	264	49	=	=	SYM
ma-99	264	50	γȳ	γȳ	NOUN
ma-99	264	51	∆δρ̂n	∆δρ̂n	PROPN
ma-99	264	52	,	,	PUNCT
ma-99	264	53	ρ̂n	ρ̂n	NOUN
ma-99	264	54	:	:	PUNCT
ma-99	264	55	=	=	SYM
ma-99	264	56	γ(γs2	γ(γs2	ADJ
ma-99	264	57	y	y	PROPN
ma-99	264	58	−	−	PROPN
ma-99	264	59	∆δ	∆δ	PROPN
ma-99	264	60	)	)	PUNCT
ma-99	265	1	2ȳwhere	2ȳwhere	NUM
ma-99	265	2	ȳ	ȳ	NOUN
ma-99	265	3	:	:	PUNCT
ma-99	265	4	=	=	SYM
ma-99	265	5	1	1	NUM
ma-99	265	6	n	n	NUM
ma-99	265	7	n∑	n∑	PROPN
ma-99	265	8	j=1	j=1	PROPN
ma-99	265	9	yj	yj	PROPN
ma-99	265	10	,	,	PUNCT
ma-99	265	11	yj	yj	PROPN
ma-99	265	12	:	:	PUNCT
ma-99	265	13	=	=	SYM
ma-99	265	14	yj∆	yj∆	PROPN
ma-99	265	15	−	−	PROPN
ma-99	266	1	y(j−1)∆	y(j−1)∆	PROPN
ma-99	266	2	,	,	PUNCT
ma-99	266	3	s2	s2	VERB
ma-99	266	4	y	y	NOUN
ma-99	266	5	:	:	PUNCT
ma-99	266	6	=	=	SYM
ma-99	266	7	1	1	NUM
ma-99	266	8	n	n	NUM
ma-99	266	9	n∑	n∑	NOUN
ma-99	266	10	j=1	j=1	NOUN
ma-99	266	11	(	(	PUNCT
ma-99	266	12	yj	yj	PROPN
ma-99	266	13	−	−	PROPN
ma-99	266	14	ȳ)2	ȳ)2	PROPN
ma-99	266	15	=	=	SYM
ma-99	266	16	1	1	NUM
ma-99	266	17	n	n	NUM
ma-99	266	18	n∑	n∑	NOUN
ma-99	266	19	j=1	j=1	NOUN
ma-99	267	1	y2	y2	PROPN
ma-99	267	2	j	j	NOUN
ma-99	268	1	−	−	PROPN
ma-99	268	2	(	(	PUNCT
ma-99	268	3	ȳ)2	ȳ)2	PROPN
ma-99	268	4	.	.	PUNCT
ma-99	269	1	when	when	SCONJ
ma-99	269	2	z	z	NOUN
ma-99	269	3	is	be	AUX
ma-99	269	4	a	a	DET
ma-99	269	5	gamma	gamma	NOUN
ma-99	269	6	process	process	NOUN
ma-99	269	7	,	,	PUNCT
ma-99	269	8	the	the	DET
ma-99	269	9	moment	moment	NOUN
ma-99	269	10	estimators	estimator	NOUN
ma-99	269	11	are	be	AUX
ma-99	269	12	given	give	VERB
ma-99	269	13	by	by	ADP
ma-99	269	14	θ̂n	θ̂n	ADP
ma-99	269	15	:	:	PUNCT
ma-99	269	16	=	=	SYM
ma-99	269	17	1	1	NUM
ma-99	269	18	n2	n2	NOUN
ma-99	269	19	[	[	X
ma-99	269	20	∑n	∑n	PROPN
ma-99	269	21	i=1(yi∆	i=1(yi∆	NOUN
ma-99	269	22	−	−	PROPN
ma-99	269	23	y(i−1)∆	y(i−1)∆	NUM
ma-99	269	24	)	)	PUNCT
ma-99	269	25	]	]	PUNCT
ma-99	269	26	2	2	NUM
ma-99	269	27	1	1	NUM
ma-99	269	28	n2	n2	ADJ
ma-99	269	29	∑n	∑n	PROPN
ma-99	269	30	i=1(yi∆	i=1(yi∆	NOUN
ma-99	269	31	−	−	PROPN
ma-99	269	32	y(i−1)∆)2	y(i−1)∆)2	NOUN
ma-99	269	33	−	−	PROPN
ma-99	269	34	∆	∆	PROPN
ma-99	269	35	n	n	CCONJ
ma-99	269	36	[	[	X
ma-99	269	37	∑n	∑n	NUM
ma-99	269	38	i=1(yi∆	i=1(yi∆	NOUN
ma-99	269	39	−	−	PROPN
ma-99	269	40	y(i−1)∆	y(i−1)∆	NUM
ma-99	269	41	)	)	PUNCT
ma-99	269	42	]	]	PUNCT
ma-99	270	1	2a3(a	2a3(a	NUM
ma-99	270	2	+	+	CCONJ
ma-99	270	3	1	1	X
ma-99	270	4	)	)	PUNCT
ma-99	270	5	b4∆	b4∆	NOUN
ma-99	270	6	,	,	PUNCT
ma-99	270	7	ρ̂n	ρ̂n	NOUN
ma-99	270	8	:	:	PUNCT
ma-99	270	9	=	=	SYM
ma-99	270	10	1	1	NUM
ma-99	270	11	n2	n2	ADJ
ma-99	270	12	∑n	∑n	PROPN
ma-99	270	13	i=1(yi∆	i=1(yi∆	NOUN
ma-99	270	14	−	−	PROPN
ma-99	270	15	y(i−1)∆)2	y(i−1)∆)2	NOUN
ma-99	270	16	−	−	PROPN
ma-99	270	17	∆	∆	PROPN
ma-99	270	18	n	n	CCONJ
ma-99	271	1	[	[	X
ma-99	271	2	∑n	∑n	NUM
ma-99	271	3	i=1(yi∆	i=1(yi∆	NOUN
ma-99	271	4	−	−	PROPN
ma-99	271	5	y(i−1)∆	y(i−1)∆	NUM
ma-99	271	6	)	)	PUNCT
ma-99	271	7	]	]	PUNCT
ma-99	271	8	1	1	NUM
ma-99	271	9	n2	n2	NOUN
ma-99	271	10	[	[	X
ma-99	271	11	∑n	∑n	PROPN
ma-99	271	12	i=1(yi∆	i=1(yi∆	NOUN
ma-99	271	13	−	−	PROPN
ma-99	271	14	y(i−1)∆	y(i−1)∆	NUM
ma-99	271	15	)	)	PUNCT
ma-99	271	16	]	]	PUNCT
ma-99	271	17	b3∆	b3∆	PROPN
ma-99	271	18	2a2(a	2a2(a	NUM
ma-99	271	19	+	+	NOUN
ma-99	271	20	1	1	NUM
ma-99	271	21	)	)	PUNCT
ma-99	271	22	.	.	PUNCT
ma-99	272	1	for	for	ADP
ma-99	272	2	the	the	DET
ma-99	272	3	mts	mts	PROPN
ma-99	272	4	-	-	PUNCT
ma-99	272	5	ou	ou	NOUN
ma-99	272	6	model	model	NOUN
ma-99	272	7	,	,	PUNCT
ma-99	272	8	the	the	DET
ma-99	272	9	estimating	estimate	VERB
ma-99	272	10	functions	function	NOUN
ma-99	272	11	are	be	AUX
ma-99	272	12	given	give	VERB
ma-99	272	13	by	by	ADP
ma-99	272	14	c1(y1	c1(y1	NOUN
ma-99	272	15	)	)	PUNCT
ma-99	272	16	=	=	PUNCT
ma-99	273	1	λρ∆c1(z	λρ∆c1(z	X
ma-99	273	2	)	)	PUNCT
ma-99	273	3	,	,	PUNCT
ma-99	273	4	c2(y1	c2(y1	NOUN
ma-99	273	5	)	)	PUNCT
ma-99	273	6	=	=	SYM
ma-99	273	7	∆c1(z	∆c1(z	PROPN
ma-99	273	8	)	)	PUNCT
ma-99	273	9	+	+	NUM
ma-99	273	10	2λρ2∆c1(z	2λρ2∆c1(z	NUM
ma-99	273	11	)	)	PUNCT
ma-99	273	12	,	,	PUNCT
ma-99	273	13	c3(y1	c3(y1	PROPN
ma-99	273	14	)	)	PUNCT
ma-99	273	15	=	=	SYM
ma-99	273	16	∆c1(z	∆c1(z	PROPN
ma-99	273	17	)	)	PUNCT
ma-99	273	18	+	+	NUM
ma-99	273	19	2λρ2∆c2(z	2λρ2∆c2(z	NUM
ma-99	273	20	)	)	PUNCT
ma-99	273	21	,	,	PUNCT
ma-99	273	22	c4(y1	c4(y1	NOUN
ma-99	273	23	)	)	PUNCT
ma-99	273	24	=	=	SYM
ma-99	273	25	∆c1(z	∆c1(z	PROPN
ma-99	273	26	)	)	PUNCT
ma-99	273	27	+	+	CCONJ
ma-99	273	28	2λρ2∆c3(z)which	2λρ2∆c3(z)which	PROPN
ma-99	273	29	give	give	VERB
ma-99	273	30	e(y1	e(y1	NOUN
ma-99	273	31	)	)	PUNCT
ma-99	273	32	=	=	SYM
ma-99	273	33	c1(y1	c1(y1	NOUN
ma-99	273	34	)	)	PUNCT
ma-99	273	35	=	=	PUNCT
ma-99	273	36	µ+	µ+	PUNCT
ma-99	273	37	2−	2−	NUM
ma-99	273	38	α+1	α+1	NUM
ma-99	273	39	2	2	NUM
ma-99	273	40	cγ	cγ	NOUN
ma-99	273	41	(	(	PUNCT
ma-99	273	42	1−	1−	NUM
ma-99	273	43	α	α	NOUN
ma-99	273	44	2	2	NUM
ma-99	273	45	)	)	PUNCT
ma-99	273	46	(	(	PUNCT
ma-99	273	47	λα−1	λα−1	PROPN
ma-99	273	48	+	+	CCONJ
ma-99	273	49	−	−	PROPN
ma-99	274	1	λα−1	λα−1	PROPN
ma-99	274	2	−	−	PROPN
ma-99	274	3	)	)	PUNCT
ma-99	274	4	,	,	PUNCT
ma-99	274	5	v	v	X
ma-99	274	6	(	(	PUNCT
ma-99	274	7	y1	y1	NOUN
ma-99	274	8	)	)	PUNCT
ma-99	274	9	=	=	SYM
ma-99	274	10	c2(y1	c2(y1	ADJ
ma-99	274	11	)	)	PUNCT
ma-99	274	12	=	=	PUNCT
ma-99	275	1	2−	2−	NUM
ma-99	275	2	α+1	α+1	NUM
ma-99	275	3	2	2	NUM
ma-99	275	4	√	√	NUM
ma-99	275	5	πcγ	πcγ	NOUN
ma-99	275	6	(	(	PUNCT
ma-99	275	7	1−	1−	NUM
ma-99	275	8	α	α	NOUN
ma-99	275	9	2	2	NUM
ma-99	275	10	)	)	PUNCT
ma-99	275	11	(	(	PUNCT
ma-99	275	12	λα−2	λα−2	VERB
ma-99	275	13	+	+	CCONJ
ma-99	275	14	+	+	CCONJ
ma-99	275	15	λα−2	λα−2	NOUN
ma-99	275	16	−	−	PROPN
ma-99	275	17	)	)	PUNCT
ma-99	275	18	.this	.this	PROPN
ma-99	275	19	gives	give	VERB
ma-99	275	20	the	the	DET
ma-99	275	21	moment	moment	NOUN
ma-99	275	22	estimators	estimator	NOUN
ma-99	275	23	for	for	ADP
ma-99	275	24	the	the	DET
ma-99	275	25	sou	sou	PROPN
ma-99	275	26	model	model	NOUN
ma-99	275	27	θ̂n	θ̂n	ADP
ma-99	275	28	:	:	PUNCT
ma-99	275	29	=	=	SYM
ma-99	275	30	1	1	NUM
ma-99	275	31	n2	n2	NOUN
ma-99	275	32	[	[	X
ma-99	275	33	∑n	∑n	PROPN
ma-99	275	34	i=1(yi∆	i=1(yi∆	NOUN
ma-99	275	35	−	−	PROPN
ma-99	275	36	y(i−1)∆	y(i−1)∆	NUM
ma-99	275	37	)	)	PUNCT
ma-99	275	38	]	]	PUNCT
ma-99	275	39	2	2	NUM
ma-99	275	40	1	1	NUM
ma-99	275	41	n2	n2	ADJ
ma-99	275	42	∑n	∑n	PROPN
ma-99	275	43	i=1(yi∆	i=1(yi∆	NOUN
ma-99	275	44	−	−	PROPN
ma-99	275	45	y(i−1)∆)2	y(i−1)∆)2	NOUN
ma-99	275	46	−	−	PROPN
ma-99	275	47	∆	∆	PROPN
ma-99	275	48	n	n	CCONJ
ma-99	276	1	[	[	X
ma-99	276	2	∑n	∑n	NUM
ma-99	276	3	i=1(yi∆	i=1(yi∆	NOUN
ma-99	276	4	−	−	PROPN
ma-99	276	5	y(i−1)∆	y(i−1)∆	NUM
ma-99	276	6	)	)	PUNCT
ma-99	276	7	]	]	PUNCT
ma-99	277	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	277	2	eur	eur	PROPN
ma-99	277	3	.	.	PUNCT
ma-99	278	1	j.	j.	PROPN
ma-99	278	2	math	math	PROPN
ma-99	278	3	.	.	PUNCT
ma-99	279	1	anal	anal	PROPN
ma-99	279	2	.	.	PUNCT
ma-99	280	1	10.28924	10.28924	NUM
ma-99	280	2	/	/	SYM
ma-99	280	3	ada	ada	PROPN
ma-99	280	4	/	/	SYM
ma-99	280	5	ma.3.4	ma.3.4	PROPN
ma-99	280	6	12	12	NUM
ma-99	280	7	×	×	NOUN
ma-99	281	1	[	[	X
ma-99	281	2	2−	2−	NUM
ma-99	281	3	α+1	α+1	NUM
ma-99	281	4	2	2	NUM
ma-99	281	5	cγ	cγ	NOUN
ma-99	281	6	(	(	PUNCT
ma-99	281	7	1−	1−	NUM
ma-99	281	8	α	α	NOUN
ma-99	281	9	2	2	NUM
ma-99	281	10	)	)	PUNCT
ma-99	281	11	(	(	PUNCT
ma-99	281	12	λα−1	λα−1	PROPN
ma-99	281	13	+	+	CCONJ
ma-99	281	14	−	−	PROPN
ma-99	281	15	λα−1	λα−1	PROPN
ma-99	281	16	−	−	PROPN
ma-99	281	17	)	)	PUNCT
ma-99	281	18	]	]	SYM
ma-99	281	19	2[2−	2[2−	X
ma-99	281	20	α+1	α+1	NUM
ma-99	281	21	2	2	NUM
ma-99	281	22	√	√	NUM
ma-99	281	23	πcγ	πcγ	NOUN
ma-99	281	24	(	(	PUNCT
ma-99	281	25	1−	1−	NUM
ma-99	281	26	α	α	NOUN
ma-99	281	27	2	2	NUM
ma-99	281	28	)	)	PUNCT
ma-99	281	29	(	(	PUNCT
ma-99	281	30	λα−2	λα−2	VERB
ma-99	281	31	+	+	CCONJ
ma-99	281	32	+	+	CCONJ
ma-99	281	33	λα−2	λα−2	NOUN
ma-99	281	34	−	−	PROPN
ma-99	281	35	)	)	PUNCT
ma-99	281	36	]	]	SYM
ma-99	281	37	2∆−1	2∆−1	X
ma-99	281	38	.	.	PUNCT
ma-99	282	1	ρ̂n	ρ̂n	NUM
ma-99	282	2	:	:	PUNCT
ma-99	282	3	=	=	SYM
ma-99	282	4	1	1	NUM
ma-99	282	5	n2	n2	ADJ
ma-99	282	6	∑n	∑n	PROPN
ma-99	282	7	i=1(yi∆	i=1(yi∆	NOUN
ma-99	282	8	−	−	PROPN
ma-99	282	9	y(i−1)∆)2	y(i−1)∆)2	NOUN
ma-99	282	10	−	−	PROPN
ma-99	282	11	∆	∆	PROPN
ma-99	282	12	n	n	CCONJ
ma-99	283	1	[	[	X
ma-99	283	2	∑n	∑n	NUM
ma-99	283	3	i=1(yi∆	i=1(yi∆	NOUN
ma-99	283	4	−	−	PROPN
ma-99	283	5	y(i−1)∆	y(i−1)∆	NUM
ma-99	283	6	)	)	PUNCT
ma-99	283	7	]	]	PUNCT
ma-99	283	8	1	1	NUM
ma-99	283	9	n2	n2	NOUN
ma-99	283	10	[	[	X
ma-99	283	11	∑n	∑n	PROPN
ma-99	283	12	i=1(yi∆	i=1(yi∆	NOUN
ma-99	283	13	−	−	PROPN
ma-99	283	14	y(i−1)∆	y(i−1)∆	NUM
ma-99	283	15	)	)	PUNCT
ma-99	283	16	]	]	PUNCT
ma-99	284	1	×	×	NOUN
ma-99	285	1	[	[	X
ma-99	285	2	2−	2−	NUM
ma-99	285	3	α+1	α+1	NUM
ma-99	285	4	2	2	NUM
ma-99	285	5	cγ	cγ	NOUN
ma-99	285	6	(	(	PUNCT
ma-99	285	7	1−	1−	NUM
ma-99	285	8	α	α	NOUN
ma-99	285	9	2	2	NUM
ma-99	285	10	)	)	PUNCT
ma-99	285	11	(	(	PUNCT
ma-99	285	12	λα−1	λα−1	PROPN
ma-99	285	13	+	+	CCONJ
ma-99	285	14	−	−	PROPN
ma-99	285	15	λα−1	λα−1	PROPN
ma-99	285	16	−	−	PROPN
ma-99	285	17	)	)	PUNCT
ma-99	285	18	2−	2−	NUM
ma-99	285	19	α+1	α+1	NUM
ma-99	285	20	2	2	NUM
ma-99	285	21	√	√	NUM
ma-99	285	22	πcγ	πcγ	NOUN
ma-99	285	23	(	(	PUNCT
ma-99	285	24	1−	1−	NUM
ma-99	285	25	α	α	NOUN
ma-99	285	26	2	2	NUM
ma-99	285	27	)	)	PUNCT
ma-99	285	28	(	(	PUNCT
ma-99	285	29	λα−2	λα−2	VERB
ma-99	285	30	+	+	CCONJ
ma-99	285	31	+	+	CCONJ
ma-99	285	32	λα−2	λα−2	NOUN
ma-99	285	33	−	−	PROPN
ma-99	285	34	)	)	PUNCT
ma-99	285	35	]	]	PUNCT
ma-99	285	36	−12−1∆.	−12−1∆.	PROPN
ma-99	285	37	let	let	VERB
ma-99	285	38	ϑ	ϑ	X
ma-99	285	39	=	=	X
ma-99	285	40	(	(	PUNCT
ma-99	285	41	ρ	ρ	PROPN
ma-99	285	42	,	,	PUNCT
ma-99	285	43	θ	θ	NOUN
ma-99	285	44	)	)	PUNCT
ma-99	285	45	and	and	CCONJ
ma-99	285	46	ϑ̂n	ϑ̂n	X
ma-99	285	47	=	=	X
ma-99	285	48	(	(	PUNCT
ma-99	285	49	ρ̂n	ρ̂n	X
ma-99	285	50	,	,	PUNCT
ma-99	285	51	θ̂n	θ̂n	NUM
ma-99	285	52	)	)	PUNCT
ma-99	285	53	.	.	PUNCT
ma-99	286	1	by	by	ADP
ma-99	286	2	using	use	VERB
ma-99	286	3	theorem	theorem	NOUN
ma-99	286	4	2.2	2.2	NUM
ma-99	286	5	in	in	ADP
ma-99	286	6	masuda	masuda	PROPN
ma-99	286	7	[	[	X
ma-99	286	8	34	34	NUM
ma-99	286	9	]	]	PUNCT
ma-99	286	10	(	(	PUNCT
ma-99	286	11	see	see	VERB
ma-99	286	12	also	also	ADV
ma-99	286	13	theorem	theorem	VERB
ma-99	286	14	4.1	4.1	NUM
ma-99	286	15	vander	vander	NOUN
ma-99	286	16	vaart	vaart	PROPN
ma-99	287	1	[	[	X
ma-99	287	2	41	41	NUM
ma-99	287	3	]	]	PUNCT
ma-99	287	4	)	)	PUNCT
ma-99	287	5	,	,	PUNCT
ma-99	287	6	we	we	PRON
ma-99	287	7	obtain	obtain	VERB
ma-99	287	8	the	the	DET
ma-99	287	9	strong	strong	ADJ
ma-99	287	10	consistency	consistency	NOUN
ma-99	287	11	and	and	CCONJ
ma-99	287	12	asymptotic	asymptotic	ADJ
ma-99	287	13	normality	normality	NOUN
ma-99	287	14	of	of	ADP
ma-99	287	15	the	the	DET
ma-99	287	16	mm	mm	PROPN
ma-99	287	17	estimators	estimator	NOUN
ma-99	287	18	:	:	PUNCT
ma-99	287	19	proposition	proposition	NOUN
ma-99	287	20	2.1	2.1	NUM
ma-99	287	21	for	for	ADP
ma-99	287	22	fixed	fix	VERB
ma-99	287	23	∆	∆	X
ma-99	287	24	>	>	X
ma-99	287	25	0	0	PUNCT
ma-99	288	1	as	as	ADP
ma-99	288	2	n	n	PROPN
ma-99	288	3	→∞	→∞	PROPN
ma-99	288	4	,	,	PUNCT
ma-99	288	5	(	(	PUNCT
ma-99	288	6	a	a	X
ma-99	288	7	)	)	PUNCT
ma-99	288	8	ϑ̂n	ϑ̂n	PROPN
ma-99	288	9	→	→	SYM
ma-99	288	10	ϑ0	ϑ0	PROPN
ma-99	288	11	a.s	a.s	PROPN
ma-99	288	12	.	.	PROPN
ma-99	288	13	as	as	ADP
ma-99	288	14	n	n	PROPN
ma-99	288	15	→∞.	→∞.	PROPN
ma-99	288	16	(	(	PUNCT
ma-99	288	17	b	b	NOUN
ma-99	288	18	)	)	PUNCT
ma-99	288	19	√	√	NOUN
ma-99	288	20	n(ϑ̂n	n(ϑ̂n	NUM
ma-99	288	21	−	−	NOUN
ma-99	288	22	ϑ0)→d	ϑ0)→d	ADP
ma-99	288	23	n2(0	n2(0	PROPN
ma-99	288	24	,	,	PUNCT
ma-99	288	25	(	(	PUNCT
ma-99	288	26	j−1(ϑ0	j−1(ϑ0	PROPN
ma-99	288	27	)	)	PUNCT
ma-99	288	28	)	)	PUNCT
ma-99	288	29	as	as	ADP
ma-99	288	30	n	n	X
ma-99	288	31	→∞.	→∞.	PROPN
ma-99	288	32	where	where	SCONJ
ma-99	288	33	j(ϑ0	j(ϑ0	NOUN
ma-99	288	34	)	)	PUNCT
ma-99	288	35	is	be	AUX
ma-99	288	36	the	the	DET
ma-99	288	37	fisher	fisher	PROPN
ma-99	288	38	information	information	NOUN
ma-99	288	39	.	.	PUNCT
ma-99	289	1	3	3	X
ma-99	289	2	.	.	X
ma-99	289	3	spdes	spde	NOUN
ma-99	289	4	with	with	ADP
ma-99	289	5	additive	additive	ADJ
ma-99	289	6	noise	noise	NOUN
ma-99	289	7	consider	consider	VERB
ma-99	289	8	the	the	DET
ma-99	289	9	parabolic	parabolic	ADJ
ma-99	289	10	spde	spde	NOUN
ma-99	289	11	duθ(t	duθ(t	PROPN
ma-99	289	12	,	,	PUNCT
ma-99	289	13	x	x	NOUN
ma-99	289	14	)	)	PUNCT
ma-99	289	15	=	=	SYM
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ma-99	289	17	,	,	PUNCT
ma-99	289	18	x	x	NOUN
ma-99	289	19	)	)	PUNCT
ma-99	290	1	+	+	CCONJ
ma-99	290	2	∂2	∂2	NUM
ma-99	290	3	∂x2	∂x2	NOUN
ma-99	290	4	uθ(t	uθ(t	NOUN
ma-99	290	5	,	,	PUNCT
ma-99	290	6	x)dt	x)dt	PROPN
ma-99	290	7	+	+	NUM
ma-99	290	8	dz(t	dz(t	NOUN
ma-99	290	9	,	,	PUNCT
ma-99	290	10	x	x	NOUN
ma-99	290	11	)	)	PUNCT
ma-99	290	12	,	,	PUNCT
ma-99	290	13	t	t	PROPN
ma-99	290	14	≥	≥	NUM
ma-99	290	15	0	0	NUM
ma-99	290	16	,	,	PUNCT
ma-99	290	17	x	x	SYM
ma-99	290	18	∈	∈	PROPN
ma-99	291	1	[	[	X
ma-99	291	2	0	0	NUM
ma-99	291	3	,	,	PUNCT
ma-99	291	4	1	1	NUM
ma-99	291	5	]	]	PUNCT
ma-99	291	6	(	(	PUNCT
ma-99	291	7	3.1	3.1	NUM
ma-99	291	8	)	)	PUNCT
ma-99	291	9	u(0	u(0	PROPN
ma-99	291	10	,	,	PUNCT
ma-99	291	11	x	x	NOUN
ma-99	291	12	)	)	PUNCT
ma-99	291	13	=	=	SYM
ma-99	291	14	u0(x	u0(x	NUM
ma-99	291	15	)	)	PUNCT
ma-99	291	16	∈	∈	NOUN
ma-99	291	17	l2([0	l2([0	VERB
ma-99	291	18	,	,	PUNCT
ma-99	291	19	1	1	NUM
ma-99	291	20	]	]	NUM
ma-99	291	21	)	)	PUNCT
ma-99	291	22	,	,	PUNCT
ma-99	291	23	(	(	PUNCT
ma-99	291	24	3.2	3.2	NUM
ma-99	291	25	)	)	PUNCT
ma-99	291	26	uθ(t	uθ(t	NOUN
ma-99	291	27	,	,	PUNCT
ma-99	291	28	0	0	NUM
ma-99	291	29	)	)	PUNCT
ma-99	291	30	=	=	SYM
ma-99	292	1	uθ(t	uθ(t	NOUN
ma-99	292	2	,	,	PUNCT
ma-99	292	3	1	1	NUM
ma-99	292	4	)	)	PUNCT
ma-99	292	5	,	,	PUNCT
ma-99	292	6	t	t	PROPN
ma-99	292	7	∈	∈	PROPN
ma-99	293	1	[	[	X
ma-99	293	2	0	0	NUM
ma-99	293	3	,	,	PUNCT
ma-99	293	4	t	t	X
ma-99	293	5	]	]	PUNCT
ma-99	293	6	.	.	PUNCT
ma-99	294	1	(	(	PUNCT
ma-99	294	2	3.3	3.3	NUM
ma-99	294	3	)	)	PUNCT
ma-99	294	4	here	here	ADV
ma-99	294	5	θ	θ	PROPN
ma-99	295	1	∈	∈	PROPN
ma-99	295	2	θ	θ	NOUN
ma-99	295	3	⊆	⊆	NUM
ma-99	295	4	r	r	NOUN
ma-99	295	5	is	be	AUX
ma-99	295	6	the	the	DET
ma-99	295	7	unknown	unknown	ADJ
ma-99	295	8	parameter	parameter	NOUN
ma-99	295	9	to	to	PART
ma-99	295	10	be	be	AUX
ma-99	295	11	estimated	estimate	VERB
ma-99	295	12	on	on	ADP
ma-99	295	13	the	the	DET
ma-99	295	14	basis	basis	NOUN
ma-99	295	15	of	of	ADP
ma-99	295	16	the	the	DET
ma-99	295	17	observations	observation	NOUN
ma-99	295	18	ofthe	ofthe	ADJ
ma-99	295	19	field	field	NOUN
ma-99	295	20	uθ(t	uθ(t	NOUN
ma-99	295	21	,	,	PUNCT
ma-99	295	22	x	x	NOUN
ma-99	295	23	)	)	PUNCT
ma-99	295	24	,	,	PUNCT
ma-99	295	25	t	t	PROPN
ma-99	295	26	≥	≥	NUM
ma-99	295	27	0	0	NUM
ma-99	295	28	,	,	PUNCT
ma-99	295	29	x	x	SYM
ma-99	295	30	∈	∈	PROPN
ma-99	296	1	[	[	X
ma-99	296	2	0	0	NUM
ma-99	296	3	,	,	PUNCT
ma-99	296	4	1].let	1].let	PROPN
ma-99	296	5	s3	s3	PROPN
ma-99	296	6	and	and	CCONJ
ma-99	296	7	s4	s4	PROPN
ma-99	296	8	be	be	AUX
ma-99	296	9	independent	independent	ADJ
ma-99	296	10	stable	stable	ADJ
ma-99	296	11	random	random	ADJ
ma-99	296	12	variables	variable	NOUN
ma-99	296	13	,	,	PUNCT
ma-99	296	14	s3	s3	PROPN
ma-99	296	15	is	be	AUX
ma-99	296	16	positive	positive	ADJ
ma-99	296	17	α/2	α/2	NOUN
ma-99	296	18	-	-	PUNCT
ma-99	296	19	stable	stable	ADJ
ma-99	296	20	with	with	ADP
ma-99	296	21	distri	distri	NOUN
ma-99	296	22	-	-	NOUN
ma-99	296	23	bution	bution	NOUN
ma-99	296	24	sα/2(σ1	sα/2(σ1	NOUN
ma-99	296	25	,	,	PUNCT
ma-99	296	26	1	1	NUM
ma-99	296	27	,	,	PUNCT
ma-99	296	28	0	0	NUM
ma-99	296	29	)	)	PUNCT
ma-99	296	30	and	and	CCONJ
ma-99	296	31	s4	s4	PROPN
ma-99	296	32	is	be	AUX
ma-99	296	33	symmetric	symmetric	ADJ
ma-99	296	34	α	α	ADJ
ma-99	296	35	-	-	ADJ
ma-99	296	36	stable	stable	ADJ
ma-99	296	37	random	random	ADJ
ma-99	296	38	variable	variable	NOUN
ma-99	296	39	with	with	ADP
ma-99	296	40	distribution	distribution	NOUN
ma-99	296	41	sα(σ2	sα(σ2	NOUN
ma-99	296	42	,	,	PUNCT
ma-99	296	43	0	0	NUM
ma-99	296	44	,	,	PUNCT
ma-99	296	45	0	0	NUM
ma-99	296	46	)	)	PUNCT
ma-99	296	47	,	,	PUNCT
ma-99	296	48	σ1	σ1	NOUN
ma-99	296	49	=	=	PUNCT
ma-99	296	50	c	c	PROPN
ma-99	296	51	−2	−2	PROPN
ma-99	296	52	/	/	SYM
ma-99	296	53	α	α	PROPN
ma-99	296	54	α/2	α/2	NUM
ma-99	296	55	,	,	PUNCT
ma-99	296	56	σ2	σ2	PROPN
ma-99	296	57	=	=	SYM
ma-99	296	58	c	c	PROPN
ma-99	296	59	−1	−1	NOUN
ma-99	296	60	/	/	SYM
ma-99	296	61	α	α	NOUN
ma-99	296	62	α	α	NOUN
ma-99	296	63	,	,	PUNCT
ma-99	296	64	cα	cα	NOUN
ma-99	296	65	=	=	SYM
ma-99	296	66	(	(	PUNCT
ma-99	296	67	∫∞	∫∞	NOUN
ma-99	296	68	0	0	NUM
ma-99	296	69	x−α	x−α	PROPN
ma-99	296	70	sin	sin	VERB
ma-99	296	71	xdx)−1	xdx)−1	PROPN
ma-99	297	1	=	=	PUNCT
ma-99	298	1	[	[	X
ma-99	298	2	γ(1−	γ(1−	X
ma-99	298	3	α	α	X
ma-99	298	4	)	)	PUNCT
ma-99	298	5	cos(πα/2)]−1	cos(πα/2)]−1	NOUN
ma-99	298	6	.	.	PUNCT
ma-99	299	1	in	in	ADP
ma-99	299	2	this	this	DET
ma-99	299	3	case	case	NOUN
ma-99	299	4	,	,	PUNCT
ma-99	299	5	in	in	ADP
ma-99	299	6	the	the	DET
ma-99	299	7	limiting	limit	VERB
ma-99	299	8	distribution	distribution	NOUN
ma-99	299	9	,	,	PUNCT
ma-99	299	10	s3	s3	PROPN
ma-99	299	11	and	and	CCONJ
ma-99	299	12	s4	s4	PROPN
ma-99	299	13	are	be	AUX
ma-99	299	14	independent	independent	ADJ
ma-99	299	15	stable	stable	ADJ
ma-99	299	16	random	random	ADJ
ma-99	299	17	variables	variable	NOUN
ma-99	299	18	witha	witha	NOUN
ma-99	299	19	rate	rate	NOUN
ma-99	299	20	faster	fast	ADV
ma-99	299	21	than	than	ADP
ma-99	299	22	the	the	DET
ma-99	299	23	cylindrical	cylindrical	ADJ
ma-99	299	24	brownian	brownian	ADJ
ma-99	299	25	motion	motion	NOUN
ma-99	299	26	case.for	case.for	ADP
ma-99	299	27	x	x	SYM
ma-99	299	28	∈	∈	PROPN
ma-99	300	1	[	[	X
ma-99	300	2	0	0	NUM
ma-99	300	3	,	,	PUNCT
ma-99	300	4	1	1	NUM
ma-99	300	5	]	]	PUNCT
ma-99	300	6	,	,	PUNCT
ma-99	300	7	we	we	PRON
ma-99	300	8	observe	observe	VERB
ma-99	300	9	the	the	DET
ma-99	300	10	process	process	NOUN
ma-99	300	11	{	{	PUNCT
ma-99	300	12	ut	ut	PROPN
ma-99	300	13	,	,	PUNCT
ma-99	300	14	t	t	PROPN
ma-99	300	15	≥	≥	NUM
ma-99	300	16	0	0	NUM
ma-99	300	17	}	}	PUNCT
ma-99	300	18	at	at	ADP
ma-99	300	19	times	time	NOUN
ma-99	300	20	{	{	PUNCT
ma-99	300	21	t0	t0	PROPN
ma-99	300	22	,	,	PUNCT
ma-99	300	23	t1	t1	NOUN
ma-99	300	24	,	,	PUNCT
ma-99	300	25	t2	t2	NOUN
ma-99	300	26	,	,	PUNCT
ma-99	300	27	.	.	PUNCT
ma-99	300	28	.	.	PUNCT
ma-99	300	29	.	.	PUNCT
ma-99	300	30	}	}	PUNCT
ma-99	300	31	.	.	PUNCT
ma-99	301	1	we	we	PRON
ma-99	301	2	assume	assume	VERB
ma-99	301	3	thatthe	thatthe	NOUN
ma-99	301	4	sampling	sample	VERB
ma-99	301	5	instants	instant	NOUN
ma-99	301	6	{	{	PUNCT
ma-99	301	7	ti	ti	NOUN
ma-99	301	8	,	,	PUNCT
ma-99	301	9	i	i	PRON
ma-99	301	10	=	=	NOUN
ma-99	301	11	0	0	NUM
ma-99	301	12	,	,	PUNCT
ma-99	301	13	1	1	NUM
ma-99	301	14	,	,	PUNCT
ma-99	301	15	2	2	NUM
ma-99	301	16	,	,	PUNCT
ma-99	301	17	.	.	PUNCT
ma-99	301	18	.	.	PUNCT
ma-99	302	1	.	.	PUNCT
ma-99	302	2	}	}	PUNCT
ma-99	302	3	are	be	AUX
ma-99	302	4	generated	generate	VERB
ma-99	302	5	by	by	ADP
ma-99	302	6	a	a	DET
ma-99	302	7	poisson	poisson	NOUN
ma-99	302	8	process	process	NOUN
ma-99	302	9	on	on	ADP
ma-99	302	10	[	[	X
ma-99	302	11	0,∞	0,∞	NOUN
ma-99	302	12	)	)	PUNCT
ma-99	302	13	,	,	PUNCT
ma-99	302	14	i.e.	i.e.	X
ma-99	302	15	,	,	PUNCT
ma-99	302	16	t0	t0	X
ma-99	302	17	=	=	SYM
ma-99	302	18	0	0	NUM
ma-99	302	19	,	,	PUNCT
ma-99	302	20	ti	ti	X
ma-99	302	21	=	=	X
ma-99	302	22	ti−1	ti−1	NOUN
ma-99	302	23	+	+	NOUN
ma-99	302	24	αi	αi	VERB
ma-99	302	25	,	,	PUNCT
ma-99	302	26	i	i	PRON
ma-99	302	27	=	=	NOUN
ma-99	302	28	1	1	NUM
ma-99	302	29	,	,	PUNCT
ma-99	302	30	2	2	NUM
ma-99	302	31	,	,	PUNCT
ma-99	302	32	...	...	PUNCT
ma-99	302	33	where	where	SCONJ
ma-99	302	34	αi	αi	NOUN
ma-99	302	35	are	be	AUX
ma-99	302	36	i.i.d	i.i.d	ADP
ma-99	302	37	.	.	PUNCT
ma-99	303	1	positive	positive	ADJ
ma-99	303	2	random	random	ADJ
ma-99	303	3	variables	variable	NOUN
ma-99	303	4	with	with	ADP
ma-99	303	5	a	a	DET
ma-99	303	6	commonexponential	commonexponential	ADJ
ma-99	303	7	distribution	distribution	NOUN
ma-99	303	8	f	f	X
ma-99	303	9	(	(	PUNCT
ma-99	303	10	x	x	X
ma-99	303	11	)	)	PUNCT
ma-99	303	12	=	=	SYM
ma-99	303	13	1	1	NUM
ma-99	303	14	−	−	NOUN
ma-99	303	15	exp(−λx	exp(−λx	NOUN
ma-99	303	16	)	)	PUNCT
ma-99	303	17	.	.	PUNCT
ma-99	304	1	note	note	VERB
ma-99	304	2	that	that	SCONJ
ma-99	304	3	intensity	intensity	NOUN
ma-99	304	4	parameter	parameter	NOUN
ma-99	304	5	λ	λ	INTJ
ma-99	304	6	>	>	X
ma-99	304	7	0	0	PUNCT
ma-99	304	8	is	be	AUX
ma-99	304	9	theaverage	theaverage	NOUN
ma-99	304	10	sampling	sampling	NOUN
ma-99	304	11	rate	rate	NOUN
ma-99	304	12	which	which	PRON
ma-99	304	13	is	be	AUX
ma-99	304	14	assumed	assume	VERB
ma-99	304	15	to	to	PART
ma-99	304	16	be	be	AUX
ma-99	304	17	known	know	VERB
ma-99	304	18	.	.	PUNCT
ma-99	305	1	it	it	PRON
ma-99	305	2	is	be	AUX
ma-99	305	3	also	also	ADV
ma-99	305	4	assumed	assume	VERB
ma-99	305	5	that	that	SCONJ
ma-99	305	6	the	the	DET
ma-99	305	7	sampling	sampling	NOUN
ma-99	305	8	process	process	NOUN
ma-99	305	9	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	305	10	eur	eur	NOUN
ma-99	305	11	.	.	PUNCT
ma-99	306	1	j.	j.	PROPN
ma-99	306	2	math	math	PROPN
ma-99	306	3	.	.	PUNCT
ma-99	307	1	anal	anal	PROPN
ma-99	307	2	.	.	PUNCT
ma-99	308	1	10.28924	10.28924	NUM
ma-99	308	2	/	/	SYM
ma-99	308	3	ada	ada	PROPN
ma-99	308	4	/	/	SYM
ma-99	308	5	ma.3.4	ma.3.4	PROPN
ma-99	308	6	13	13	NUM
ma-99	308	7	ti	ti	NOUN
ma-99	308	8	,	,	PUNCT
ma-99	308	9	i	i	PRON
ma-99	308	10	=	=	NOUN
ma-99	308	11	0	0	NUM
ma-99	308	12	,	,	PUNCT
ma-99	308	13	1	1	NUM
ma-99	308	14	,	,	PUNCT
ma-99	308	15	2	2	NUM
ma-99	308	16	,	,	PUNCT
ma-99	308	17	...	...	PUNCT
ma-99	308	18	is	be	AUX
ma-99	308	19	independent	independent	ADJ
ma-99	308	20	of	of	ADP
ma-99	308	21	the	the	DET
ma-99	308	22	observation	observation	NOUN
ma-99	308	23	process	process	NOUN
ma-99	308	24	{	{	PUNCT
ma-99	308	25	xt	xt	PROPN
ma-99	308	26	,	,	PUNCT
ma-99	308	27	t	t	PROPN
ma-99	308	28	≥	≥	NOUN
ma-99	308	29	0	0	NUM
ma-99	308	30	}	}	PUNCT
ma-99	308	31	.	.	PUNCT
ma-99	309	1	we	we	PRON
ma-99	309	2	note	note	VERB
ma-99	309	3	that	that	SCONJ
ma-99	309	4	the	the	DET
ma-99	309	5	probabilitydensity	probabilitydensity	NOUN
ma-99	309	6	function	function	NOUN
ma-99	309	7	of	of	ADP
ma-99	309	8	tk+i	tk+i	NOUN
ma-99	309	9	−	−	PROPN
ma-99	309	10	tk	tk	PROPN
ma-99	309	11	is	be	AUX
ma-99	309	12	independent	independent	ADJ
ma-99	309	13	of	of	ADP
ma-99	309	14	k	k	PROPN
ma-99	309	15	and	and	CCONJ
ma-99	309	16	is	be	AUX
ma-99	309	17	given	give	VERB
ma-99	309	18	by	by	ADP
ma-99	309	19	the	the	DET
ma-99	309	20	gamma	gamma	PROPN
ma-99	309	21	density	density	NOUN
ma-99	309	22	fi(t	fi(t	NOUN
ma-99	309	23	)	)	PUNCT
ma-99	309	24	=	=	PUNCT
ma-99	310	1	λ(λt)i−1	λ(λt)i−1	NOUN
ma-99	310	2	exp(−λt)it/(i	exp(−λt)it/(i	NOUN
ma-99	310	3	−	−	PROPN
ma-99	310	4	1	1	NUM
ma-99	310	5	)	)	PUNCT
ma-99	310	6	!	!	PUNCT
ma-99	310	7	,	,	PUNCT
ma-99	310	8	i	i	PRON
ma-99	310	9	=	=	NOUN
ma-99	310	10	0	0	NUM
ma-99	310	11	,	,	PUNCT
ma-99	310	12	1	1	NUM
ma-99	310	13	,	,	PUNCT
ma-99	310	14	2	2	NUM
ma-99	310	15	,	,	PUNCT
ma-99	310	16	....	....	PUNCT
ma-99	310	17	(	(	PUNCT
ma-99	310	18	3.4	3.4	NUM
ma-99	310	19	)	)	PUNCT
ma-99	310	20	where	where	SCONJ
ma-99	310	21	it	it	PRON
ma-99	310	22	=	=	PUNCT
ma-99	310	23	1	1	NUM
ma-99	310	24	if	if	SCONJ
ma-99	310	25	t	t	PROPN
ma-99	310	26	≥	≥	NOUN
ma-99	310	27	0	0	PUNCT
ma-99	310	28	and	and	CCONJ
ma-99	310	29	it	it	PRON
ma-99	311	1	=	=	SYM
ma-99	311	2	0	0	PUNCT
ma-99	312	1	if	if	SCONJ
ma-99	312	2	t	t	PROPN
ma-99	312	3	<	<	X
ma-99	312	4	0.consider	0.consider	NUM
ma-99	312	5	the	the	DET
ma-99	312	6	fourier	fourier	ADJ
ma-99	312	7	expansion	expansion	NOUN
ma-99	312	8	of	of	ADP
ma-99	312	9	the	the	DET
ma-99	312	10	process	process	NOUN
ma-99	312	11	uθ(t	uθ(t	NOUN
ma-99	312	12	,	,	PUNCT
ma-99	312	13	x	x	X
ma-99	312	14	)	)	PUNCT
ma-99	312	15	=	=	PUNCT
ma-99	313	1	∞∑	∞∑	NUM
ma-99	313	2	t=1	t=1	ADV
ma-99	313	3	uθi	uθi	NOUN
ma-99	313	4	(	(	PUNCT
ma-99	313	5	t)φi(x	t)φi(x	NUM
ma-99	313	6	)	)	PUNCT
ma-99	313	7	(	(	PUNCT
ma-99	313	8	3.5	3.5	NUM
ma-99	313	9	)	)	PUNCT
ma-99	313	10	corresponding	correspond	VERB
ma-99	313	11	to	to	ADP
ma-99	313	12	some	some	DET
ma-99	313	13	orthogonal	orthogonal	ADJ
ma-99	313	14	basis	basis	NOUN
ma-99	313	15	{	{	PUNCT
ma-99	313	16	φi(x)}∞i=1	φi(x)}∞i=1	NOUN
ma-99	313	17	.	.	PUNCT
ma-99	313	18	note	note	VERB
ma-99	313	19	that	that	DET
ma-99	313	20	uθi	uθi	NOUN
ma-99	313	21	(	(	PUNCT
ma-99	313	22	t	t	PROPN
ma-99	313	23	)	)	PUNCT
ma-99	313	24	,	,	PUNCT
ma-99	313	25	i	i	PRON
ma-99	313	26	≥	≥	VERB
ma-99	313	27	1	1	NUM
ma-99	313	28	are	be	AUX
ma-99	313	29	independent	independent	ADJ
ma-99	313	30	onedimensional	onedimensional	ADJ
ma-99	313	31	stable	stable	ADJ
ma-99	313	32	ornstein	ornstein	PROPN
ma-99	313	33	-	-	PUNCT
ma-99	313	34	uhlenbeck	uhlenbeck	PROPN
ma-99	313	35	processes	process	NOUN
ma-99	313	36	duθi	duθi	NOUN
ma-99	313	37	(	(	PUNCT
ma-99	313	38	t	t	NOUN
ma-99	313	39	)	)	PUNCT
ma-99	313	40	=	=	PUNCT
ma-99	313	41	µθi	µθi	VERB
ma-99	313	42	u	u	NOUN
ma-99	313	43	θ	θ	NOUN
ma-99	313	44	i	i	PRON
ma-99	313	45	(	(	PUNCT
ma-99	313	46	t)dt	t)dt	PROPN
ma-99	313	47	+	+	CCONJ
ma-99	313	48	β−αi	β−αi	PROPN
ma-99	313	49	dzi(t	dzi(t	PROPN
ma-99	313	50	)	)	PUNCT
ma-99	313	51	(	(	PUNCT
ma-99	313	52	3.6	3.6	NUM
ma-99	313	53	)	)	PUNCT
ma-99	313	54	uθi	uθi	NOUN
ma-99	313	55	(	(	PUNCT
ma-99	313	56	0	0	NUM
ma-99	313	57	)	)	PUNCT
ma-99	313	58	=	=	VERB
ma-99	314	1	uθ0i	uθ0i	ADJ
ma-99	314	2	,	,	PUNCT
ma-99	314	3	recall	recall	VERB
ma-99	314	4	that	that	PRON
ma-99	314	5	µi(θ	µi(θ	NOUN
ma-99	314	6	)	)	PUNCT
ma-99	314	7	=	=	SYM
ma-99	315	1	k(θ)−	k(θ)−	PROPN
ma-99	315	2	β2	β2	VERB
ma-99	315	3	m	m	NOUN
ma-99	315	4	i	i	PRON
ma-99	315	5	.	.	PUNCT
ma-99	316	1	thus	thus	ADV
ma-99	316	2	duθi	duθi	NOUN
ma-99	316	3	(	(	PUNCT
ma-99	316	4	t	t	NOUN
ma-99	316	5	)	)	PUNCT
ma-99	316	6	=	=	PUNCT
ma-99	316	7	(	(	PUNCT
ma-99	316	8	k(θ)−	k(θ)−	PROPN
ma-99	316	9	β2	β2	PROPN
ma-99	316	10	m	m	PROPN
ma-99	316	11	i	i	NOUN
ma-99	316	12	)	)	PUNCT
ma-99	316	13	uθi	uθi	NOUN
ma-99	316	14	(	(	PUNCT
ma-99	316	15	t)dt	t)dt	PROPN
ma-99	316	16	+	+	NUM
ma-99	316	17	β−αi	β−αi	PROPN
ma-99	316	18	dzi(t	dzi(t	PROPN
ma-99	316	19	)	)	PUNCT
ma-99	316	20	(	(	PUNCT
ma-99	316	21	3.7	3.7	NUM
ma-99	316	22	)	)	PUNCT
ma-99	316	23	the	the	DET
ma-99	316	24	random	random	ADJ
ma-99	316	25	field	field	NOUN
ma-99	316	26	u(t	u(t	NOUN
ma-99	316	27	,	,	PUNCT
ma-99	316	28	x	x	X
ma-99	316	29	)	)	PUNCT
ma-99	316	30	is	be	AUX
ma-99	316	31	observed	observe	VERB
ma-99	316	32	at	at	ADP
ma-99	316	33	discrete	discrete	ADJ
ma-99	316	34	times	time	NOUN
ma-99	316	35	t	t	NOUN
ma-99	316	36	and	and	CCONJ
ma-99	316	37	discrete	discrete	ADJ
ma-99	316	38	positions	position	NOUN
ma-99	316	39	x	x	X
ma-99	316	40	.	.	PUNCT
ma-99	317	1	equivalently	equivalently	ADV
ma-99	317	2	,	,	PUNCT
ma-99	317	3	thefourier	thefouri	ADJ
ma-99	317	4	coefficients	coefficient	NOUN
ma-99	317	5	uθi	uθi	PROPN
ma-99	317	6	(	(	PUNCT
ma-99	317	7	t	t	NOUN
ma-99	317	8	)	)	PUNCT
ma-99	317	9	are	be	AUX
ma-99	317	10	observed	observe	VERB
ma-99	317	11	at	at	ADP
ma-99	317	12	discrete	discrete	ADJ
ma-99	317	13	time	time	NOUN
ma-99	317	14	points.define	points.define	PROPN
ma-99	317	15	ρ	ρ	NOUN
ma-99	317	16	:	:	PUNCT
ma-99	317	17	=	=	SYM
ma-99	317	18	ρ(λ	ρ(λ	PROPN
ma-99	317	19	,	,	PUNCT
ma-99	317	20	θ	θ	NOUN
ma-99	317	21	)	)	PUNCT
ma-99	317	22	=	=	SYM
ma-99	318	1	λ	λ	PROPN
ma-99	318	2	λ−	λ−	PROPN
ma-99	318	3	κ(θ	κ(θ	PROPN
ma-99	318	4	)	)	PUNCT
ma-99	319	1	+	+	CCONJ
ma-99	320	1	β2	β2	ADJ
ma-99	320	2	m	m	PROPN
ma-99	320	3	i	i	NOUN
ma-99	320	4	.	.	PUNCT
ma-99	321	1	the	the	DET
ma-99	321	2	quasi	quasi	ADJ
ma-99	321	3	-	-	ADJ
ma-99	321	4	likelihood	likelihood	ADJ
ma-99	321	5	estimator	estimator	NOUN
ma-99	321	6	is	be	AUX
ma-99	321	7	the	the	DET
ma-99	321	8	solution	solution	NOUN
ma-99	321	9	of	of	ADP
ma-99	321	10	the	the	DET
ma-99	321	11	estimating	estimate	VERB
ma-99	321	12	equation	equation	NOUN
ma-99	321	13	:	:	PUNCT
ma-99	321	14	g∗n(θ	g∗n(θ	PROPN
ma-99	321	15	)	)	PUNCT
ma-99	322	1	=	=	SYM
ma-99	322	2	0	0	PUNCT
ma-99	322	3	(	(	PUNCT
ma-99	322	4	3.8	3.8	NUM
ma-99	322	5	)	)	PUNCT
ma-99	322	6	where	where	SCONJ
ma-99	322	7	g∗n(θ	g∗n(θ	PROPN
ma-99	322	8	)	)	PUNCT
ma-99	323	1	=	=	PUNCT
ma-99	324	1	β2α	β2α	PUNCT
ma-99	325	1	i	i	PRON
ma-99	325	2	λ(ρ(λ	λ(ρ(λ	PROPN
ma-99	325	3	,	,	PUNCT
ma-99	325	4	θ))2	θ))2	NOUN
ma-99	325	5	ρ(λ	ρ(λ	PROPN
ma-99	325	6	,	,	PUNCT
ma-99	325	7	2θ	2θ	NUM
ma-99	325	8	)	)	PUNCT
ma-99	325	9	n∑	n∑	NOUN
ma-99	325	10	i=1	i=1	X
ma-99	326	1	uti−1	uti−1	PROPN
ma-99	326	2	(	(	PUNCT
ma-99	326	3	(	(	PUNCT
ma-99	326	4	uti−1	uti−1	PROPN
ma-99	326	5	θρ(λ	θρ(λ	NUM
ma-99	326	6	,	,	PUNCT
ma-99	326	7	θ))2	θ))2	NOUN
ma-99	326	8	+	+	CCONJ
ma-99	326	9	λ	λ	NOUN
ma-99	326	10	)	)	PUNCT
ma-99	326	11	−1	−1	NOUN
ma-99	326	12	(	(	PUNCT
ma-99	326	13	uti	uti	PROPN
ma-99	326	14	−	−	PROPN
ma-99	326	15	ρ(λ	ρ(λ	PROPN
ma-99	326	16	,	,	PUNCT
ma-99	326	17	θ)uti−1	θ)uti−1	PROPN
ma-99	326	18	)	)	PUNCT
ma-99	326	19	.	.	PUNCT
ma-99	327	1	(	(	PUNCT
ma-99	327	2	3.9	3.9	NUM
ma-99	327	3	)	)	PUNCT
ma-99	327	4	we	we	PRON
ma-99	327	5	call	call	VERB
ma-99	327	6	the	the	DET
ma-99	327	7	solution	solution	NOUN
ma-99	327	8	of	of	ADP
ma-99	327	9	the	the	DET
ma-99	327	10	estimating	estimate	VERB
ma-99	327	11	equation	equation	NOUN
ma-99	327	12	the	the	DET
ma-99	327	13	quasi	quasi	ADJ
ma-99	327	14	-	-	ADJ
ma-99	327	15	likelihood	likelihood	ADJ
ma-99	327	16	estimator	estimator	NOUN
ma-99	327	17	.	.	PUNCT
ma-99	328	1	there	there	PRON
ma-99	328	2	is	be	VERB
ma-99	328	3	no	no	DET
ma-99	328	4	explicitsolution	explicitsolution	NOUN
ma-99	328	5	for	for	ADP
ma-99	328	6	this	this	DET
ma-99	328	7	equation.the	equation.the	DET
ma-99	328	8	optimal	optimal	ADJ
ma-99	328	9	estimating	estimating	NOUN
ma-99	328	10	function	function	NOUN
ma-99	328	11	for	for	ADP
ma-99	328	12	estimation	estimation	NOUN
ma-99	328	13	of	of	ADP
ma-99	328	14	the	the	DET
ma-99	328	15	unknown	unknown	ADJ
ma-99	328	16	parameter	parameter	NOUN
ma-99	328	17	θ	θ	PROPN
ma-99	328	18	is	be	AUX
ma-99	328	19	gn(θ	gn(θ	PUNCT
ma-99	328	20	)	)	PUNCT
ma-99	329	1	=	=	PUNCT
ma-99	329	2	β2α	β2α	PUNCT
ma-99	330	1	i	i	PRON
ma-99	330	2	n∑	n∑	INTJ
ma-99	330	3	i=1	i=1	PRON
ma-99	331	1	uti−1	uti−1	PROPN
ma-99	332	1	[	[	X
ma-99	332	2	uti	uti	PROPN
ma-99	332	3	−	−	PROPN
ma-99	332	4	ρ(λ	ρ(λ	PROPN
ma-99	332	5	,	,	PUNCT
ma-99	332	6	θ)uti−1	θ)uti−1	PROPN
ma-99	332	7	]	]	PUNCT
ma-99	332	8	.	.	PUNCT
ma-99	333	1	(	(	PUNCT
ma-99	333	2	3.10	3.10	NUM
ma-99	333	3	)	)	PUNCT
ma-99	333	4	the	the	DET
ma-99	333	5	martingale	martingale	NOUN
ma-99	333	6	estimation	estimation	NOUN
ma-99	333	7	function	function	NOUN
ma-99	333	8	(	(	PUNCT
ma-99	333	9	mef	mef	NOUN
ma-99	333	10	)	)	PUNCT
ma-99	333	11	estimator	estimator	NOUN
ma-99	333	12	of	of	ADP
ma-99	333	13	ρ	ρ	PROPN
ma-99	333	14	is	be	AUX
ma-99	333	15	the	the	DET
ma-99	333	16	solution	solution	NOUN
ma-99	333	17	of	of	ADP
ma-99	333	18	gn(θ	gn(θ	NOUN
ma-99	333	19	)	)	PUNCT
ma-99	334	1	=	=	SYM
ma-99	334	2	0	0	PUNCT
ma-99	335	1	(	(	PUNCT
ma-99	335	2	3.11)and	3.11)and	NUM
ma-99	335	3	is	be	AUX
ma-99	335	4	given	give	VERB
ma-99	335	5	by	by	ADP
ma-99	335	6	ρ̂n	ρ̂n	NOUN
ma-99	335	7	:	:	PUNCT
ma-99	336	1	=	=	SYM
ma-99	336	2	∑n	∑n	PROPN
ma-99	336	3	i=1	i=1	PROPN
ma-99	337	1	uti−1	uti−1	PROPN
ma-99	337	2	uti∑n	uti∑n	NOUN
ma-99	337	3	i=1	i=1	PROPN
ma-99	337	4	u	u	NOUN
ma-99	337	5	2	2	NUM
ma-99	337	6	ti−1	ti−1	NOUN
ma-99	337	7	.	.	PUNCT
ma-99	338	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	338	2	eur	eur	PROPN
ma-99	338	3	.	.	PUNCT
ma-99	339	1	j.	j.	PROPN
ma-99	339	2	math	math	PROPN
ma-99	339	3	.	.	PUNCT
ma-99	340	1	anal	anal	PROPN
ma-99	340	2	.	.	PUNCT
ma-99	341	1	10.28924	10.28924	NUM
ma-99	341	2	/	/	SYM
ma-99	341	3	ada	ada	PROPN
ma-99	341	4	/	/	SYM
ma-99	341	5	ma.3.4	ma.3.4	PROPN
ma-99	341	6	14	14	NUM
ma-99	341	7	we	we	PRON
ma-99	341	8	do	do	VERB
ma-99	341	9	the	the	DET
ma-99	341	10	parameter	parameter	NOUN
ma-99	341	11	estimation	estimation	NOUN
ma-99	341	12	in	in	ADP
ma-99	341	13	two	two	NUM
ma-99	341	14	steps	step	NOUN
ma-99	341	15	:	:	PUNCT
ma-99	341	16	the	the	DET
ma-99	341	17	rate	rate	NOUN
ma-99	341	18	λ	λ	PROPN
ma-99	341	19	of	of	ADP
ma-99	341	20	the	the	DET
ma-99	341	21	poisson	poisson	NOUN
ma-99	341	22	process	process	NOUN
ma-99	341	23	can	can	AUX
ma-99	341	24	be	be	AUX
ma-99	341	25	estimatedgiven	estimatedgiven	VERB
ma-99	341	26	the	the	DET
ma-99	341	27	arrival	arrival	NOUN
ma-99	341	28	times	time	NOUN
ma-99	341	29	ti	ti	PROPN
ma-99	341	30	,	,	PUNCT
ma-99	341	31	therefore	therefore	ADV
ma-99	341	32	it	it	PRON
ma-99	341	33	is	be	AUX
ma-99	341	34	done	do	VERB
ma-99	341	35	at	at	ADP
ma-99	341	36	a	a	DET
ma-99	341	37	first	first	ADJ
ma-99	341	38	step	step	NOUN
ma-99	341	39	.	.	PUNCT
ma-99	342	1	since	since	SCONJ
ma-99	342	2	we	we	PRON
ma-99	342	3	observe	observe	VERB
ma-99	342	4	total	total	ADJ
ma-99	342	5	number	number	NOUN
ma-99	342	6	ofarrivals	ofarrival	NOUN
ma-99	342	7	n	n	ADP
ma-99	342	8	of	of	ADP
ma-99	342	9	the	the	DET
ma-99	342	10	poisson	poisson	NOUN
ma-99	342	11	process	process	NOUN
ma-99	342	12	over	over	ADP
ma-99	342	13	the	the	DET
ma-99	342	14	t	t	NOUN
ma-99	342	15	intervals	interval	NOUN
ma-99	342	16	of	of	ADP
ma-99	342	17	length	length	NOUN
ma-99	342	18	one	one	NUM
ma-99	342	19	,	,	PUNCT
ma-99	342	20	the	the	DET
ma-99	342	21	mle	mle	NOUN
ma-99	342	22	of	of	ADP
ma-99	342	23	λ	λ	PROPN
ma-99	342	24	is	be	AUX
ma-99	342	25	given	give	VERB
ma-99	342	26	by	by	ADP
ma-99	342	27	λ̂n	λ̂n	PUNCT
ma-99	342	28	:	:	PUNCT
ma-99	342	29	=	=	SYM
ma-99	342	30	n	n	PRON
ma-99	342	31	t	t	NOUN
ma-99	342	32	.	.	PUNCT
ma-99	343	1	theorem	theorem	VERB
ma-99	343	2	3.1	3.1	NUM
ma-99	343	3	we	we	PRON
ma-99	343	4	have	have	VERB
ma-99	343	5	λ̂n	λ̂n	X
ma-99	343	6	→	→	SYM
ma-99	343	7	λ	λ	X
ma-99	343	8	a.s	a.s	PROPN
ma-99	343	9	.	.	PROPN
ma-99	343	10	as	as	ADP
ma-99	343	11	n	n	PROPN
ma-99	343	12	→∞.	→∞.	NOUN
ma-99	343	13	√	√	PROPN
ma-99	343	14	n(λ̂n	n(λ̂n	PROPN
ma-99	343	15	−	−	PROPN
ma-99	343	16	λ)→d	λ)→d	PROPN
ma-99	343	17	n	n	PROPN
ma-99	343	18	(	(	PUNCT
ma-99	343	19	0	0	NUM
ma-99	343	20	,	,	PUNCT
ma-99	343	21	eλ(1−	eλ(1−	PROPN
ma-99	343	22	e−λ	e−λ	NOUN
ma-99	343	23	)	)	PUNCT
ma-99	343	24	)	)	PUNCT
ma-99	343	25	as	as	ADP
ma-99	343	26	n	n	X
ma-99	343	27	→∞.	→∞.	NOUN
ma-99	343	28	proof	proof	NOUN
ma-99	343	29	.	.	PUNCT
ma-99	344	1	let	let	VERB
ma-99	344	2	vi	vi	NOUN
ma-99	344	3	be	be	AUX
ma-99	344	4	the	the	DET
ma-99	344	5	number	number	NOUN
ma-99	344	6	of	of	ADP
ma-99	344	7	arrivals	arrival	NOUN
ma-99	344	8	in	in	ADP
ma-99	344	9	the	the	DET
ma-99	344	10	interval	interval	NOUN
ma-99	344	11	(	(	PUNCT
ma-99	344	12	i	i	PRON
ma-99	344	13	−	−	PROPN
ma-99	344	14	1	1	NUM
ma-99	344	15	,	,	PUNCT
ma-99	344	16	i	i	PRON
ma-99	344	17	]	]	PUNCT
ma-99	344	18	.	.	PUNCT
ma-99	345	1	then	then	ADV
ma-99	345	2	vi	vi	VERB
ma-99	345	3	,	,	PUNCT
ma-99	345	4	i	i	PRON
ma-99	345	5	=	=	NOUN
ma-99	345	6	1	1	NUM
ma-99	345	7	,	,	PUNCT
ma-99	345	8	2	2	NUM
ma-99	345	9	,	,	PUNCT
ma-99	345	10	.	.	PUNCT
ma-99	345	11	.	.	PUNCT
ma-99	345	12	.	.	PUNCT
ma-99	346	1	,	,	PUNCT
ma-99	346	2	n	n	PRON
ma-99	346	3	are	be	AUX
ma-99	346	4	i.i.d.poisson	i.i.d.poisson	NOUN
ma-99	346	5	distributed	distribute	VERB
ma-99	346	6	with	with	ADP
ma-99	346	7	parameter	parameter	PROPN
ma-99	346	8	λ	λ	PROPN
ma-99	346	9	.	.	PUNCT
ma-99	347	1	since	since	SCONJ
ma-99	347	2	φ	φ	PROPN
ma-99	347	3	is	be	AUX
ma-99	347	4	continuous	continuous	ADJ
ma-99	347	5	,	,	PUNCT
ma-99	347	6	we	we	PRON
ma-99	347	7	have	have	VERB
ma-99	347	8	i{0}(vi	i{0}(vi	NOUN
ma-99	347	9	)	)	PUNCT
ma-99	347	10	=	=	SYM
ma-99	347	11	i{0}(u(ti	i{0}(u(ti	NOUN
ma-99	347	12	)	)	PUNCT
ma-99	347	13	)	)	PUNCT
ma-99	348	1	a.s	a.s	PROPN
ma-99	349	1	.	.	PROPN
ma-99	349	2	i	i	PROPN
ma-99	349	3	=	=	NOUN
ma-99	349	4	1	1	NUM
ma-99	349	5	,	,	PUNCT
ma-99	349	6	2	2	NUM
ma-99	349	7	,	,	PUNCT
ma-99	349	8	.	.	PUNCT
ma-99	349	9	.	.	PUNCT
ma-99	350	1	.	.	PUNCT
ma-99	351	1	,	,	PUNCT
ma-99	351	2	n.	n.	PROPN
ma-99	351	3	note	note	VERB
ma-99	351	4	that	that	SCONJ
ma-99	351	5	1	1	NUM
ma-99	351	6	n	n	NUM
ma-99	351	7	n∑	n∑	NOUN
ma-99	351	8	i=1	i=1	PROPN
ma-99	351	9	i{0}(uti	i{0}(uti	PROPN
ma-99	351	10	)	)	PUNCT
ma-99	352	1	→	→	SYM
ma-99	352	2	a.s	a.s	PROPN
ma-99	352	3	.	.	PROPN
ma-99	352	4	e(i{0}v1	e(i{0}v1	PROPN
ma-99	352	5	)	)	PUNCT
ma-99	353	1	=	=	SYM
ma-99	353	2	p	p	X
ma-99	353	3	(	(	PUNCT
ma-99	353	4	v1	v1	NOUN
ma-99	353	5	=	=	SYM
ma-99	353	6	0	0	NUM
ma-99	353	7	)	)	PUNCT
ma-99	353	8	=	=	PRON
ma-99	353	9	e−λ	e−λ	NOUN
ma-99	353	10	as	as	ADP
ma-99	353	11	n	n	PROPN
ma-99	353	12	→∞.	→∞.	PROPN
ma-99	353	13	lln	lln	PROPN
ma-99	353	14	and	and	CCONJ
ma-99	353	15	clt	clt	PROPN
ma-99	353	16	and	and	CCONJ
ma-99	353	17	delta	delta	NOUN
ma-99	353	18	method	method	NOUN
ma-99	353	19	applied	apply	VERB
ma-99	353	20	to	to	ADP
ma-99	353	21	the	the	DET
ma-99	353	22	sequence	sequence	NOUN
ma-99	353	23	i{0}(uti	i{0}(uti	PROPN
ma-99	353	24	)	)	PUNCT
ma-99	353	25	,	,	PUNCT
ma-99	353	26	i	i	PRON
ma-99	353	27	=	=	NOUN
ma-99	353	28	1	1	NUM
ma-99	353	29	,	,	PUNCT
ma-99	353	30	2	2	NUM
ma-99	353	31	,	,	PUNCT
ma-99	353	32	.	.	PUNCT
ma-99	353	33	.	.	PUNCT
ma-99	354	1	.	.	PUNCT
ma-99	355	1	,	,	PUNCT
ma-99	355	2	n	n	PRON
ma-99	355	3	give	give	VERB
ma-99	355	4	the	the	DET
ma-99	355	5	results	result	NOUN
ma-99	355	6	.	.	PUNCT
ma-99	356	1	the	the	DET
ma-99	356	2	clt	clt	PROPN
ma-99	356	3	result	result	NOUN
ma-99	356	4	above	above	ADV
ma-99	356	5	allows	allow	VERB
ma-99	356	6	us	we	PRON
ma-99	356	7	to	to	PART
ma-99	356	8	construct	construct	VERB
ma-99	356	9	confidence	confidence	NOUN
ma-99	356	10	interval	interval	NOUN
ma-99	356	11	for	for	ADP
ma-99	356	12	the	the	DET
ma-99	356	13	jump	jump	NOUN
ma-99	356	14	rate	rate	NOUN
ma-99	356	15	λ	λ	PROPN
ma-99	356	16	.	.	PUNCT
ma-99	356	17	corollary	corollary	ADJ
ma-99	356	18	3.1	3.1	NUM
ma-99	356	19	a	a	DET
ma-99	356	20	100(1−	100(1−	NUM
ma-99	356	21	α)%	α)%	NOUN
ma-99	356	22	confidence	confidence	NOUN
ma-99	356	23	interval	interval	NOUN
ma-99	356	24	for	for	ADP
ma-99	356	25	λ	λ	PROPN
ma-99	356	26	is	be	AUX
ma-99	356	27	given	give	VERB
ma-99	356	28	by	by	ADP
ma-99	356	29	[	[	PUNCT
ma-99	356	30	n	n	NOUN
ma-99	356	31	t	t	NOUN
ma-99	357	1	−	−	PROPN
ma-99	357	2	z1−α	z1−α	PROPN
ma-99	357	3	2	2	NUM
ma-99	357	4	√	√	ADP
ma-99	357	5	1	1	NUM
ma-99	357	6	n	n	CCONJ
ma-99	357	7	−	−	NUM
ma-99	357	8	1	1	NUM
ma-99	357	9	t	t	NOUN
ma-99	357	10	,	,	PUNCT
ma-99	357	11	n	n	NOUN
ma-99	357	12	t	t	NOUN
ma-99	358	1	+	+	CCONJ
ma-99	358	2	z1−α	z1−α	PROPN
ma-99	358	3	2	2	NUM
ma-99	358	4	√	√	ADP
ma-99	358	5	1	1	NUM
ma-99	358	6	n	n	CCONJ
ma-99	358	7	−	−	NUM
ma-99	358	8	1	1	NUM
ma-99	358	9	t	t	NOUN
ma-99	358	10	]	]	PUNCT
ma-99	358	11	where	where	SCONJ
ma-99	358	12	z1−α	z1−α	PROPN
ma-99	358	13	2	2	NUM
ma-99	358	14	is	be	AUX
ma-99	358	15	the	the	DET
ma-99	358	16	(	(	PUNCT
ma-99	358	17	1−	1−	NUM
ma-99	358	18	α	α	NOUN
ma-99	358	19	2	2	X
ma-99	358	20	)	)	PUNCT
ma-99	358	21	-quantile	-quantile	NOUN
ma-99	358	22	of	of	ADP
ma-99	358	23	the	the	DET
ma-99	358	24	standard	standard	ADJ
ma-99	358	25	normal	normal	ADJ
ma-99	358	26	distribution	distribution	NOUN
ma-99	358	27	.	.	PUNCT
ma-99	359	1	we	we	PRON
ma-99	359	2	obtain	obtain	VERB
ma-99	359	3	the	the	DET
ma-99	359	4	strong	strong	ADJ
ma-99	359	5	consistency	consistency	NOUN
ma-99	359	6	and	and	CCONJ
ma-99	359	7	asymptotic	asymptotic	ADJ
ma-99	359	8	normality	normality	NOUN
ma-99	359	9	of	of	ADP
ma-99	359	10	the	the	DET
ma-99	359	11	mef	mef	NOUN
ma-99	359	12	estimator	estimator	NOUN
ma-99	359	13	.	.	PUNCT
ma-99	360	1	theorem	theorem	VERB
ma-99	360	2	3.2	3.2	NUM
ma-99	360	3	when	when	SCONJ
ma-99	360	4	α	α	PROPN
ma-99	360	5	=	=	SYM
ma-99	360	6	2	2	NUM
ma-99	360	7	,	,	PUNCT
ma-99	360	8	we	we	PRON
ma-99	360	9	have	have	VERB
ma-99	360	10	ρ̂n	ρ̂n	ADJ
ma-99	360	11	→a.s	→a.s	NUM
ma-99	360	12	.	.	PUNCT
ma-99	361	1	ρ	ρ	PROPN
ma-99	361	2	as	as	ADP
ma-99	361	3	n	n	PROPN
ma-99	361	4	→∞	→∞	PROPN
ma-99	361	5	√	√	PROPN
ma-99	361	6	n(ρ̂n	n(ρ̂n	NOUN
ma-99	361	7	−	−	NOUN
ma-99	361	8	ρ)→d	ρ)→d	NOUN
ma-99	361	9	n	n	PROPN
ma-99	361	10	(	(	PUNCT
ma-99	361	11	0	0	NUM
ma-99	361	12	,	,	PUNCT
ma-99	361	13	λ−i(1−	λ−i(1−	X
ma-99	361	14	e−ρ	e−ρ	PROPN
ma-99	361	15	)	)	PUNCT
ma-99	361	16	)	)	PUNCT
ma-99	361	17	as	as	ADP
ma-99	361	18	n	n	X
ma-99	361	19	→∞.	→∞.	SYM
ma-99	361	20	proof	proof	NOUN
ma-99	361	21	:	:	PUNCT
ma-99	361	22	by	by	ADP
ma-99	361	23	using	use	VERB
ma-99	361	24	the	the	DET
ma-99	361	25	fact	fact	NOUN
ma-99	361	26	that	that	SCONJ
ma-99	361	27	every	every	DET
ma-99	361	28	stationary	stationary	ADJ
ma-99	361	29	mixing	mixing	NOUN
ma-99	361	30	process	process	NOUN
ma-99	361	31	is	be	AUX
ma-99	361	32	ergodic	ergodic	ADJ
ma-99	361	33	,	,	PUNCT
ma-99	361	34	it	it	PRON
ma-99	361	35	is	be	AUX
ma-99	361	36	easy	easy	ADJ
ma-99	361	37	to	to	PART
ma-99	361	38	show	show	VERB
ma-99	361	39	that	that	SCONJ
ma-99	361	40	if	if	SCONJ
ma-99	361	41	utis	utis	NOUN
ma-99	361	42	a	a	DET
ma-99	361	43	stationary	stationary	ADJ
ma-99	361	44	ergodic	ergodic	ADJ
ma-99	361	45	o	o	ADJ
ma-99	361	46	-	-	PUNCT
ma-99	361	47	u	u	NOUN
ma-99	361	48	markov	markov	NOUN
ma-99	361	49	process	process	NOUN
ma-99	361	50	and	and	CCONJ
ma-99	361	51	ti	ti	NOUN
ma-99	361	52	is	be	AUX
ma-99	361	53	a	a	DET
ma-99	361	54	process	process	NOUN
ma-99	361	55	with	with	ADP
ma-99	361	56	nonnegative	nonnegative	ADJ
ma-99	361	57	i.i.d	i.i.d	PROPN
ma-99	361	58	.	.	PUNCT
ma-99	362	1	incrementswhich	incrementswhich	PROPN
ma-99	362	2	is	be	AUX
ma-99	362	3	independent	independent	ADJ
ma-99	362	4	of	of	ADP
ma-99	362	5	ut	ut	PROPN
ma-99	362	6	,	,	PUNCT
ma-99	362	7	then	then	ADV
ma-99	362	8	{	{	PUNCT
ma-99	362	9	uti	uti	PROPN
ma-99	362	10	,	,	PUNCT
ma-99	362	11	i	i	PRON
ma-99	362	12	≥	≥	VERB
ma-99	362	13	1	1	NUM
ma-99	362	14	}	}	PUNCT
ma-99	362	15	is	be	AUX
ma-99	362	16	a	a	DET
ma-99	362	17	stationary	stationary	ADJ
ma-99	362	18	ergodic	ergodic	ADJ
ma-99	362	19	markov	markov	NOUN
ma-99	362	20	process	process	NOUN
ma-99	362	21	.	.	PUNCT
ma-99	363	1	hence	hence	ADV
ma-99	363	2	{	{	PUNCT
ma-99	363	3	uti	uti	PROPN
ma-99	363	4	,	,	PUNCT
ma-99	363	5	i	i	PRON
ma-99	363	6	≥	≥	VERB
ma-99	363	7	1	1	NUM
ma-99	363	8	}	}	PUNCT
ma-99	363	9	is	be	AUX
ma-99	363	10	a	a	DET
ma-99	363	11	stationary	stationary	ADJ
ma-99	363	12	ergodic	ergodic	ADJ
ma-99	363	13	markov	markov	NOUN
ma-99	363	14	process	process	NOUN
ma-99	363	15	.	.	PUNCT
ma-99	364	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	364	2	eur	eur	PROPN
ma-99	364	3	.	.	PUNCT
ma-99	365	1	j.	j.	PROPN
ma-99	365	2	math	math	PROPN
ma-99	365	3	.	.	PUNCT
ma-99	366	1	anal	anal	PROPN
ma-99	366	2	.	.	PUNCT
ma-99	367	1	10.28924	10.28924	NUM
ma-99	367	2	/	/	SYM
ma-99	367	3	ada	ada	PROPN
ma-99	367	4	/	/	SYM
ma-99	367	5	ma.3.4	ma.3.4	PROPN
ma-99	367	6	15observe	15observe	PROPN
ma-99	367	7	that	that	DET
ma-99	367	8	uθi	uθi	PROPN
ma-99	367	9	(	(	PUNCT
ma-99	367	10	t	t	PROPN
ma-99	367	11	)	)	PUNCT
ma-99	367	12	:	:	PUNCT
ma-99	367	13	=	=	SYM
ma-99	367	14	vi	vi	PROPN
ma-99	367	15	is	be	AUX
ma-99	367	16	a	a	DET
ma-99	367	17	stationary	stationary	ADJ
ma-99	367	18	ergodic	ergodic	ADJ
ma-99	367	19	markov	markov	NOUN
ma-99	367	20	chain	chain	NOUN
ma-99	367	21	and	and	CCONJ
ma-99	367	22	vi	vi	NOUN
ma-99	367	23	∼	∼	NOUN
ma-99	367	24	n	n	CCONJ
ma-99	367	25	(	(	PUNCT
ma-99	367	26	0	0	NUM
ma-99	367	27	,	,	PUNCT
ma-99	367	28	σ2	σ2	NOUN
ma-99	367	29	)	)	PUNCT
ma-99	367	30	where	where	SCONJ
ma-99	367	31	σ2	σ2	PROPN
ma-99	367	32	isthe	isthe	ADJ
ma-99	367	33	variance	variance	NOUN
ma-99	367	34	of	of	ADP
ma-99	367	35	u0	u0	PROPN
ma-99	367	36	.	.	PUNCT
ma-99	368	1	thus	thus	ADV
ma-99	368	2	by	by	ADP
ma-99	368	3	slln	slln	NOUN
ma-99	368	4	for	for	ADP
ma-99	368	5	zero	zero	NUM
ma-99	368	6	mean	mean	PROPN
ma-99	368	7	square	square	PROPN
ma-99	368	8	integrable	integrable	ADJ
ma-99	368	9	martingales	martingale	NOUN
ma-99	368	10	,	,	PUNCT
ma-99	368	11	we	we	PRON
ma-99	368	12	have	have	VERB
ma-99	368	13	1	1	NUM
ma-99	368	14	n	n	NUM
ma-99	368	15	n∑	n∑	NOUN
ma-99	368	16	i=1	i=1	PUNCT
ma-99	369	1	uti−1	uti−1	PROPN
ma-99	369	2	uti	uti	PROPN
ma-99	369	3	→	→	SYM
ma-99	369	4	a.s	a.s	PROPN
ma-99	369	5	.	.	PROPN
ma-99	369	6	e(ut0ut1	e(ut0ut1	ADJ
ma-99	369	7	)	)	PUNCT
ma-99	369	8	=	=	SYM
ma-99	369	9	ρe(u2	ρe(u2	NUM
ma-99	369	10	t0	t0	PROPN
ma-99	369	11	)	)	PUNCT
ma-99	369	12	1	1	NUM
ma-99	370	1	n	n	NUM
ma-99	370	2	n∑	n∑	NOUN
ma-99	370	3	i=1	i=1	PROPN
ma-99	371	1	u2	u2	PROPN
ma-99	371	2	ti−1	ti−1	PROPN
ma-99	371	3	→a.s	→a.s	NUM
ma-99	371	4	.	.	PUNCT
ma-99	372	1	e(u2	e(u2	PROPN
ma-99	372	2	t0	t0	PROPN
ma-99	372	3	)	)	PUNCT
ma-99	372	4	thus	thus	ADV
ma-99	372	5	∑n	∑n	PROPN
ma-99	372	6	i=1	i=1	PROPN
ma-99	373	1	uti−1	uti−1	PROPN
ma-99	373	2	uti∑n	uti∑n	NOUN
ma-99	373	3	i=1	i=1	PROPN
ma-99	373	4	u	u	NOUN
ma-99	373	5	2	2	NUM
ma-99	373	6	ti−1	ti−1	NOUN
ma-99	373	7	→a.s	→a.s	NUM
ma-99	373	8	.	.	PUNCT
ma-99	374	1	ρ	ρ	PROPN
ma-99	374	2	.	.	PUNCT
ma-99	375	1	further	far	ADV
ma-99	375	2	,	,	PUNCT
ma-99	375	3	√	√	PRON
ma-99	375	4	n(ρ̂n	n(ρ̂n	NOUN
ma-99	375	5	−	−	PROPN
ma-99	375	6	ρ	ρ	NOUN
ma-99	375	7	)	)	PUNCT
ma-99	375	8	=	=	VERB
ma-99	376	1	n−1/2	n−1/2	PROPN
ma-99	376	2	∑n	∑n	NOUN
ma-99	376	3	i=1	i=1	PROPN
ma-99	377	1	uti−1	uti−1	PROPN
ma-99	377	2	(	(	PUNCT
ma-99	377	3	uti	uti	PROPN
ma-99	377	4	−	−	PROPN
ma-99	377	5	θuti−1	θuti−1	PROPN
ma-99	377	6	)	)	PUNCT
ma-99	378	1	n−1	n−1	PROPN
ma-99	378	2	∑n	∑n	PROPN
ma-99	378	3	i=1	i=1	PROPN
ma-99	378	4	u	u	NOUN
ma-99	378	5	2	2	NUM
ma-99	378	6	ti−1	ti−1	NOUN
ma-99	378	7	.	.	PUNCT
ma-99	379	1	since	since	SCONJ
ma-99	379	2	e(ut1ut2	e(ut1ut2	NOUN
ma-99	379	3	|ut1	|ut1	PROPN
ma-99	379	4	)	)	PUNCT
ma-99	379	5	=	=	PUNCT
ma-99	379	6	θu2	θu2	NOUN
ma-99	379	7	t1it	t1it	NOUN
ma-99	379	8	follows	follow	VERB
ma-99	379	9	by	by	ADP
ma-99	379	10	lemma	lemma	PROPN
ma-99	379	11	3.1	3.1	NUM
ma-99	379	12	in	in	ADP
ma-99	379	13	bibby	bibby	PROPN
ma-99	379	14	and	and	CCONJ
ma-99	379	15	srensen	srensen	NOUN
ma-99	380	1	[	[	X
ma-99	380	2	2	2	NUM
ma-99	380	3	]	]	PUNCT
ma-99	380	4	n−1/2	n−1/2	PROPN
ma-99	380	5	n∑	n∑	NOUN
ma-99	380	6	i=1	i=1	PROPN
ma-99	381	1	uti−1	uti−1	PROPN
ma-99	381	2	(	(	PUNCT
ma-99	381	3	uti	uti	PROPN
ma-99	381	4	−	−	PROPN
ma-99	381	5	θuti−1	θuti−1	PROPN
ma-99	381	6	)	)	PUNCT
ma-99	381	7	converges	converge	VERB
ma-99	381	8	in	in	ADP
ma-99	381	9	distribution	distribution	NOUN
ma-99	381	10	to	to	ADP
ma-99	381	11	normal	normal	ADJ
ma-99	381	12	distribution	distribution	NOUN
ma-99	381	13	with	with	ADP
ma-99	381	14	mean	mean	NOUN
ma-99	381	15	zero	zero	NUM
ma-99	381	16	and	and	CCONJ
ma-99	381	17	variance	variance	NOUN
ma-99	381	18	equal	equal	ADJ
ma-99	381	19	to	to	ADP
ma-99	381	20	e[(ut1ut2	e[(ut1ut2	NOUN
ma-99	381	21	)	)	PUNCT
ma-99	381	22	−	−	PROPN
ma-99	381	23	e(ut1ut2	e(ut1ut2	NOUN
ma-99	381	24	|ut1	|ut1	PROPN
ma-99	381	25	)	)	PUNCT
ma-99	381	26	]	]	SYM
ma-99	381	27	2	2	X
ma-99	381	28	=	=	SYM
ma-99	381	29	1−	1−	NUM
ma-99	381	30	e2(θ−βiδ){2(βi	e2(θ−βiδ){2(βi	NUM
ma-99	381	31	−	−	PROPN
ma-99	381	32	θ)(βi	θ)(βi	PRON
ma-99	382	1	+	+	CCONJ
ma-99	382	2	1)}−1	1)}−1	ADJ
ma-99	382	3	.	.	PUNCT
ma-99	383	1	applying	apply	VERB
ma-99	383	2	delta	delta	NOUN
ma-99	383	3	method	method	NOUN
ma-99	383	4	the	the	DET
ma-99	383	5	result	result	NOUN
ma-99	383	6	follows	follow	VERB
ma-99	383	7	.	.	PUNCT
ma-99	384	1	in	in	ADP
ma-99	384	2	the	the	DET
ma-99	384	3	next	next	ADJ
ma-99	384	4	step	step	NOUN
ma-99	384	5	,	,	PUNCT
ma-99	384	6	we	we	PRON
ma-99	384	7	use	use	VERB
ma-99	384	8	the	the	DET
ma-99	384	9	estimator	estimator	NOUN
ma-99	384	10	of	of	ADP
ma-99	384	11	λ	λ	PROPN
ma-99	384	12	to	to	PART
ma-99	384	13	estimate	estimate	VERB
ma-99	384	14	θ.note	θ.note	PRON
ma-99	384	15	that	that	SCONJ
ma-99	384	16	1	1	NUM
ma-99	384	17	ρ̂n	ρ̂n	NOUN
ma-99	384	18	=	=	SYM
ma-99	384	19	∑n	∑n	PROPN
ma-99	384	20	i=1	i=1	PROPN
ma-99	384	21	u	u	NOUN
ma-99	384	22	2	2	NUM
ma-99	384	23	ti−1∑n	ti−1∑n	NOUN
ma-99	384	24	i=1	i=1	X
ma-99	385	1	uti−1	uti−1	PROPN
ma-99	385	2	uti	uti	PROPN
ma-99	385	3	.	.	PUNCT
ma-99	386	1	thus	thus	ADV
ma-99	386	2	1	1	NUM
ma-99	386	3	+	+	NUM
ma-99	386	4	β2	β2	ADJ
ma-99	386	5	m	m	NOUN
ma-99	386	6	1	1	NUM
ma-99	386	7	−	−	PROPN
ma-99	386	8	κ(θ	κ(θ	PROPN
ma-99	386	9	)	)	PUNCT
ma-99	386	10	λ	λ	NOUN
ma-99	387	1	=	=	SYM
ma-99	387	2	∑n	∑n	PROPN
ma-99	387	3	i=1	i=1	PROPN
ma-99	387	4	u	u	NOUN
ma-99	387	5	2	2	NUM
ma-99	387	6	ti−1∑n	ti−1∑n	NOUN
ma-99	387	7	i=1	i=1	X
ma-99	388	1	uti−1	uti−1	ADP
ma-99	388	2	utiwhich	utiwhich	NOUN
ma-99	388	3	gives	give	VERB
ma-99	388	4	β2	β2	PROPN
ma-99	388	5	m	m	PROPN
ma-99	388	6	1	1	NUM
ma-99	388	7	−	−	PROPN
ma-99	388	8	κ(θ	κ(θ	PROPN
ma-99	388	9	)	)	PUNCT
ma-99	388	10	λ	λ	NOUN
ma-99	389	1	=	=	SYM
ma-99	389	2	∑n	∑n	PROPN
ma-99	389	3	i=1	i=1	PROPN
ma-99	389	4	u	u	NOUN
ma-99	389	5	2	2	NUM
ma-99	389	6	ti−1∑n	ti−1∑n	NOUN
ma-99	389	7	i=1	i=1	PUNCT
ma-99	390	1	uti−1	uti−1	PROPN
ma-99	390	2	uti	uti	PROPN
ma-99	390	3	−	−	PROPN
ma-99	391	1	1	1	NUM
ma-99	391	2	=	=	SYM
ma-99	391	3	−	−	PROPN
ma-99	391	4	∑n	∑n	PROPN
ma-99	391	5	i=1	i=1	PROPN
ma-99	392	1	uti−1	uti−1	PROPN
ma-99	393	1	[	[	X
ma-99	393	2	uti	uti	PROPN
ma-99	393	3	−	−	PROPN
ma-99	394	1	uti−1	uti−1	PROPN
ma-99	394	2	]	]	SYM
ma-99	394	3	∑n	∑n	PROPN
ma-99	394	4	i=1	i=1	PROPN
ma-99	394	5	uti−1	uti−1	PROPN
ma-99	394	6	utinow	utinow	NOUN
ma-99	394	7	replace	replace	NOUN
ma-99	394	8	λ	λ	NOUN
ma-99	394	9	by	by	ADP
ma-99	394	10	its	its	PRON
ma-99	394	11	estimator	estimator	NOUN
ma-99	394	12	mle	mle	PROPN
ma-99	394	13	λ̂n	λ̂n	PROPN
ma-99	394	14	.	.	PUNCT
ma-99	395	1	β2	β2	PROPN
ma-99	395	2	m	m	PROPN
ma-99	395	3	1	1	NUM
ma-99	395	4	−	−	PROPN
ma-99	395	5	κ(θ	κ(θ	PROPN
ma-99	395	6	)	)	PUNCT
ma-99	396	1	=	=	PUNCT
ma-99	397	1	−	−	PROPN
ma-99	397	2	∑n	∑n	PROPN
ma-99	397	3	i=1	i=1	PROPN
ma-99	398	1	uti−1	uti−1	PROPN
ma-99	399	1	[	[	X
ma-99	399	2	uti	uti	PROPN
ma-99	399	3	−	−	PROPN
ma-99	400	1	uti−1	uti−1	PROPN
ma-99	400	2	]	]	PUNCT
ma-99	400	3	t	t	PROPN
ma-99	400	4	n	n	PROPN
ma-99	400	5	∑n	∑n	PROPN
ma-99	400	6	i=1	i=1	X
ma-99	401	1	uti−1	uti−1	PROPN
ma-99	401	2	utithus	utithus	NOUN
ma-99	401	3	θ̂n	θ̂n	ADP
ma-99	401	4	=	=	PUNCT
ma-99	401	5	κ−1	κ−1	PROPN
ma-99	401	6	(	(	PUNCT
ma-99	401	7	β2	β2	NOUN
ma-99	401	8	m	m	PROPN
ma-99	401	9	i	i	PRON
ma-99	401	10	+	+	NUM
ma-99	401	11	∑n	∑n	PROPN
ma-99	402	1	i=1	i=1	X
ma-99	402	2	uti−1	uti−1	PROPN
ma-99	403	1	[	[	X
ma-99	403	2	uti	uti	PROPN
ma-99	403	3	−	−	PROPN
ma-99	404	1	uti−1	uti−1	PROPN
ma-99	404	2	]	]	PUNCT
ma-99	404	3	t	t	PROPN
ma-99	404	4	n	n	PROPN
ma-99	404	5	∑n	∑n	PROPN
ma-99	404	6	i=1	i=1	PROPN
ma-99	405	1	uti−1	uti−1	PROPN
ma-99	405	2	uti	uti	PROPN
ma-99	405	3	)	)	PUNCT
ma-99	405	4	.	.	PUNCT
ma-99	406	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	406	2	eur	eur	PROPN
ma-99	406	3	.	.	PUNCT
ma-99	407	1	j.	j.	PROPN
ma-99	407	2	math	math	PROPN
ma-99	407	3	.	.	PUNCT
ma-99	408	1	anal	anal	PROPN
ma-99	408	2	.	.	PUNCT
ma-99	409	1	10.28924	10.28924	NUM
ma-99	409	2	/	/	SYM
ma-99	409	3	ada	ada	PROPN
ma-99	409	4	/	/	SYM
ma-99	409	5	ma.3.4	ma.3.4	PROPN
ma-99	409	6	16since	16since	NUM
ma-99	409	7	the	the	DET
ma-99	409	8	function	function	NOUN
ma-99	409	9	κ−1	κ−1	PROPN
ma-99	409	10	(	(	PUNCT
ma-99	409	11	·	·	PUNCT
ma-99	409	12	)	)	PUNCT
ma-99	409	13	is	be	AUX
ma-99	409	14	a	a	DET
ma-99	409	15	continuous	continuous	ADJ
ma-99	409	16	function	function	NOUN
ma-99	409	17	,	,	PUNCT
ma-99	409	18	by	by	ADP
ma-99	409	19	application	application	NOUN
ma-99	409	20	of	of	ADP
ma-99	409	21	delta	delta	PROPN
ma-99	409	22	method	method	NOUN
ma-99	409	23	,	,	PUNCT
ma-99	409	24	the	the	DET
ma-99	409	25	followingresult	followingresult	NOUN
ma-99	409	26	is	be	AUX
ma-99	409	27	a	a	DET
ma-99	409	28	consequence	consequence	NOUN
ma-99	409	29	of	of	ADP
ma-99	409	30	theorem	theorem	ADJ
ma-99	409	31	3.2	3.2	NUM
ma-99	409	32	.	.	PUNCT
ma-99	410	1	theorem	theorem	VERB
ma-99	410	2	3.3	3.3	NUM
ma-99	410	3	when	when	SCONJ
ma-99	410	4	α	α	NOUN
ma-99	410	5	=	=	SYM
ma-99	410	6	2	2	NUM
ma-99	410	7	,	,	PUNCT
ma-99	410	8	a	a	PRON
ma-99	410	9	)	)	PUNCT
ma-99	410	10	θ̂n	θ̂n	NUM
ma-99	410	11	→	→	PUNCT
ma-99	410	12	θ	θ	PROPN
ma-99	410	13	a.s	a.s	PROPN
ma-99	410	14	.	.	PROPN
ma-99	410	15	as	as	ADP
ma-99	410	16	n	n	PROPN
ma-99	410	17	→∞	→∞	PROPN
ma-99	410	18	b	b	PROPN
ma-99	410	19	)	)	PUNCT
ma-99	410	20	√	√	PROPN
ma-99	411	1	n(θ̂n	n(θ̂n	NUM
ma-99	411	2	−	−	PROPN
ma-99	411	3	θ)→d	θ)→d	NOUN
ma-99	411	4	n	n	X
ma-99	411	5	(	(	PUNCT
ma-99	411	6	0	0	NUM
ma-99	411	7	,	,	PUNCT
ma-99	411	8	(	(	PUNCT
ma-99	411	9	κ′(θ))−2λ2(1−	κ′(θ))−2λ2(1−	NUM
ma-99	411	10	e−2λ−1(κ(θ)−β2	e−2λ−1(κ(θ)−β2	NUM
ma-99	411	11	m	m	NOUN
ma-99	411	12	1	1	NUM
ma-99	411	13	)	)	PUNCT
ma-99	411	14	)	)	PUNCT
ma-99	411	15	)	)	PUNCT
ma-99	412	1	as	as	ADP
ma-99	412	2	n	n	PROPN
ma-99	412	3	→∞.in	→∞.in	PROPN
ma-99	412	4	the	the	DET
ma-99	412	5	second	second	ADJ
ma-99	412	6	stage	stage	NOUN
ma-99	412	7	,	,	PUNCT
ma-99	412	8	we	we	PRON
ma-99	412	9	substitute	substitute	VERB
ma-99	412	10	λ	λ	NOUN
ma-99	412	11	by	by	ADP
ma-99	412	12	its	its	PRON
ma-99	412	13	estimator	estimator	NOUN
ma-99	412	14	λ̂n	λ̂n	PROPN
ma-99	412	15	.	.	PUNCT
ma-99	412	16	theorem	theorem	VERB
ma-99	412	17	3.4	3.4	NUM
ma-99	412	18	when	when	SCONJ
ma-99	412	19	0	0	NUM
ma-99	412	20	<	<	X
ma-99	412	21	α	α	X
ma-99	412	22	<	<	X
ma-99	412	23	2	2	NUM
ma-99	412	24	,	,	PUNCT
ma-99	412	25	a	a	PRON
ma-99	412	26	)	)	PUNCT
ma-99	412	27	θ̂n	θ̂n	ADP
ma-99	412	28	→a.s	→a.s	X
ma-99	412	29	.	.	PUNCT
ma-99	413	1	θ	θ	PROPN
ma-99	413	2	as	as	ADP
ma-99	413	3	n	n	PROPN
ma-99	413	4	→∞	→∞	PROPN
ma-99	413	5	b	b	PROPN
ma-99	413	6	)	)	PUNCT
ma-99	413	7	n(α−1)/α2	n(α−1)/α2	NUM
ma-99	413	8	(	(	PUNCT
ma-99	413	9	θ̂n	θ̂n	NUM
ma-99	413	10	−	−	PROPN
ma-99	413	11	θ)→d	θ)→d	NOUN
ma-99	413	12	(	(	PUNCT
ma-99	413	13	κ′(θ))−2λ2(1−	κ′(θ))−2λ2(1−	NUM
ma-99	413	14	e−2λ−1(κ(θ)−β2	e−2λ−1(κ(θ)−β2	NUM
ma-99	413	15	m	m	NOUN
ma-99	413	16	1	1	NUM
ma-99	413	17	)	)	PUNCT
ma-99	413	18	)	)	PUNCT
ma-99	413	19	1	1	X
ma-99	413	20	/	/	SYM
ma-99	413	21	α	α	PROPN
ma-99	413	22	s4	s4	PROPN
ma-99	413	23	s3	s3	PROPN
ma-99	413	24	as	as	ADP
ma-99	413	25	n	n	NUM
ma-99	413	26	→∞.where	→∞.where	X
ma-99	413	27	s4	s4	PROPN
ma-99	413	28	and	and	CCONJ
ma-99	413	29	s3	s3	PROPN
ma-99	413	30	are	be	AUX
ma-99	413	31	independent	independent	ADJ
ma-99	413	32	stable	stable	ADJ
ma-99	413	33	random	random	ADJ
ma-99	413	34	variables	variable	NOUN
ma-99	413	35	.	.	PUNCT
ma-99	414	1	in	in	ADP
ma-99	414	2	the	the	DET
ma-99	414	3	second	second	ADJ
ma-99	414	4	stage	stage	NOUN
ma-99	414	5	,	,	PUNCT
ma-99	414	6	we	we	PRON
ma-99	414	7	substitute	substitute	VERB
ma-99	414	8	λ	λ	NOUN
ma-99	414	9	by	by	ADP
ma-99	414	10	its	its	PRON
ma-99	414	11	estimator	estimator	NOUN
ma-99	414	12	λ̂n	λ̂n	PROPN
ma-99	414	13	.	.	PUNCT
ma-99	415	1	the	the	DET
ma-99	415	2	limit	limit	NOUN
ma-99	415	3	distribution	distribution	NOUN
ma-99	415	4	is	be	AUX
ma-99	415	5	normal	normal	ADJ
ma-99	415	6	onlyin	onlyin	NOUN
ma-99	415	7	the	the	DET
ma-99	415	8	gaussian	gaussian	ADJ
ma-99	415	9	case	case	NOUN
ma-99	415	10	α	α	X
ma-99	415	11	=	=	SYM
ma-99	415	12	2	2	NUM
ma-99	415	13	.	.	NOUN
ma-99	415	14	4	4	NUM
ma-99	415	15	.	.	X
ma-99	415	16	spdes	spde	NOUN
ma-99	415	17	with	with	ADP
ma-99	415	18	linear	linear	PROPN
ma-99	415	19	multiplicative	multiplicative	ADJ
ma-99	415	20	noise	noise	NOUN
ma-99	415	21	consider	consider	VERB
ma-99	415	22	the	the	DET
ma-99	415	23	spde	spde	NOUN
ma-99	415	24	with	with	ADP
ma-99	415	25	multiplicative	multiplicative	ADJ
ma-99	415	26	noise	noise	NOUN
ma-99	415	27	:	:	PUNCT
ma-99	415	28	duθ(t	duθ(t	PROPN
ma-99	415	29	,	,	PUNCT
ma-99	415	30	x	x	NOUN
ma-99	415	31	)	)	PUNCT
ma-99	415	32	=	=	SYM
ma-99	415	33	(	(	PUNCT
ma-99	415	34	a0	a0	PROPN
ma-99	415	35	+	+	CCONJ
ma-99	415	36	θa1)uθ(t	θa1)uθ(t	PROPN
ma-99	415	37	,	,	PUNCT
ma-99	415	38	x)dt	x)dt	PROPN
ma-99	415	39	+	+	PROPN
ma-99	415	40	muθ(t	muθ(t	PROPN
ma-99	415	41	,	,	PUNCT
ma-99	415	42	x)dz(t	x)dz(t	PROPN
ma-99	415	43	,	,	PUNCT
ma-99	415	44	x	x	X
ma-99	415	45	)	)	PUNCT
ma-99	415	46	,	,	PUNCT
ma-99	416	1	t	t	PROPN
ma-99	416	2	≥	≥	NUM
ma-99	416	3	0	0	NUM
ma-99	416	4	,	,	PUNCT
ma-99	416	5	x	x	SYM
ma-99	416	6	∈	∈	PROPN
ma-99	416	7	[	[	X
ma-99	416	8	0	0	NUM
ma-99	416	9	,	,	PUNCT
ma-99	416	10	1	1	NUM
ma-99	416	11	]	]	PUNCT
ma-99	416	12	(	(	PUNCT
ma-99	416	13	4.1	4.1	NUM
ma-99	416	14	)	)	PUNCT
ma-99	416	15	where	where	SCONJ
ma-99	416	16	m	m	NOUN
ma-99	416	17	is	be	AUX
ma-99	416	18	a	a	DET
ma-99	416	19	known	know	VERB
ma-99	416	20	linear	linear	NOUN
ma-99	416	21	operator.equation	operator.equation	NUM
ma-99	416	22	(	(	PUNCT
ma-99	416	23	4.1	4.1	NUM
ma-99	416	24	)	)	PUNCT
ma-99	416	25	is	be	AUX
ma-99	416	26	called	call	VERB
ma-99	416	27	diagonalizable	diagonalizable	ADJ
ma-99	416	28	if	if	SCONJ
ma-99	416	29	a0	a0	PROPN
ma-99	416	30	,	,	PUNCT
ma-99	416	31	a1	a1	NOUN
ma-99	416	32	and	and	CCONJ
ma-99	416	33	m	m	VERB
ma-99	416	34	have	have	AUX
ma-99	416	35	point	point	NOUN
ma-99	416	36	spectrum	spectrum	NOUN
ma-99	416	37	and	and	CCONJ
ma-99	416	38	a	a	DET
ma-99	416	39	commonsystem	commonsystem	NOUN
ma-99	416	40	of	of	ADP
ma-99	416	41	eigenfunction	eigenfunction	NOUN
ma-99	416	42	{	{	PUNCT
ma-99	416	43	hj	hj	PROPN
ma-99	416	44	,	,	PUNCT
ma-99	416	45	j	j	PROPN
ma-99	416	46	≥	≥	PROPN
ma-99	416	47	1	1	NUM
ma-99	416	48	}	}	PUNCT
ma-99	416	49	.	.	PUNCT
ma-99	417	1	denote	denote	VERB
ma-99	417	2	by	by	ADP
ma-99	417	3	ρk	ρk	PRON
ma-99	417	4	,	,	PUNCT
ma-99	417	5	νk	νk	NOUN
ma-99	417	6	and	and	CCONJ
ma-99	417	7	µk	µk	INTJ
ma-99	417	8	,	,	PUNCT
ma-99	417	9	the	the	DET
ma-99	417	10	eigenvalues	eigenvalue	NOUN
ma-99	417	11	of	of	ADP
ma-99	417	12	the	the	DET
ma-99	417	13	operators	operator	NOUN
ma-99	417	14	a0	a0	PROPN
ma-99	417	15	,	,	PUNCT
ma-99	417	16	a1	a1	NOUN
ma-99	417	17	and	and	CCONJ
ma-99	417	18	m	m	NOUN
ma-99	417	19	respectively.then	respectively.then	ADV
ma-99	417	20	uθ(t	uθ(t	NOUN
ma-99	417	21	,	,	PUNCT
ma-99	417	22	x	x	NOUN
ma-99	417	23	)	)	PUNCT
ma-99	417	24	=	=	PUNCT
ma-99	418	1	∑	∑	PROPN
ma-99	418	2	j≥1	j≥1	PROPN
ma-99	418	3	uj	uj	PROPN
ma-99	418	4	,	,	PUNCT
ma-99	418	5	thj	thj	PROPN
ma-99	418	6	.	.	PUNCT
ma-99	419	1	the	the	DET
ma-99	419	2	fourier	fourier	ADJ
ma-99	419	3	coefficients	coefficient	NOUN
ma-99	419	4	have	have	VERB
ma-99	419	5	the	the	DET
ma-99	419	6	dynamics	dynamic	NOUN
ma-99	419	7	duk(t	duk(t	PROPN
ma-99	419	8	)	)	PUNCT
ma-99	419	9	=	=	PUNCT
ma-99	420	1	(	(	PUNCT
ma-99	420	2	θνk	θνk	VERB
ma-99	420	3	+	+	CCONJ
ma-99	420	4	ρk)uk(t)dt	ρk)uk(t)dt	PROPN
ma-99	420	5	+	+	X
ma-99	420	6	σkuk(t)dzk(t	σkuk(t)dzk(t	NOUN
ma-99	420	7	)	)	PUNCT
ma-99	420	8	,	,	PUNCT
ma-99	420	9	k	k	PROPN
ma-99	420	10	≥	≥	NUM
ma-99	420	11	1	1	NUM
ma-99	420	12	which	which	PRON
ma-99	420	13	is	be	AUX
ma-99	420	14	the	the	DET
ma-99	420	15	stable	stable	ADJ
ma-99	420	16	black	black	ADJ
ma-99	420	17	-	-	PUNCT
ma-99	420	18	scholes	schole	NOUN
ma-99	420	19	model	model	NOUN
ma-99	420	20	whose	whose	DET
ma-99	420	21	solution	solution	NOUN
ma-99	420	22	is	be	AUX
ma-99	420	23	geometric	geometric	ADJ
ma-99	420	24	stable	stable	ADJ
ma-99	420	25	process.let	process.let	NOUN
ma-99	420	26	θνk	θνk	VERB
ma-99	421	1	+	+	CCONJ
ma-99	421	2	ρk	ρk	NOUN
ma-99	421	3	=	=	NOUN
ma-99	421	4	:	:	PUNCT
ma-99	421	5	µk(θ	µk(θ	NOUN
ma-99	421	6	)	)	PUNCT
ma-99	421	7	,	,	PUNCT
ma-99	421	8	ṽk	ṽk	NOUN
ma-99	421	9	,	,	PUNCT
ma-99	421	10	t	t	NOUN
ma-99	421	11	:	:	PUNCT
ma-99	421	12	=	=	SYM
ma-99	421	13	ln(uk	ln(uk	PROPN
ma-99	421	14	,	,	PUNCT
ma-99	421	15	t	t	PROPN
ma-99	421	16	/uk,0).conditional	/uk,0).conditional	ADJ
ma-99	421	17	characteristic	characteristic	ADJ
ma-99	421	18	function	function	NOUN
ma-99	421	19	(	(	PUNCT
ma-99	421	20	ccf	ccf	PROPN
ma-99	421	21	)	)	PUNCT
ma-99	421	22	estimator	estimator	NOUN
ma-99	421	23	is	be	AUX
ma-99	421	24	given	give	VERB
ma-99	421	25	by	by	ADP
ma-99	421	26	µ̂k(θ	µ̂k(θ	PROPN
ma-99	421	27	)	)	PUNCT
ma-99	422	1	=	=	PUNCT
ma-99	422	2	ṽk	ṽk	NOUN
ma-99	422	3	,	,	PUNCT
ma-99	422	4	t	t	PROPN
ma-99	422	5	t	t	PROPN
ma-99	422	6	2(α−1)/α2	2(α−1)/α2	NUM
ma-99	422	7	+	+	PROPN
ma-99	422	8	σ2	σ2	PROPN
ma-99	422	9	k	k	PROPN
ma-99	422	10	b1t−((α−1)2	b1t−((α−1)2	PROPN
ma-99	422	11	+	+	PROPN
ma-99	422	12	1)/α2	1)/α2	NUM
ma-99	422	13	.	.	PUNCT
ma-99	423	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	423	2	eur	eur	PROPN
ma-99	423	3	.	.	PUNCT
ma-99	424	1	j.	j.	PROPN
ma-99	424	2	math	math	PROPN
ma-99	424	3	.	.	PUNCT
ma-99	425	1	anal	anal	PROPN
ma-99	425	2	.	.	PUNCT
ma-99	426	1	10.28924	10.28924	NUM
ma-99	426	2	/	/	SYM
ma-99	426	3	ada	ada	PROPN
ma-99	426	4	/	/	SYM
ma-99	426	5	ma.3.4	ma.3.4	PROPN
ma-99	426	6	17since	17since	NUM
ma-99	426	7	µk(θ	µk(θ	NOUN
ma-99	426	8	)	)	PUNCT
ma-99	426	9	is	be	AUX
ma-99	426	10	strictly	strictly	ADV
ma-99	426	11	monotone	monotone	ADJ
ma-99	426	12	function	function	NOUN
ma-99	426	13	of	of	ADP
ma-99	426	14	θ	θ	PROPN
ma-99	426	15	,	,	PUNCT
ma-99	426	16	by	by	ADP
ma-99	426	17	invariance	invariance	NOUN
ma-99	426	18	principle	principle	NOUN
ma-99	426	19	of	of	ADP
ma-99	426	20	ccfe	ccfe	NOUN
ma-99	426	21	,	,	PUNCT
ma-99	426	22	under	under	ADP
ma-99	426	23	invertibletransformations	invertibletransformation	NOUN
ma-99	426	24	,	,	PUNCT
ma-99	426	25	we	we	PRON
ma-99	426	26	can	can	AUX
ma-99	426	27	find	find	VERB
ma-99	426	28	the	the	DET
ma-99	426	29	ccfe	ccfe	NOUN
ma-99	426	30	of	of	ADP
ma-99	426	31	the	the	DET
ma-99	426	32	parameter	parameter	NOUN
ma-99	426	33	θ	θ	PROPN
ma-99	426	34	θ̂k	θ̂k	PROPN
ma-99	426	35	,	,	PUNCT
ma-99	426	36	t	t	NOUN
ma-99	426	37	=	=	SYM
ma-99	426	38	ṽk	ṽk	NOUN
ma-99	426	39	,	,	PUNCT
ma-99	426	40	t	t	PROPN
ma-99	426	41	νkt	νkt	PROPN
ma-99	426	42	2(α−1)/α2	2(α−1)/α2	NUM
ma-99	426	43	+	+	PROPN
ma-99	426	44	σ2	σ2	PROPN
ma-99	426	45	k	k	PROPN
ma-99	426	46	b1νkt−((α−1)2	b1νkt−((α−1)2	PROPN
ma-99	426	47	+	+	PROPN
ma-99	426	48	1)/α2	1)/α2	NUM
ma-99	426	49	−	−	NOUN
ma-99	426	50	ρk	ρk	ADP
ma-99	426	51	νkwhich	νkwhich	NOUN
ma-99	426	52	can	can	AUX
ma-99	426	53	be	be	AUX
ma-99	426	54	represented	represent	VERB
ma-99	426	55	as	as	ADP
ma-99	426	56	θ̂k	θ̂k	NOUN
ma-99	426	57	,	,	PUNCT
ma-99	426	58	t	t	NOUN
ma-99	426	59	=	=	SYM
ma-99	426	60	θ0	θ0	PROPN
ma-99	426	61	+	+	CCONJ
ma-99	426	62	σkmt	σkmt	PROPN
ma-99	426	63	νkt	νkt	PROPN
ma-99	426	64	2(α−1)/α2where	2(α−1)/α2where	PROPN
ma-99	426	65	mt	mt	PROPN
ma-99	426	66	is	be	AUX
ma-99	426	67	a	a	DET
ma-99	426	68	square	square	ADJ
ma-99	426	69	-	-	PUNCT
ma-99	426	70	integrable	integrable	ADJ
ma-99	426	71	martingale	martingale	NOUN
ma-99	426	72	.	.	PUNCT
ma-99	427	1	due	due	ADP
ma-99	427	2	to	to	ADP
ma-99	427	3	the	the	DET
ma-99	427	4	lln	lln	NOUN
ma-99	427	5	for	for	ADP
ma-99	427	6	martingales	martingale	NOUN
ma-99	427	7	,	,	PUNCT
ma-99	427	8	we	we	PRON
ma-99	427	9	have	have	AUX
ma-99	427	10	strongconsistency.note	strongconsistency.note	VERB
ma-99	427	11	that	that	PRON
ma-99	427	12	in	in	ADP
ma-99	427	13	the	the	DET
ma-99	427	14	standard	standard	ADJ
ma-99	427	15	black	black	ADJ
ma-99	427	16	-	-	PUNCT
ma-99	427	17	scholes	schole	NOUN
ma-99	427	18	case	case	NOUN
ma-99	427	19	where	where	SCONJ
ma-99	427	20	α	α	NOUN
ma-99	427	21	=	=	SYM
ma-99	427	22	2	2	NUM
ma-99	427	23	,	,	PUNCT
ma-99	427	24	σk	σk	ADV
ma-99	427	25	=	=	PROPN
ma-99	427	26	σ	σ	PROPN
ma-99	427	27	,	,	PUNCT
ma-99	427	28	the	the	DET
ma-99	427	29	mle	mle	NOUN
ma-99	427	30	of	of	ADP
ma-99	427	31	the	the	DET
ma-99	427	32	driftcoefficient	driftcoefficient	NOUN
ma-99	427	33	of	of	ADP
ma-99	427	34	the	the	DET
ma-99	427	35	geometric	geometric	ADJ
ma-99	427	36	brownian	brownian	ADJ
ma-99	427	37	motion	motion	NOUN
ma-99	427	38	is	be	AUX
ma-99	427	39	given	give	VERB
ma-99	427	40	by	by	ADP
ma-99	427	41	θ̂t	θ̂t	X
ma-99	427	42	=	=	ADJ
ma-99	427	43	ln(ut	ln(ut	PROPN
ma-99	427	44	/u0	/u0	PUNCT
ma-99	427	45	)	)	PUNCT
ma-99	427	46	t	t	PROPN
ma-99	428	1	+	+	CCONJ
ma-99	428	2	σ2	σ2	NOUN
ma-99	428	3	2	2	NUM
ma-99	428	4	=	=	SYM
ma-99	428	5	θ0	θ0	PROPN
ma-99	428	6	+	+	X
ma-99	428	7	σ	σ	PROPN
ma-99	428	8	wt	wt	PROPN
ma-99	428	9	t	t	NOUN
ma-99	428	10	.	.	PUNCT
ma-99	429	1	due	due	ADP
ma-99	429	2	to	to	ADP
ma-99	429	3	the	the	DET
ma-99	429	4	law	law	NOUN
ma-99	429	5	of	of	ADP
ma-99	429	6	iterated	iterated	ADJ
ma-99	429	7	logarithm	logarithm	NOUN
ma-99	429	8	for	for	ADP
ma-99	429	9	brownian	brownian	ADJ
ma-99	429	10	motion	motion	NOUN
ma-99	429	11	,	,	PUNCT
ma-99	429	12	the	the	DET
ma-99	429	13	mle	mle	PROPN
ma-99	429	14	is	be	AUX
ma-99	429	15	strongly	strongly	ADV
ma-99	429	16	consistent	consistent	ADJ
ma-99	429	17	as	as	ADP
ma-99	429	18	t	t	PROPN
ma-99	429	19	→∞.	→∞.	PUNCT
ma-99	429	20	theorem	theorem	VERB
ma-99	429	21	4.1	4.1	NUM
ma-99	429	22	when	when	SCONJ
ma-99	429	23	0	0	NUM
ma-99	429	24	<	<	X
ma-99	429	25	α	α	X
ma-99	429	26	<	<	X
ma-99	429	27	2	2	NUM
ma-99	429	28	,	,	PUNCT
ma-99	429	29	a	a	PRON
ma-99	429	30	)	)	PUNCT
ma-99	429	31	θ̂k	θ̂k	NOUN
ma-99	429	32	,	,	PUNCT
ma-99	429	33	t	t	PROPN
ma-99	429	34	is	be	AUX
ma-99	429	35	an	an	DET
ma-99	429	36	unbiased	unbiased	ADJ
ma-99	429	37	estimator	estimator	NOUN
ma-99	429	38	of	of	ADP
ma-99	429	39	θ.b	θ.b	PROPN
ma-99	429	40	)	)	PUNCT
ma-99	429	41	θ̂k	θ̂k	PROPN
ma-99	429	42	,	,	PUNCT
ma-99	429	43	t	t	PROPN
ma-99	429	44	→	→	SYM
ma-99	429	45	θ	θ	PROPN
ma-99	429	46	a.s	a.s	PROPN
ma-99	429	47	.	.	PROPN
ma-99	429	48	as	as	ADP
ma-99	429	49	t	t	PROPN
ma-99	429	50	→∞.c	→∞.c	NUM
ma-99	429	51	)	)	PUNCT
ma-99	429	52	t	t	NOUN
ma-99	429	53	(	(	PUNCT
ma-99	429	54	α−1)/α2	α−1)/α2	X
ma-99	429	55	(	(	PUNCT
ma-99	429	56	θ̂k	θ̂k	NOUN
ma-99	429	57	,	,	PUNCT
ma-99	429	58	t	t	NOUN
ma-99	429	59	−	−	PROPN
ma-99	429	60	θ)→d	θ)→d	NOUN
ma-99	429	61	(	(	PUNCT
ma-99	429	62	σ2	σ2	NOUN
ma-99	429	63	k	k	PROPN
ma-99	429	64	ν2	ν2	PROPN
ma-99	429	65	k	k	PROPN
ma-99	429	66	)	)	PUNCT
ma-99	429	67	1	1	NUM
ma-99	429	68	/	/	SYM
ma-99	429	69	α	α	PROPN
ma-99	429	70	s4	s4	PROPN
ma-99	429	71	s3	s3	PROPN
ma-99	429	72	as	as	ADP
ma-99	429	73	t	t	PROPN
ma-99	429	74	→∞	→∞	NUM
ma-99	429	75	where	where	SCONJ
ma-99	429	76	s4	s4	PROPN
ma-99	429	77	and	and	CCONJ
ma-99	429	78	s3	s3	PROPN
ma-99	429	79	are	be	AUX
ma-99	429	80	independent	independent	ADJ
ma-99	429	81	stable	stable	ADJ
ma-99	429	82	random	random	ADJ
ma-99	429	83	variables.d	variables.d	PROPN
ma-99	429	84	)	)	PUNCT
ma-99	429	85	if	if	SCONJ
ma-99	429	86	in	in	ADP
ma-99	429	87	addition	addition	NOUN
ma-99	429	88	,	,	PUNCT
ma-99	429	89	lim	lim	PROPN
ma-99	429	90	k→∞	k→∞	NOUN
ma-99	429	91	∣∣∣∣σkνk	∣∣∣∣σkνk	PROPN
ma-99	429	92	∣∣∣∣	∣∣∣∣	PROPN
ma-99	429	93	=	=	SYM
ma-99	429	94	0	0	NUM
ma-99	429	95	,	,	PUNCT
ma-99	429	96	then	then	ADV
ma-99	429	97	for	for	ADP
ma-99	429	98	every	every	DET
ma-99	429	99	fixed	fix	VERB
ma-99	429	100	t	t	PROPN
ma-99	429	101	>	>	X
ma-99	429	102	0	0	NUM
ma-99	429	103	,	,	PUNCT
ma-99	429	104	θ̂k	θ̂k	PROPN
ma-99	429	105	,	,	PUNCT
ma-99	429	106	t	t	PROPN
ma-99	429	107	→	→	SYM
ma-99	429	108	θ	θ	PROPN
ma-99	429	109	a.s	a.s	PROPN
ma-99	429	110	.	.	PROPN
ma-99	429	111	as	as	ADP
ma-99	429	112	k	k	PROPN
ma-99	429	113	→∞and	→∞and	PROPN
ma-99	429	114	∣∣∣∣νkσk	∣∣∣∣νkσk	PROPN
ma-99	429	115	∣∣∣∣	∣∣∣∣	PROPN
ma-99	429	116	(	(	PUNCT
ma-99	429	117	θ̂k	θ̂k	PROPN
ma-99	429	118	,	,	PUNCT
ma-99	429	119	t	t	NOUN
ma-99	429	120	−	−	PROPN
ma-99	429	121	θ)→d	θ)→d	NOUN
ma-99	429	122	(	(	PUNCT
ma-99	429	123	t	t	PROPN
ma-99	429	124	(	(	PUNCT
ma-99	429	125	α−1)/α2	α−1)/α2	NUM
ma-99	429	126	)	)	SYM
ma-99	429	127	1	1	NUM
ma-99	429	128	/	/	SYM
ma-99	429	129	α	α	PROPN
ma-99	429	130	s4	s4	PROPN
ma-99	429	131	s3	s3	PROPN
ma-99	429	132	as	as	SCONJ
ma-99	429	133	k	k	PROPN
ma-99	429	134	→∞.	→∞.	PROPN
ma-99	429	135	remark	remark	PROPN
ma-99	429	136	:	:	PUNCT
ma-99	429	137	the	the	DET
ma-99	429	138	parabolicity	parabolicity	NOUN
ma-99	429	139	condition	condition	NOUN
ma-99	429	140	and	and	CCONJ
ma-99	429	141	the	the	DET
ma-99	429	142	mle	mle	PROPN
ma-99	429	143	consistency	consistency	NOUN
ma-99	429	144	condition	condition	NOUN
ma-99	429	145	in	in	ADP
ma-99	429	146	general	general	ADJ
ma-99	429	147	are	be	AUX
ma-99	429	148	notconnected	notconnecte	VERB
ma-99	429	149	.	.	PUNCT
ma-99	430	1	in	in	ADP
ma-99	430	2	terms	term	NOUN
ma-99	430	3	of	of	ADP
ma-99	430	4	operator	operator	NOUN
ma-99	430	5	’s	’s	PART
ma-99	430	6	order	order	NOUN
ma-99	430	7	,	,	PUNCT
ma-99	430	8	parabolicity	parabolicity	NOUN
ma-99	430	9	states	state	VERB
ma-99	430	10	that	that	SCONJ
ma-99	430	11	the	the	DET
ma-99	430	12	order	order	NOUN
ma-99	430	13	of	of	ADP
ma-99	430	14	operator	operator	NOUN
ma-99	430	15	m	m	VERB
ma-99	430	16	from	from	ADP
ma-99	430	17	thediffusion	thediffusion	NOUN
ma-99	430	18	term	term	NOUN
ma-99	430	19	is	be	AUX
ma-99	430	20	smaller	small	ADJ
ma-99	430	21	than	than	ADP
ma-99	430	22	half	half	NOUN
ma-99	430	23	of	of	ADP
ma-99	430	24	the	the	DET
ma-99	430	25	order	order	NOUN
ma-99	430	26	of	of	ADP
ma-99	430	27	operators	operator	NOUN
ma-99	430	28	a0	a0	PROPN
ma-99	430	29	and	and	CCONJ
ma-99	430	30	a1	a1	NOUN
ma-99	430	31	from	from	ADP
ma-99	430	32	deterministic	deterministic	ADJ
ma-99	430	33	part.the	part.the	DET
ma-99	430	34	consistency	consistency	NOUN
ma-99	430	35	condition	condition	NOUN
ma-99	430	36	assumes	assume	VERB
ma-99	430	37	that	that	SCONJ
ma-99	430	38	the	the	DET
ma-99	430	39	order	order	NOUN
ma-99	430	40	of	of	ADP
ma-99	430	41	the	the	DET
ma-99	430	42	operator	operator	NOUN
ma-99	430	43	m	m	VERB
ma-99	430	44	from	from	ADP
ma-99	430	45	the	the	DET
ma-99	430	46	diffusion	diffusion	NOUN
ma-99	430	47	part	part	NOUN
ma-99	430	48	doesnot	doesnot	INTJ
ma-99	430	49	exceed	exceed	VERB
ma-99	430	50	the	the	DET
ma-99	430	51	order	order	NOUN
ma-99	430	52	of	of	ADP
ma-99	430	53	the	the	DET
ma-99	430	54	operator	operator	NOUN
ma-99	430	55	a1	a1	NOUN
ma-99	430	56	from	from	ADP
ma-99	430	57	the	the	DET
ma-99	430	58	deterministic	deterministic	ADJ
ma-99	430	59	part	part	NOUN
ma-99	430	60	that	that	PRON
ma-99	430	61	contains	contain	VERB
ma-99	430	62	the	the	DET
ma-99	430	63	parameter	parameter	NOUN
ma-99	430	64	ofinterest	ofinter	ADJ
ma-99	430	65	θ	θ	X
ma-99	430	66	.	.	PUNCT
ma-99	431	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	431	2	eur	eur	PROPN
ma-99	431	3	.	.	PUNCT
ma-99	432	1	j.	j.	PROPN
ma-99	432	2	math	math	PROPN
ma-99	432	3	.	.	PUNCT
ma-99	433	1	anal	anal	PROPN
ma-99	433	2	.	.	PUNCT
ma-99	434	1	10.28924	10.28924	NUM
ma-99	434	2	/	/	SYM
ma-99	434	3	ada	ada	PROPN
ma-99	434	4	/	/	SYM
ma-99	434	5	ma.3.4	ma.3.4	PROPN
ma-99	434	6	18	18	NUM
ma-99	434	7	5	5	NUM
ma-99	434	8	.	.	PUNCT
ma-99	435	1	spdes	spde	NOUN
ma-99	435	2	with	with	ADP
ma-99	435	3	nonlinear	nonlinear	ADJ
ma-99	435	4	multiplicative	multiplicative	ADJ
ma-99	435	5	noise	noise	NOUN
ma-99	435	6	consider	consider	VERB
ma-99	435	7	the	the	DET
ma-99	435	8	spde	spde	NOUN
ma-99	435	9	with	with	ADP
ma-99	435	10	multiplicative	multiplicative	ADJ
ma-99	435	11	noise	noise	NOUN
ma-99	435	12	:	:	PUNCT
ma-99	435	13	duθ(t	duθ(t	PROPN
ma-99	435	14	,	,	PUNCT
ma-99	435	15	x	x	NOUN
ma-99	435	16	)	)	PUNCT
ma-99	435	17	=	=	SYM
ma-99	435	18	(	(	PUNCT
ma-99	435	19	a0	a0	PROPN
ma-99	435	20	+	+	CCONJ
ma-99	435	21	θa1)uθ(t	θa1)uθ(t	PROPN
ma-99	435	22	,	,	PUNCT
ma-99	435	23	x)dt	x)dt	PROPN
ma-99	436	1	+	+	PROPN
ma-99	436	2	muθ(t	muθ(t	PROPN
ma-99	436	3	,	,	PUNCT
ma-99	436	4	x)dz(t	x)dz(t	PROPN
ma-99	436	5	,	,	PUNCT
ma-99	436	6	x	x	X
ma-99	436	7	)	)	PUNCT
ma-99	436	8	,	,	PUNCT
ma-99	436	9	t	t	PROPN
ma-99	436	10	≥	≥	NUM
ma-99	436	11	0	0	NUM
ma-99	436	12	,	,	PUNCT
ma-99	436	13	x	x	SYM
ma-99	436	14	∈	∈	PROPN
ma-99	437	1	[	[	X
ma-99	437	2	0	0	NUM
ma-99	437	3	,	,	PUNCT
ma-99	437	4	1	1	NUM
ma-99	437	5	]	]	PUNCT
ma-99	437	6	(	(	PUNCT
ma-99	437	7	5.1	5.1	NUM
ma-99	437	8	)	)	PUNCT
ma-99	437	9	where	where	SCONJ
ma-99	437	10	m	m	NOUN
ma-99	437	11	is	be	AUX
ma-99	437	12	a	a	DET
ma-99	437	13	known	know	VERB
ma-99	437	14	nonlinear	nonlinear	NOUN
ma-99	437	15	operator.equation	operator.equation	NOUN
ma-99	437	16	(	(	PUNCT
ma-99	437	17	5.1	5.1	NUM
ma-99	437	18	)	)	PUNCT
ma-99	437	19	is	be	AUX
ma-99	437	20	called	call	VERB
ma-99	437	21	diagonalizable	diagonalizable	ADJ
ma-99	437	22	if	if	SCONJ
ma-99	437	23	a0	a0	PROPN
ma-99	437	24	,	,	PUNCT
ma-99	437	25	a1	a1	NOUN
ma-99	437	26	and	and	CCONJ
ma-99	437	27	m	m	VERB
ma-99	437	28	have	have	AUX
ma-99	437	29	point	point	NOUN
ma-99	437	30	spectrum	spectrum	NOUN
ma-99	437	31	and	and	CCONJ
ma-99	437	32	a	a	DET
ma-99	437	33	commonsystem	commonsystem	NOUN
ma-99	437	34	of	of	ADP
ma-99	437	35	eigenfunction	eigenfunction	NOUN
ma-99	437	36	{	{	PUNCT
ma-99	437	37	hj	hj	PROPN
ma-99	437	38	,	,	PUNCT
ma-99	437	39	j	j	PROPN
ma-99	437	40	≥	≥	PROPN
ma-99	437	41	1	1	NUM
ma-99	437	42	}	}	PUNCT
ma-99	437	43	.	.	PUNCT
ma-99	438	1	denote	denote	VERB
ma-99	438	2	by	by	ADP
ma-99	438	3	ρk	ρk	PRON
ma-99	438	4	,	,	PUNCT
ma-99	438	5	νk	νk	NOUN
ma-99	438	6	and	and	CCONJ
ma-99	438	7	µk	µk	INTJ
ma-99	438	8	,	,	PUNCT
ma-99	438	9	the	the	DET
ma-99	438	10	eigenvalues	eigenvalue	NOUN
ma-99	438	11	of	of	ADP
ma-99	438	12	the	the	DET
ma-99	438	13	operators	operator	NOUN
ma-99	438	14	a0	a0	PROPN
ma-99	438	15	,	,	PUNCT
ma-99	438	16	a1	a1	NOUN
ma-99	438	17	and	and	CCONJ
ma-99	438	18	m	m	NOUN
ma-99	438	19	respectively.then	respectively.then	ADV
ma-99	438	20	uθ(t	uθ(t	NOUN
ma-99	438	21	,	,	PUNCT
ma-99	438	22	x	x	NOUN
ma-99	438	23	)	)	PUNCT
ma-99	438	24	=	=	PUNCT
ma-99	439	1	∞∑	∞∑	NUM
ma-99	439	2	j=1	j=1	PROPN
ma-99	439	3	uj	uj	PROPN
ma-99	439	4	,	,	PUNCT
ma-99	439	5	thj	thj	PROPN
ma-99	439	6	.	.	PUNCT
ma-99	440	1	we	we	PRON
ma-99	440	2	consider	consider	VERB
ma-99	440	3	stable	stable	ADJ
ma-99	440	4	cir	cir	NOUN
ma-99	440	5	model	model	NOUN
ma-99	440	6	as	as	ADP
ma-99	440	7	example	example	NOUN
ma-99	440	8	.	.	PUNCT
ma-99	441	1	here	here	ADV
ma-99	441	2	s1	s1	PROPN
ma-99	441	3	and	and	CCONJ
ma-99	441	4	s2	s2	NOUN
ma-99	441	5	are	be	AUX
ma-99	441	6	dependent	dependent	ADJ
ma-99	441	7	stable	stable	ADJ
ma-99	441	8	randomvariables	randomvariable	NOUN
ma-99	441	9	unlike	unlike	ADP
ma-99	441	10	the	the	DET
ma-99	441	11	linear	linear	ADJ
ma-99	441	12	case	case	NOUN
ma-99	441	13	where	where	SCONJ
ma-99	441	14	s3	s3	PROPN
ma-99	441	15	and	and	CCONJ
ma-99	441	16	s4	s4	PROPN
ma-99	441	17	are	be	AUX
ma-99	441	18	independent	independent	ADJ
ma-99	441	19	stable	stable	ADJ
ma-99	441	20	random	random	ADJ
ma-99	441	21	variables	variable	NOUN
ma-99	441	22	.	.	PUNCT
ma-99	442	1	the	the	DET
ma-99	442	2	existence	existence	NOUN
ma-99	442	3	and	and	CCONJ
ma-99	442	4	pathwise	pathwise	NOUN
ma-99	442	5	uniqueness	uniqueness	NOUN
ma-99	442	6	of	of	ADP
ma-99	442	7	solutions	solution	NOUN
ma-99	442	8	to	to	ADP
ma-99	442	9	the	the	DET
ma-99	442	10	sdes	sde	NOUN
ma-99	442	11	with	with	ADP
ma-99	442	12	non	non	ADJ
ma-99	442	13	-	-	ADJ
ma-99	442	14	lipschitz	lipschitz	ADJ
ma-99	442	15	coefficientdriven	coefficientdriven	NOUN
ma-99	442	16	by	by	ADP
ma-99	442	17	spectrally	spectrally	ADV
ma-99	442	18	positive	positive	ADJ
ma-99	442	19	levy	levy	NOUN
ma-99	442	20	processes	process	NOUN
ma-99	442	21	were	be	AUX
ma-99	442	22	studied	study	VERB
ma-99	442	23	in	in	ADP
ma-99	442	24	fu	fu	NOUN
ma-99	442	25	and	and	CCONJ
ma-99	442	26	li	li	NOUN
ma-99	443	1	[	[	X
ma-99	443	2	17].consider	17].consider	NUM
ma-99	443	3	the	the	DET
ma-99	443	4	nonlinear	nonlinear	ADJ
ma-99	443	5	spde	spde	NOUN
ma-99	443	6	dx(t	dx(t	PROPN
ma-99	443	7	,	,	PUNCT
ma-99	443	8	x	x	X
ma-99	443	9	)	)	PUNCT
ma-99	443	10	=	=	SYM
ma-99	443	11	θ	θ	NOUN
ma-99	443	12	2	2	NUM
ma-99	443	13	xxx(t	xxx(t	PROPN
ma-99	443	14	,	,	PUNCT
ma-99	443	15	x)dt	x)dt	PROPN
ma-99	443	16	+	+	CCONJ
ma-99	443	17	√	√	PROPN
ma-99	443	18	x(t	x(t	PROPN
ma-99	443	19	,	,	PUNCT
ma-99	443	20	x)dw	x)dw	PROPN
ma-99	443	21	(	(	PUNCT
ma-99	443	22	t	t	PROPN
ma-99	443	23	,	,	PUNCT
ma-99	443	24	x	x	NOUN
ma-99	443	25	)	)	PUNCT
ma-99	443	26	where	where	SCONJ
ma-99	443	27	w	w	PROPN
ma-99	443	28	(	(	PUNCT
ma-99	443	29	t	t	PROPN
ma-99	443	30	,	,	PUNCT
ma-99	443	31	x	x	X
ma-99	443	32	)	)	PUNCT
ma-99	443	33	is	be	AUX
ma-99	443	34	a	a	DET
ma-99	443	35	space	space	NOUN
ma-99	443	36	-	-	PUNCT
ma-99	443	37	time	time	NOUN
ma-99	443	38	white	white	ADJ
ma-99	443	39	noise	noise	NOUN
ma-99	443	40	.	.	PUNCT
ma-99	444	1	konno	konno	NOUN
ma-99	444	2	and	and	CCONJ
ma-99	444	3	shiga	shiga	ADJ
ma-99	445	1	[	[	X
ma-99	445	2	26	26	NUM
ma-99	445	3	]	]	PUNCT
ma-99	445	4	studied	study	VERB
ma-99	445	5	the	the	DET
ma-99	445	6	existence	existence	NOUN
ma-99	445	7	and	and	CCONJ
ma-99	445	8	weakuniqueness	weakuniqueness	NOUN
ma-99	445	9	of	of	ADP
ma-99	445	10	the	the	DET
ma-99	445	11	above	above	ADJ
ma-99	445	12	equation	equation	NOUN
ma-99	445	13	as	as	ADP
ma-99	445	14	a	a	DET
ma-99	445	15	martingale	martingale	ADJ
ma-99	445	16	problem	problem	NOUN
ma-99	445	17	for	for	ADP
ma-99	445	18	the	the	DET
ma-99	445	19	associated	associated	ADJ
ma-99	445	20	super	super	ADJ
ma-99	445	21	-	-	ADJ
ma-99	445	22	brownian	brownian	ADJ
ma-99	445	23	mo	mo	NOUN
ma-99	445	24	-	-	NOUN
ma-99	445	25	tion	tion	NOUN
ma-99	445	26	.	.	PUNCT
ma-99	446	1	the	the	DET
ma-99	446	2	pathwise	pathwise	NOUN
ma-99	446	3	uniqueness	uniqueness	NOUN
ma-99	446	4	of	of	ADP
ma-99	446	5	nonnegative	nonnegative	ADJ
ma-99	446	6	solution	solution	NOUN
ma-99	446	7	still	still	ADV
ma-99	446	8	remains	remain	VERB
ma-99	446	9	open	open	ADJ
ma-99	446	10	.	.	PUNCT
ma-99	447	1	the	the	DET
ma-99	447	2	main	main	ADJ
ma-99	447	3	difficultycomes	difficultycome	NOUN
ma-99	447	4	from	from	ADP
ma-99	447	5	the	the	DET
ma-99	447	6	unbounded	unbounded	ADJ
ma-99	447	7	drift	drift	NOUN
ma-99	447	8	coefficient	coefficient	NOUN
ma-99	447	9	and	and	CCONJ
ma-99	447	10	non	non	ADJ
ma-99	447	11	-	-	ADJ
ma-99	447	12	lipschitz	lipschitz	ADJ
ma-99	447	13	diffusion	diffusion	NOUN
ma-99	447	14	coefficient	coefficient	NOUN
ma-99	447	15	.	.	PUNCT
ma-99	448	1	wang	wang	PROPN
ma-99	448	2	et	et	PROPN
ma-99	448	3	al	al	PROPN
ma-99	448	4	.	.	PUNCT
ma-99	449	1	[	[	X
ma-99	449	2	42]studied	42]studied	NUM
ma-99	449	3	proved	prove	VERB
ma-99	449	4	a	a	DET
ma-99	449	5	comparison	comparison	NOUN
ma-99	449	6	theorem	theorem	VERB
ma-99	449	7	and	and	CCONJ
ma-99	449	8	showed	show	VERB
ma-99	449	9	that	that	SCONJ
ma-99	449	10	the	the	DET
ma-99	449	11	solution	solution	NOUN
ma-99	449	12	of	of	ADP
ma-99	449	13	the	the	DET
ma-99	449	14	nonlinear	nonlinear	ADJ
ma-99	449	15	spde	spde	NOUN
ma-99	449	16	is	be	AUX
ma-99	449	17	distri	distri	VERB
ma-99	449	18	-	-	NOUN
ma-99	449	19	bution	bution	NOUN
ma-99	449	20	function	function	NOUN
ma-99	449	21	valued	value	VERB
ma-99	449	22	.	.	PUNCT
ma-99	450	1	they	they	PRON
ma-99	450	2	also	also	ADV
ma-99	450	3	established	establish	VERB
ma-99	450	4	pathwise	pathwise	NOUN
ma-99	450	5	uniqueness	uniqueness	NOUN
ma-99	450	6	.	.	PUNCT
ma-99	451	1	as	as	ADP
ma-99	451	2	application	application	NOUN
ma-99	451	3	they	they	PRON
ma-99	451	4	obtainedwell	obtainedwell	ADJ
ma-99	451	5	-	-	PUNCT
ma-99	451	6	posedness	posedness	NOUN
ma-99	451	7	of	of	ADP
ma-99	451	8	martingale	martingale	ADJ
ma-99	451	9	problems	problem	NOUN
ma-99	451	10	for	for	ADP
ma-99	451	11	two	two	NUM
ma-99	451	12	classes	class	NOUN
ma-99	451	13	of	of	ADP
ma-99	451	14	measure	measure	NOUN
ma-99	451	15	-	-	PUNCT
ma-99	451	16	valued	value	VERB
ma-99	451	17	diffusions	diffusion	NOUN
ma-99	451	18	:	:	PUNCT
ma-99	451	19	interactingsuper	interactingsuper	NOUN
ma-99	451	20	-	-	PUNCT
ma-99	451	21	brownian	brownian	ADJ
ma-99	451	22	motions	motion	NOUN
ma-99	451	23	and	and	CCONJ
ma-99	451	24	interacting	interact	VERB
ma-99	451	25	fleming	fleming	NOUN
ma-99	451	26	-	-	PUNCT
ma-99	451	27	viot	viot	NOUN
ma-99	451	28	processes	process	NOUN
ma-99	451	29	.	.	PUNCT
ma-99	452	1	he	he	PRON
ma-99	452	2	et	et	PROPN
ma-99	452	3	al	al	PROPN
ma-99	452	4	.	.	PUNCT
ma-99	453	1	[	[	X
ma-99	453	2	18	18	NUM
ma-99	453	3	]	]	PUNCT
ma-99	453	4	obtained	obtain	VERB
ma-99	453	5	pathwiseunique	pathwiseunique	NOUN
ma-99	453	6	solution	solution	NOUN
ma-99	453	7	to	to	ADP
ma-99	453	8	nonlinear	nonlinear	ADJ
ma-99	453	9	spde	spde	NOUN
ma-99	453	10	with	with	ADP
ma-99	453	11	super	super	ADJ
ma-99	453	12	levy	levy	NOUN
ma-99	453	13	process	process	NOUN
ma-99	453	14	,	,	PUNCT
ma-99	453	15	which	which	PRON
ma-99	453	16	is	be	AUX
ma-99	453	17	a	a	DET
ma-99	453	18	combination	combination	NOUN
ma-99	453	19	of	of	ADP
ma-99	453	20	space	space	NOUN
ma-99	453	21	-	-	PUNCT
ma-99	453	22	time	time	NOUN
ma-99	453	23	gaussian	gaussian	ADJ
ma-99	453	24	white	white	ADJ
ma-99	453	25	noises	noise	NOUN
ma-99	453	26	and	and	CCONJ
ma-99	453	27	poisson	poisson	NOUN
ma-99	453	28	random	random	ADJ
ma-99	453	29	measures	measure	NOUN
ma-99	453	30	which	which	PRON
ma-99	453	31	is	be	AUX
ma-99	453	32	a	a	DET
ma-99	453	33	generalization	generalization	NOUN
ma-99	453	34	of	of	ADP
ma-99	453	35	work	work	NOUN
ma-99	453	36	ofxiong	ofxiong	NOUN
ma-99	454	1	[	[	X
ma-99	454	2	43	43	NUM
ma-99	454	3	]	]	PUNCT
ma-99	454	4	where	where	SCONJ
ma-99	454	5	the	the	DET
ma-99	454	6	result	result	NOUN
ma-99	454	7	for	for	ADP
ma-99	454	8	a	a	DET
ma-99	454	9	super	super	ADJ
ma-99	454	10	-	-	ADJ
ma-99	454	11	brownian	brownian	ADJ
ma-99	454	12	motion	motion	NOUN
ma-99	454	13	with	with	ADP
ma-99	454	14	binary	binary	ADJ
ma-99	454	15	branching	branch	VERB
ma-99	454	16	mechanism	mechanism	NOUN
ma-99	454	17	wasobtained	wasobtaine	VERB
ma-99	454	18	.	.	PUNCT
ma-99	455	1	using	use	VERB
ma-99	455	2	an	an	DET
ma-99	455	3	extended	extended	ADJ
ma-99	455	4	yamada	yamada	PROPN
ma-99	455	5	-	-	PUNCT
ma-99	455	6	watanabe	watanabe	PROPN
ma-99	455	7	argument	argument	NOUN
ma-99	455	8	,	,	PUNCT
ma-99	455	9	xiong	xiong	PROPN
ma-99	456	1	[	[	X
ma-99	456	2	43	43	NUM
ma-99	456	3	]	]	PUNCT
ma-99	456	4	established	establish	VERB
ma-99	456	5	strong	strong	ADJ
ma-99	456	6	exis	exis	NOUN
ma-99	456	7	-	-	PUNCT
ma-99	456	8	tence	tence	NOUN
ma-99	456	9	and	and	CCONJ
ma-99	456	10	uniqueness	uniqueness	NOUN
ma-99	456	11	of	of	ADP
ma-99	456	12	the	the	DET
ma-99	456	13	solution	solution	NOUN
ma-99	456	14	to	to	ADP
ma-99	456	15	the	the	DET
ma-99	456	16	spde	spde	NOUN
ma-99	456	17	.	.	PUNCT
ma-99	457	1	super	super	ADJ
ma-99	457	2	-	-	ADJ
ma-99	457	3	brownian	brownian	ADJ
ma-99	457	4	motion	motion	NOUN
ma-99	457	5	(	(	PUNCT
ma-99	457	6	smb	smb	NOUN
ma-99	457	7	)	)	PUNCT
ma-99	457	8	,	,	PUNCT
ma-99	457	9	also	also	ADV
ma-99	457	10	calledthe	calledthe	PROPN
ma-99	457	11	dawson	dawson	PROPN
ma-99	457	12	-	-	PUNCT
ma-99	457	13	watanabe	watanabe	PROPN
ma-99	457	14	process	process	NOUN
ma-99	457	15	introduced	introduce	VERB
ma-99	457	16	by	by	ADP
ma-99	457	17	sawson	sawson	NOUN
ma-99	457	18	and	and	CCONJ
ma-99	457	19	watanabe	watanabe	PROPN
ma-99	457	20	is	be	AUX
ma-99	457	21	a	a	DET
ma-99	457	22	measure	measure	NOUN
ma-99	457	23	valued	value	VERB
ma-99	457	24	processarising	processarising	NOUN
ma-99	457	25	as	as	ADP
ma-99	457	26	the	the	DET
ma-99	457	27	limit	limit	NOUN
ma-99	457	28	of	of	ADP
ma-99	457	29	empirical	empirical	ADJ
ma-99	457	30	measure	measure	NOUN
ma-99	457	31	process	process	NOUN
ma-99	457	32	of	of	ADP
ma-99	457	33	a	a	DET
ma-99	457	34	branching	branch	VERB
ma-99	457	35	particle	particle	NOUN
ma-99	457	36	system	system	NOUN
ma-99	457	37	.	.	PUNCT
ma-99	458	1	sbm	sbm	PROPN
ma-99	458	2	satisfiesa	satisfiesa	PROPN
ma-99	458	3	martingale	martingale	PROPN
ma-99	458	4	problem	problem	NOUN
ma-99	458	5	.	.	PUNCT
ma-99	459	1	when	when	SCONJ
ma-99	459	2	the	the	DET
ma-99	459	3	state	state	NOUN
ma-99	459	4	space	space	NOUN
ma-99	459	5	is	be	AUX
ma-99	459	6	r	r	NOUN
ma-99	459	7	,	,	PUNCT
ma-99	459	8	sbm	sbm	PROPN
ma-99	459	9	has	have	VERB
ma-99	459	10	a	a	DET
ma-99	459	11	density	density	NOUN
ma-99	459	12	w.r.t	w.r.t	NOUN
ma-99	459	13	.	.	PUNCT
ma-99	460	1	lebesgue	lebesgue	PROPN
ma-99	460	2	measureand	measureand	PROPN
ma-99	461	1	this	this	DET
ma-99	461	2	density	density	NOUN
ma-99	461	3	valued	value	VERB
ma-99	461	4	process	process	NOUN
ma-99	461	5	x(t	x(t	PROPN
ma-99	461	6	,	,	PUNCT
ma-99	461	7	x	x	X
ma-99	461	8	)	)	PUNCT
ma-99	461	9	satisfies	satisfy	VERB
ma-99	461	10	the	the	DET
ma-99	461	11	above	above	ADJ
ma-99	461	12	spde	spde	NOUN
ma-99	461	13	.	.	PUNCT
ma-99	462	1	when	when	SCONJ
ma-99	462	2	the	the	DET
ma-99	462	3	space	space	NOUN
ma-99	462	4	r	r	NOUN
ma-99	462	5	is	be	AUX
ma-99	462	6	s	s	PRON
ma-99	462	7	single	single	ADJ
ma-99	462	8	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	462	9	eur	eur	NOUN
ma-99	462	10	.	.	PUNCT
ma-99	463	1	j.	j.	PROPN
ma-99	463	2	math	math	PROPN
ma-99	463	3	.	.	PUNCT
ma-99	464	1	anal	anal	PROPN
ma-99	464	2	.	.	PUNCT
ma-99	465	1	10.28924	10.28924	NUM
ma-99	465	2	/	/	SYM
ma-99	465	3	ada	ada	PROPN
ma-99	465	4	/	/	SYM
ma-99	465	5	ma.3.4	ma.3.4	PROPN
ma-99	465	6	19point	19point	NUM
ma-99	465	7	,	,	PUNCT
ma-99	465	8	the	the	DET
ma-99	465	9	spde	spde	NOUN
ma-99	465	10	becomes	become	VERB
ma-99	465	11	an	an	DET
ma-99	465	12	sde	sde	NOUN
ma-99	465	13	which	which	PRON
ma-99	465	14	is	be	AUX
ma-99	465	15	cir	cir	NOUN
ma-99	465	16	diffusion	diffusion	NOUN
ma-99	465	17	dxt	dxt	PROPN
ma-99	465	18	=	=	PUNCT
ma-99	465	19	√	√	PROPN
ma-99	465	20	xtdwt	xtdwt	NOUN
ma-99	465	21	whose	whose	DET
ma-99	465	22	uniqueness	uniqueness	NOUN
ma-99	465	23	isestablished	isestablishe	VERB
ma-99	465	24	using	use	VERB
ma-99	465	25	the	the	DET
ma-99	465	26	yamada	yamada	PROPN
ma-99	465	27	-	-	PUNCT
ma-99	465	28	watanabe	watanabe	PROPN
ma-99	465	29	argument	argument	NOUN
ma-99	465	30	.	.	PUNCT
ma-99	466	1	xiong	xiong	PROPN
ma-99	466	2	and	and	CCONJ
ma-99	466	3	yang	yang	PROPN
ma-99	466	4	(	(	PUNCT
ma-99	466	5	2019	2019	NUM
ma-99	466	6	)	)	PUNCT
ma-99	466	7	studied	study	VERB
ma-99	466	8	existence	existence	NOUN
ma-99	466	9	andpathwise	andpathwise	NOUN
ma-99	466	10	uniqueness	uniqueness	NOUN
ma-99	466	11	to	to	ADP
ma-99	466	12	an	an	DET
ma-99	466	13	spde	spde	NOUN
ma-99	466	14	with	with	ADP
ma-99	466	15	hölder	hölder	PROPN
ma-99	466	16	continuous	continuous	ADJ
ma-99	466	17	coefficient	coefficient	NOUN
ma-99	466	18	driven	drive	VERB
ma-99	466	19	by	by	ADP
ma-99	466	20	α	α	NOUN
ma-99	466	21	-	-	ADJ
ma-99	466	22	stable	stable	ADJ
ma-99	466	23	colorednoise	colorednoise	NOUN
ma-99	466	24	.	.	PUNCT
ma-99	467	1	the	the	DET
ma-99	467	2	existence	existence	NOUN
ma-99	467	3	of	of	ADP
ma-99	467	4	the	the	DET
ma-99	467	5	solution	solution	NOUN
ma-99	467	6	is	be	AUX
ma-99	467	7	shown	show	VERB
ma-99	467	8	by	by	ADP
ma-99	467	9	considering	consider	VERB
ma-99	467	10	the	the	DET
ma-99	467	11	weak	weak	ADJ
ma-99	467	12	limit	limit	NOUN
ma-99	467	13	of	of	ADP
ma-99	467	14	a	a	DET
ma-99	467	15	sequence	sequence	NOUN
ma-99	467	16	of	of	ADP
ma-99	467	17	sdesystem	sdesystem	NOUN
ma-99	467	18	which	which	PRON
ma-99	467	19	is	be	AUX
ma-99	467	20	obtained	obtain	VERB
ma-99	467	21	by	by	ADP
ma-99	467	22	replacing	replace	VERB
ma-99	467	23	the	the	DET
ma-99	467	24	laplacian	laplacian	ADJ
ma-99	467	25	operator	operator	NOUN
ma-99	467	26	in	in	ADP
ma-99	467	27	the	the	DET
ma-99	467	28	spde	spde	NOUN
ma-99	467	29	by	by	ADP
ma-99	467	30	its	its	PRON
ma-99	467	31	discrete	discrete	NOUN
ma-99	467	32	version.the	version.the	DET
ma-99	467	33	pathwise	pathwise	NOUN
ma-99	467	34	uniqueness	uniqueness	NOUN
ma-99	467	35	is	be	AUX
ma-99	467	36	shown	show	VERB
ma-99	467	37	by	by	ADP
ma-99	467	38	using	use	VERB
ma-99	467	39	a	a	DET
ma-99	467	40	backward	backward	ADJ
ma-99	467	41	doubly	doubly	ADV
ma-99	467	42	stochastic	stochastic	ADJ
ma-99	467	43	differential	differential	ADJ
ma-99	467	44	equation	equation	NOUN
ma-99	467	45	totake	totake	VERB
ma-99	467	46	care	care	NOUN
ma-99	467	47	of	of	ADP
ma-99	467	48	the	the	DET
ma-99	467	49	laplacian	laplacian	NOUN
ma-99	467	50	.	.	PUNCT
ma-99	468	1	in	in	ADP
ma-99	468	2	the	the	DET
ma-99	468	3	case	case	NOUN
ma-99	468	4	of	of	ADP
ma-99	468	5	d	d	PROPN
ma-99	468	6	=	=	SYM
ma-99	468	7	1	1	NUM
ma-99	468	8	,	,	PUNCT
ma-99	468	9	the	the	DET
ma-99	468	10	pathwise	pathwise	NOUN
ma-99	468	11	uniqueness	uniqueness	NOUN
ma-99	468	12	of	of	ADP
ma-99	468	13	a	a	DET
ma-99	468	14	nonnegative	nonnegative	ADJ
ma-99	468	15	solutionto	solutionto	NOUN
ma-99	468	16	the	the	DET
ma-99	468	17	corresponding	corresponding	ADJ
ma-99	468	18	equation	equation	NOUN
ma-99	468	19	was	be	AUX
ma-99	468	20	established	establish	VERB
ma-99	468	21	by	by	ADP
ma-99	468	22	yang	yang	PROPN
ma-99	468	23	and	and	CCONJ
ma-99	468	24	zhou	zhou	PROPN
ma-99	469	1	[	[	X
ma-99	469	2	45	45	NUM
ma-99	469	3	]	]	PUNCT
ma-99	469	4	for	for	ADP
ma-99	469	5	1	1	NUM
ma-99	469	6	<	<	X
ma-99	469	7	α	α	X
ma-99	469	8	<	<	X
ma-99	469	9	√	√	PROPN
ma-99	469	10	5	5	NUM
ma-99	469	11	−	−	NOUN
ma-99	469	12	1	1	NUM
ma-99	469	13	andpathwise	andpathwise	NOUN
ma-99	469	14	uniqueness	uniqueness	NOUN
ma-99	469	15	for	for	ADP
ma-99	469	16	√5−	√5−	NOUN
ma-99	469	17	1	1	NUM
ma-99	469	18	<	<	X
ma-99	469	19	α	α	X
ma-99	469	20	<	<	X
ma-99	469	21	2	2	NUM
ma-99	469	22	is	be	AUX
ma-99	469	23	still	still	ADV
ma-99	469	24	open.consider	open.consider	NUM
ma-99	469	25	spde	spde	NOUN
ma-99	469	26	model	model	NOUN
ma-99	469	27	with	with	ADP
ma-99	469	28	multiplicative	multiplicative	ADJ
ma-99	469	29	noise	noise	NOUN
ma-99	469	30	and	and	CCONJ
ma-99	469	31	mean	mean	ADJ
ma-99	469	32	reversion	reversion	NOUN
ma-99	469	33	,	,	PUNCT
ma-99	469	34	where	where	SCONJ
ma-99	469	35	the	the	DET
ma-99	469	36	j	j	PROPN
ma-99	469	37	-	-	PUNCT
ma-99	469	38	th	th	PROPN
ma-99	469	39	fouriercoefficient	fouriercoefficient	NOUN
ma-99	469	40	is	be	AUX
ma-99	469	41	the	the	DET
ma-99	469	42	stable	stable	ADJ
ma-99	469	43	cox	cox	PROPN
ma-99	469	44	-	-	PUNCT
ma-99	469	45	ingersoll	ingersoll	PROPN
ma-99	469	46	-	-	PUNCT
ma-99	469	47	ross	ross	PROPN
ma-99	469	48	(	(	PUNCT
ma-99	469	49	scir	scir	PROPN
ma-99	469	50	)	)	PUNCT
ma-99	469	51	model	model	NOUN
ma-99	469	52	:	:	PUNCT
ma-99	469	53	duj	duj	PROPN
ma-99	469	54	,	,	PUNCT
ma-99	469	55	t	t	NOUN
ma-99	469	56	=	=	SYM
ma-99	469	57	(	(	PUNCT
ma-99	469	58	a	a	DET
ma-99	469	59	−	−	NOUN
ma-99	469	60	θuj	θuj	NOUN
ma-99	469	61	,	,	PUNCT
ma-99	470	1	t)dt	t)dt	PROPN
ma-99	470	2	+	+	PROPN
ma-99	470	3	σu	σu	PROPN
ma-99	470	4	1	1	NUM
ma-99	470	5	/	/	SYM
ma-99	470	6	α	α	PRON
ma-99	470	7	j	j	PROPN
ma-99	470	8	,	,	PUNCT
ma-99	470	9	t−dzj	t−dzj	ADJ
ma-99	470	10	,	,	PUNCT
ma-99	470	11	t	t	PROPN
ma-99	470	12	,	,	PUNCT
ma-99	470	13	j	j	PROPN
ma-99	470	14	≥	≥	NUM
ma-99	470	15	1	1	NUM
ma-99	470	16	(	(	PUNCT
ma-99	470	17	5.2	5.2	NUM
ma-99	470	18	)	)	PUNCT
ma-99	470	19	where	where	SCONJ
ma-99	470	20	a	a	PRON
ma-99	470	21	is	be	AUX
ma-99	470	22	the	the	DET
ma-99	470	23	mean	mean	ADJ
ma-99	470	24	reverting	revert	VERB
ma-99	470	25	level	level	NOUN
ma-99	470	26	and	and	CCONJ
ma-99	470	27	θ	θ	NOUN
ma-99	470	28	is	be	AUX
ma-99	470	29	mean	mean	VERB
ma-99	470	30	reverting	revert	VERB
ma-99	470	31	speed	speed	NOUN
ma-99	470	32	.	.	PUNCT
ma-99	471	1	recall	recall	VERB
ma-99	471	2	that	that	PRON
ma-99	471	3	for	for	ADP
ma-99	471	4	α	α	NOUN
ma-99	471	5	=	=	SYM
ma-99	471	6	2	2	NUM
ma-99	471	7	,	,	PUNCT
ma-99	471	8	for	for	ADP
ma-99	471	9	every	every	DET
ma-99	471	10	j	j	PROPN
ma-99	471	11	≥	≥	NUM
ma-99	471	12	1	1	NUM
ma-99	471	13	,	,	PUNCT
ma-99	471	14	the	the	DET
ma-99	471	15	process	process	NOUN
ma-99	471	16	zj	zj	PROPN
ma-99	471	17	,	,	PUNCT
ma-99	471	18	t	t	PROPN
ma-99	471	19	is	be	AUX
ma-99	471	20	a	a	DET
ma-99	471	21	standard	standard	ADJ
ma-99	471	22	brownian	brownian	ADJ
ma-99	471	23	motion	motion	NOUN
ma-99	471	24	,	,	PUNCT
ma-99	471	25	this	this	PRON
ma-99	471	26	is	be	AUX
ma-99	471	27	the	the	DET
ma-99	471	28	famous	famous	ADJ
ma-99	471	29	cox	cox	PROPN
ma-99	471	30	-	-	PUNCT
ma-99	471	31	ingersoll	ingersoll	PROPN
ma-99	471	32	-	-	PUNCT
ma-99	471	33	ross	ross	PROPN
ma-99	471	34	(	(	PUNCT
ma-99	471	35	cir)model	cir)model	PROPN
ma-99	471	36	used	use	VERB
ma-99	471	37	for	for	ADP
ma-99	471	38	modeling	model	VERB
ma-99	471	39	interest	interest	NOUN
ma-99	471	40	rate	rate	NOUN
ma-99	471	41	,	,	PUNCT
ma-99	471	42	which	which	PRON
ma-99	471	43	is	be	AUX
ma-99	471	44	also	also	ADV
ma-99	471	45	used	use	VERB
ma-99	471	46	a	a	DET
ma-99	471	47	stochastic	stochastic	ADJ
ma-99	471	48	volatility	volatility	NOUN
ma-99	471	49	process	process	NOUN
ma-99	471	50	in	in	ADP
ma-99	471	51	hestonmodel	hestonmodel	PROPN
ma-99	471	52	.	.	PUNCT
ma-99	472	1	note	note	VERB
ma-99	472	2	that	that	SCONJ
ma-99	472	3	there	there	PRON
ma-99	472	4	are	be	VERB
ma-99	472	5	brownian	brownian	ADJ
ma-99	472	6	cir	cir	NOUN
ma-99	472	7	models	model	NOUN
ma-99	472	8	with	with	ADP
ma-99	472	9	additive	additive	ADJ
ma-99	472	10	compound	compound	NOUN
ma-99	472	11	poisson	poisson	NOUN
ma-99	472	12	type	type	NOUN
ma-99	472	13	jumps.when	jumps.when	ADV
ma-99	472	14	1	1	NUM
ma-99	472	15	<	<	X
ma-99	472	16	α	α	X
ma-99	472	17	<	<	X
ma-99	472	18	2	2	NUM
ma-99	472	19	,	,	PUNCT
ma-99	472	20	zj	zj	PROPN
ma-99	472	21	,	,	PUNCT
ma-99	472	22	t	t	PROPN
ma-99	472	23	is	be	AUX
ma-99	472	24	stable	stable	ADJ
ma-99	472	25	process	process	NOUN
ma-99	472	26	with	with	ADP
ma-99	472	27	levy	levy	NOUN
ma-99	472	28	measure	measure	NOUN
ma-99	472	29	να(dz	να(dz	NOUN
ma-99	472	30	)	)	PUNCT
ma-99	472	31	=	=	SYM
ma-99	472	32	1{z>0}dz	1{z>0}dz	NUM
ma-99	472	33	αγ(−α)zα+1	αγ(−α)zα+1	NOUN
ma-99	472	34	.	.	PUNCT
ma-99	473	1	(	(	PUNCT
ma-99	473	2	5.3	5.3	NUM
ma-99	473	3	)	)	PUNCT
ma-99	473	4	the	the	DET
ma-99	473	5	discontinuous	discontinuous	ADJ
ma-99	473	6	scir	scir	PROPN
ma-99	473	7	model	model	PROPN
ma-99	473	8	captures	capture	VERB
ma-99	473	9	the	the	DET
ma-99	473	10	heavy	heavy	ADJ
ma-99	473	11	tailed	tail	VERB
ma-99	473	12	property	property	NOUN
ma-99	473	13	in	in	ADP
ma-99	473	14	the	the	DET
ma-99	473	15	sense	sense	NOUN
ma-99	473	16	of	of	ADP
ma-99	473	17	infinite	infinite	NOUN
ma-99	473	18	variance.there	variance.there	ADV
ma-99	473	19	is	be	VERB
ma-99	473	20	empirical	empirical	ADJ
ma-99	473	21	evidence	evidence	NOUN
ma-99	473	22	from	from	ADP
ma-99	473	23	high	high	ADJ
ma-99	473	24	frequency	frequency	NOUN
ma-99	473	25	data	datum	NOUN
ma-99	473	26	available	available	ADJ
ma-99	473	27	in	in	ADP
ma-99	473	28	support	support	NOUN
ma-99	473	29	of	of	ADP
ma-99	473	30	application	application	NOUN
ma-99	473	31	of	of	ADP
ma-99	473	32	purejump	purejump	NOUN
ma-99	473	33	models	model	NOUN
ma-99	473	34	in	in	ADP
ma-99	473	35	financial	financial	ADJ
ma-99	473	36	modeling.the	modeling.the	DET
ma-99	473	37	scir	scir	PROPN
ma-99	473	38	model	model	NOUN
ma-99	473	39	has	have	VERB
ma-99	473	40	the	the	DET
ma-99	473	41	unique	unique	ADJ
ma-99	473	42	stationary	stationary	ADJ
ma-99	473	43	distribution	distribution	NOUN
ma-99	473	44	µ	µ	NOUN
ma-99	473	45	with	with	ADP
ma-99	473	46	laplace	laplace	NOUN
ma-99	473	47	transform	transform	NOUN
ma-99	473	48	given	give	VERB
ma-99	473	49	by	by	ADP
ma-99	473	50	lµ(λ	lµ(λ	NOUN
ma-99	473	51	)	)	PUNCT
ma-99	473	52	=	=	SYM
ma-99	474	1	∫	∫	PROPN
ma-99	474	2	∞	∞	NOUN
ma-99	474	3	0	0	NUM
ma-99	475	1	e−λxµ(dx	e−λxµ(dx	ADJ
ma-99	475	2	)	)	PUNCT
ma-99	475	3	=	=	SYM
ma-99	475	4	exp	exp	NOUN
ma-99	475	5	{	{	PUNCT
ma-99	475	6	−	−	PROPN
ma-99	475	7	∫	∫	PROPN
ma-99	475	8	λ	λ	X
ma-99	475	9	0	0	PROPN
ma-99	475	10	αa	αa	PROPN
ma-99	475	11	αθ	αθ	NUM
ma-99	475	12	+	+	CCONJ
ma-99	475	13	σαzα−1	σαzα−1	NOUN
ma-99	475	14	dz	dz	X
ma-99	475	15	}	}	PUNCT
ma-99	475	16	,	,	PUNCT
ma-99	475	17	λ	λ	X
ma-99	475	18	≥	≥	NOUN
ma-99	475	19	0	0	NUM
ma-99	475	20	.	.	PUNCT
ma-99	476	1	(	(	PUNCT
ma-99	476	2	5.4	5.4	NUM
ma-99	476	3	)	)	PUNCT
ma-99	476	4	applying	apply	VERB
ma-99	476	5	itô	itô	PROPN
ma-99	476	6	’s	’s	PART
ma-99	476	7	formula	formula	NOUN
ma-99	476	8	,	,	PUNCT
ma-99	476	9	for	for	ADP
ma-99	476	10	t	t	PROPN
ma-99	476	11	≥	≥	PROPN
ma-99	476	12	r	r	NOUN
ma-99	476	13	≥	≥	NOUN
ma-99	476	14	0	0	NUM
ma-99	476	15	,	,	PUNCT
ma-99	476	16	we	we	PRON
ma-99	476	17	obtain	obtain	VERB
ma-99	476	18	uj	uj	PROPN
ma-99	476	19	,	,	PUNCT
ma-99	476	20	t	t	NOUN
ma-99	476	21	=	=	SYM
ma-99	476	22	e−θ(t−r)uj	e−θ(t−r)uj	PROPN
ma-99	476	23	,	,	PUNCT
ma-99	476	24	r	r	NOUN
ma-99	476	25	+	+	NOUN
ma-99	476	26	a	a	DET
ma-99	476	27	∫	∫	PROPN
ma-99	476	28	t	t	PROPN
ma-99	476	29	r	r	NOUN
ma-99	476	30	e−θ(t−s)ds	e−θ(t−s)ds	PROPN
ma-99	476	31	+	+	CCONJ
ma-99	476	32	σ	σ	NUM
ma-99	476	33	∫	∫	PROPN
ma-99	476	34	t	t	PROPN
ma-99	476	35	r	r	NOUN
ma-99	476	36	e−θ(t−s)u	e−θ(t−s)u	NOUN
ma-99	476	37	1	1	NUM
ma-99	476	38	/	/	SYM
ma-99	476	39	α	α	PRON
ma-99	476	40	j	j	PROPN
ma-99	476	41	,	,	PUNCT
ma-99	476	42	s−dzj	s−dzj	ADJ
ma-99	476	43	,	,	PUNCT
ma-99	476	44	s	s	PART
ma-99	476	45	,	,	PUNCT
ma-99	476	46	j	j	PROPN
ma-99	476	47	≥	≥	PROPN
ma-99	476	48	1	1	NUM
ma-99	476	49	.	.	PUNCT
ma-99	477	1	(	(	PUNCT
ma-99	477	2	5.5	5.5	NUM
ma-99	477	3	)	)	PUNCT
ma-99	477	4	let	let	VERB
ma-99	477	5	the	the	DET
ma-99	477	6	process	process	NOUN
ma-99	477	7	be	be	AUX
ma-99	477	8	observed	observe	VERB
ma-99	477	9	at	at	ADP
ma-99	477	10	{	{	PUNCT
ma-99	477	11	kh	kh	PROPN
ma-99	477	12	,	,	PUNCT
ma-99	477	13	k	k	PROPN
ma-99	477	14	=	=	SYM
ma-99	477	15	0	0	NUM
ma-99	477	16	,	,	PUNCT
ma-99	477	17	1	1	NUM
ma-99	477	18	,	,	PUNCT
ma-99	477	19	.	.	PUNCT
ma-99	477	20	.	.	PUNCT
ma-99	478	1	.	.	PUNCT
ma-99	479	1	,	,	PUNCT
ma-99	479	2	n	n	CCONJ
ma-99	479	3	}	}	PUNCT
ma-99	479	4	from	from	ADP
ma-99	479	5	a	a	DET
ma-99	479	6	single	single	ADJ
ma-99	479	7	realization	realization	NOUN
ma-99	479	8	{	{	PUNCT
ma-99	479	9	uj	uj	PROPN
ma-99	479	10	,	,	PUNCT
ma-99	479	11	t	t	PROPN
ma-99	479	12	,	,	PUNCT
ma-99	479	13	t	t	PROPN
ma-99	479	14	≥	≥	NUM
ma-99	479	15	0	0	NUM
ma-99	479	16	}	}	PUNCT
ma-99	479	17	for	for	ADP
ma-99	479	18	fixed	fix	VERB
ma-99	479	19	h.	h.	PROPN
ma-99	479	20	for	for	ADP
ma-99	479	21	simplicity	simplicity	NOUN
ma-99	479	22	,	,	PUNCT
ma-99	479	23	we	we	PRON
ma-99	479	24	take	take	VERB
ma-99	479	25	h	h	NOUN
ma-99	479	26	=	=	NOUN
ma-99	479	27	1	1	X
ma-99	479	28	.	.	PUNCT
ma-99	480	1	this	this	DET
ma-99	480	2	equation	equation	NOUN
ma-99	480	3	can	can	AUX
ma-99	480	4	be	be	AUX
ma-99	480	5	considered	consider	VERB
ma-99	480	6	as	as	ADP
ma-99	480	7	a	a	DET
ma-99	480	8	first	first	ADJ
ma-99	480	9	order	order	NOUN
ma-99	480	10	autoregressive(ar(1	autoregressive(ar(1	ADV
ma-99	480	11	)	)	PUNCT
ma-99	480	12	)	)	PUNCT
ma-99	480	13	equation	equation	NOUN
ma-99	480	14	uj	uj	PROPN
ma-99	480	15	,	,	PUNCT
ma-99	480	16	k	k	PROPN
ma-99	480	17	=	=	PROPN
ma-99	480	18	ρ+	ρ+	NUM
ma-99	480	19	γuj	γuj	VERB
ma-99	480	20	,	,	PUNCT
ma-99	480	21	k−1	k−1	PROPN
ma-99	480	22	+	+	PROPN
ma-99	480	23	εj	εj	PROPN
ma-99	480	24	,	,	PUNCT
ma-99	480	25	k	k	PROPN
ma-99	480	26	,	,	PUNCT
ma-99	480	27	j	j	PROPN
ma-99	480	28	≥	≥	NUM
ma-99	480	29	1	1	NUM
ma-99	480	30	(	(	PUNCT
ma-99	480	31	5.6	5.6	NUM
ma-99	480	32	)	)	PUNCT
ma-99	480	33	where	where	SCONJ
ma-99	480	34	γ	γ	PROPN
ma-99	480	35	=	=	SYM
ma-99	480	36	e−θ	e−θ	PROPN
ma-99	480	37	,	,	PUNCT
ma-99	480	38	ρ	ρ	X
ma-99	480	39	=	=	PUNCT
ma-99	481	1	aθ−1(1−	aθ−1(1−	PROPN
ma-99	481	2	γ	γ	PROPN
ma-99	481	3	)	)	PUNCT
ma-99	481	4	and	and	CCONJ
ma-99	481	5	εj	εj	NOUN
ma-99	481	6	,	,	PUNCT
ma-99	481	7	k	k	PROPN
ma-99	482	1	=	=	PROPN
ma-99	482	2	σ	σ	PROPN
ma-99	482	3	∫	∫	PROPN
ma-99	482	4	k	k	PROPN
ma-99	482	5	k−1	k−1	PROPN
ma-99	482	6	e−θ(k−s)u	e−θ(k−s)u	ADV
ma-99	482	7	1	1	NUM
ma-99	482	8	/	/	SYM
ma-99	482	9	α	α	PRON
ma-99	482	10	j	j	PROPN
ma-99	482	11	,	,	PUNCT
ma-99	482	12	s−dzj	s−dzj	ADJ
ma-99	482	13	,	,	PUNCT
ma-99	482	14	s	s	PART
ma-99	482	15	,	,	PUNCT
ma-99	482	16	k	k	PROPN
ma-99	482	17	≥	≥	NUM
ma-99	482	18	1	1	NUM
ma-99	482	19	,	,	PUNCT
ma-99	482	20	j	j	PROPN
ma-99	482	21	≥	≥	PROPN
ma-99	482	22	1	1	NUM
ma-99	482	23	.	.	PUNCT
ma-99	482	24	(	(	PUNCT
ma-99	482	25	5.7	5.7	NUM
ma-99	482	26	)	)	PUNCT
ma-99	482	27	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	482	28	eur	eur	PROPN
ma-99	482	29	.	.	PUNCT
ma-99	483	1	j.	j.	PROPN
ma-99	483	2	math	math	PROPN
ma-99	483	3	.	.	PUNCT
ma-99	484	1	anal	anal	PROPN
ma-99	484	2	.	.	PUNCT
ma-99	485	1	10.28924	10.28924	NUM
ma-99	485	2	/	/	SYM
ma-99	485	3	ada	ada	PROPN
ma-99	485	4	/	/	SYM
ma-99	485	5	ma.3.4	ma.3.4	PROPN
ma-99	485	6	20for	20for	PROPN
ma-99	485	7	b	b	PROPN
ma-99	485	8	∈	∈	PROPN
ma-99	485	9	b(r+	b(r+	NOUN
ma-99	485	10	)	)	PUNCT
ma-99	485	11	,	,	PUNCT
ma-99	485	12	let	let	VERB
ma-99	485	13	s2,j	s2,j	PROPN
ma-99	485	14	,	,	PUNCT
ma-99	485	15	n(b	n(b	PROPN
ma-99	485	16	)	)	PUNCT
ma-99	486	1	=	=	SYM
ma-99	486	2	n∑	n∑	NOUN
ma-99	486	3	k=1	k=1	PROPN
ma-99	486	4	uj	uj	PROPN
ma-99	486	5	,	,	PUNCT
ma-99	486	6	k−1εk	k−1εk	PROPN
ma-99	486	7	ib(|uj	ib(|uj	PROPN
ma-99	486	8	,	,	PUNCT
ma-99	486	9	k−1εj	k−1εj	PROPN
ma-99	486	10	,	,	PUNCT
ma-99	486	11	k	k	PROPN
ma-99	486	12	|	|	NOUN
ma-99	486	13	)	)	PUNCT
ma-99	486	14	,	,	PUNCT
ma-99	486	15	s1,j	s1,j	PROPN
ma-99	486	16	,	,	PUNCT
ma-99	486	17	n(b	n(b	PROPN
ma-99	486	18	)	)	PUNCT
ma-99	486	19	=	=	PUNCT
ma-99	487	1	n∑	n∑	NOUN
ma-99	487	2	k=1	k=1	PROPN
ma-99	488	1	u2	u2	PROPN
ma-99	488	2	j	j	PROPN
ma-99	488	3	,	,	PUNCT
ma-99	488	4	k−1ib(uj	k−1ib(uj	NOUN
ma-99	488	5	,	,	PUNCT
ma-99	488	6	k−1	k−1	PROPN
ma-99	488	7	)	)	PUNCT
ma-99	488	8	,	,	PUNCT
ma-99	488	9	j	j	PROPN
ma-99	488	10	≥	≥	PROPN
ma-99	488	11	1	1	NUM
ma-99	488	12	.	.	PUNCT
ma-99	489	1	(	(	PUNCT
ma-99	489	2	5.8	5.8	NUM
ma-99	489	3	)	)	PUNCT
ma-99	489	4	it	it	PRON
ma-99	489	5	is	be	AUX
ma-99	489	6	easy	easy	ADJ
ma-99	489	7	to	to	PART
ma-99	489	8	see	see	VERB
ma-99	489	9	that	that	DET
ma-99	489	10	εj	εj	NOUN
ma-99	489	11	,	,	PUNCT
ma-99	489	12	k	k	PROPN
ma-99	489	13	=	=	SYM
ma-99	489	14	uj	uj	PROPN
ma-99	489	15	,	,	PUNCT
ma-99	490	1	k	k	PROPN
ma-99	490	2	−	−	PROPN
ma-99	491	1	e(uj	e(uj	PROPN
ma-99	491	2	,	,	PUNCT
ma-99	491	3	k	k	PROPN
ma-99	491	4	|fk−1	|fk−1	NOUN
ma-99	491	5	)	)	PUNCT
ma-99	491	6	,	,	PUNCT
ma-99	491	7	k	k	PROPN
ma-99	491	8	≥	≥	NUM
ma-99	491	9	1	1	NUM
ma-99	491	10	,	,	PUNCT
ma-99	491	11	j	j	PROPN
ma-99	491	12	≥	≥	PROPN
ma-99	491	13	1	1	NUM
ma-99	491	14	.	.	PUNCT
ma-99	491	15	(	(	PUNCT
ma-99	491	16	5.9)is	5.9)is	ADJ
ma-99	491	17	a	a	DET
ma-99	491	18	sequence	sequence	NOUN
ma-99	491	19	of	of	ADP
ma-99	491	20	martingale	martingale	ADJ
ma-99	491	21	differences	difference	NOUN
ma-99	491	22	for	for	ADP
ma-99	491	23	every	every	DET
ma-99	491	24	fixed	fix	VERB
ma-99	491	25	j	j	PROPN
ma-99	491	26	.let	.let	PUNCT
ma-99	491	27	s1,j	s1,j	PROPN
ma-99	491	28	,	,	PUNCT
ma-99	491	29	n	n	NOUN
ma-99	491	30	:	:	PUNCT
ma-99	491	31	=	=	SYM
ma-99	491	32	s1,j	s1,j	PROPN
ma-99	491	33	,	,	PUNCT
ma-99	491	34	n(0,∞	n(0,∞	NOUN
ma-99	491	35	)	)	PUNCT
ma-99	491	36	,	,	PUNCT
ma-99	491	37	s2,j	s2,j	PROPN
ma-99	491	38	,	,	PUNCT
ma-99	491	39	n	n	PRON
ma-99	491	40	:	:	PUNCT
ma-99	491	41	=	=	SYM
ma-99	491	42	s2,j	s2,j	PROPN
ma-99	491	43	,	,	PUNCT
ma-99	491	44	n(0,∞	n(0,∞	NOUN
ma-99	491	45	)	)	PUNCT
ma-99	491	46	and	and	CCONJ
ma-99	491	47	recall	recall	VERB
ma-99	491	48	that	that	SCONJ
ma-99	491	49	γ	γ	PROPN
ma-99	491	50	=	=	SYM
ma-99	491	51	e−θ	e−θ	PROPN
ma-99	491	52	.then	.then	PUNCT
ma-99	491	53	θ̂j	θ̂j	PROPN
ma-99	491	54	,	,	PUNCT
ma-99	491	55	n	n	PRON
ma-99	491	56	−	−	PROPN
ma-99	491	57	θ	θ	NOUN
ma-99	491	58	=	=	SYM
ma-99	491	59	s2,j	s2,j	PROPN
ma-99	491	60	,	,	PUNCT
ma-99	491	61	n	n	PRON
ma-99	491	62	s1,j	s1,j	NOUN
ma-99	491	63	,	,	PUNCT
ma-99	491	64	n	n	CCONJ
ma-99	491	65	(	(	PUNCT
ma-99	491	66	5.10	5.10	NUM
ma-99	491	67	)	)	PUNCT
ma-99	491	68	where	where	SCONJ
ma-99	491	69	θ̂n	θ̂n	NUM
ma-99	491	70	is	be	AUX
ma-99	491	71	the	the	DET
ma-99	491	72	conditional	conditional	ADJ
ma-99	491	73	least	least	ADJ
ma-99	491	74	squares	square	NOUN
ma-99	491	75	estimator	estimator	NOUN
ma-99	491	76	(	(	PUNCT
ma-99	491	77	clse	clse	PROPN
ma-99	491	78	)	)	PUNCT
ma-99	491	79	which	which	PRON
ma-99	491	80	minimizes	minimize	VERB
ma-99	491	81	n∑	n∑	NOUN
ma-99	491	82	k=1	k=1	PROPN
ma-99	491	83	ε2	ε2	PROPN
ma-99	491	84	j	j	PROPN
ma-99	491	85	,	,	PUNCT
ma-99	491	86	k	k	PROPN
ma-99	491	87	=	=	PUNCT
ma-99	491	88	n∑	n∑	NOUN
ma-99	491	89	k=1	k=1	PUNCT
ma-99	492	1	[	[	X
ma-99	492	2	uj	uj	PROPN
ma-99	492	3	,	,	PUNCT
ma-99	492	4	k	k	PROPN
ma-99	492	5	−	−	PROPN
ma-99	492	6	e(uj	e(uj	PROPN
ma-99	492	7	,	,	PUNCT
ma-99	492	8	k	k	PROPN
ma-99	492	9	|fk−1)]2	|fk−1)]2	PROPN
ma-99	493	1	=	=	PUNCT
ma-99	493	2	n∑	n∑	NOUN
ma-99	493	3	k=1	k=1	PUNCT
ma-99	494	1	[	[	X
ma-99	494	2	uj	uj	PROPN
ma-99	494	3	,	,	PUNCT
ma-99	494	4	k	k	PROPN
ma-99	494	5	−	−	PROPN
ma-99	494	6	ρ−	ρ−	PROPN
ma-99	494	7	γuj	γuj	VERB
ma-99	494	8	,	,	PUNCT
ma-99	494	9	k−1]2	k−1]2	INTJ
ma-99	494	10	(	(	PUNCT
ma-99	494	11	5.11	5.11	NUM
ma-99	494	12	)	)	PUNCT
ma-99	494	13	and	and	CCONJ
ma-99	494	14	are	be	AUX
ma-99	494	15	given	give	VERB
ma-99	494	16	by	by	ADP
ma-99	494	17	γ̂j	γ̂j	NOUN
ma-99	494	18	,	,	PUNCT
ma-99	494	19	n	n	NOUN
ma-99	495	1	=	=	SYM
ma-99	495	2	∑n	∑n	PROPN
ma-99	495	3	k=1	k=1	PROPN
ma-99	495	4	uj	uj	PROPN
ma-99	495	5	,	,	PUNCT
ma-99	495	6	k−1	k−1	PROPN
ma-99	495	7	∑n	∑n	PROPN
ma-99	496	1	k=1	k=1	PROPN
ma-99	496	2	uj	uj	PROPN
ma-99	496	3	,	,	PUNCT
ma-99	496	4	k	k	PROPN
ma-99	496	5	−	−	PROPN
ma-99	496	6	n	n	CCONJ
ma-99	496	7	∑n	∑n	PROPN
ma-99	496	8	k=1	k=1	PROPN
ma-99	496	9	uj	uj	PROPN
ma-99	496	10	,	,	PUNCT
ma-99	496	11	k−1uj	k−1uj	PROPN
ma-99	496	12	,	,	PUNCT
ma-99	496	13	k	k	PROPN
ma-99	496	14	(	(	PUNCT
ma-99	496	15	∑n	∑n	PROPN
ma-99	496	16	k=1	k=1	PROPN
ma-99	496	17	uj	uj	PROPN
ma-99	496	18	,	,	PUNCT
ma-99	496	19	k−1)2	k−1)2	VERB
ma-99	496	20	−	−	PROPN
ma-99	496	21	n	n	NOUN
ma-99	496	22	∑n	∑n	PROPN
ma-99	496	23	k=1	k=1	PUNCT
ma-99	496	24	u	u	PROPN
ma-99	496	25	2	2	PROPN
ma-99	496	26	j	j	PROPN
ma-99	496	27	,	,	PUNCT
ma-99	496	28	k−1	k−1	PROPN
ma-99	496	29	,	,	PUNCT
ma-99	496	30	ρ̂j	ρ̂j	X
ma-99	496	31	,	,	PUNCT
ma-99	496	32	n	n	NOUN
ma-99	496	33	=	=	SYM
ma-99	496	34	1	1	NUM
ma-99	496	35	n	n	NUM
ma-99	496	36	n∑	n∑	NOUN
ma-99	496	37	k=1	k=1	PROPN
ma-99	497	1	uj	uj	PROPN
ma-99	497	2	,	,	PUNCT
ma-99	497	3	k	k	PROPN
ma-99	497	4	−	−	PROPN
ma-99	497	5	γ̂n	γ̂n	NOUN
ma-99	497	6	1	1	NUM
ma-99	497	7	n	n	NUM
ma-99	497	8	n∑	n∑	NOUN
ma-99	497	9	k=1	k=1	PROPN
ma-99	497	10	uj	uj	PROPN
ma-99	497	11	,	,	PUNCT
ma-99	497	12	k−1	k−1	PROPN
ma-99	497	13	,	,	PUNCT
ma-99	497	14	θ̂j	θ̂j	PROPN
ma-99	497	15	,	,	PUNCT
ma-99	497	16	n	n	NOUN
ma-99	497	17	=	=	SYM
ma-99	497	18	−	−	PROPN
ma-99	497	19	log	log	NOUN
ma-99	497	20	γ̂j	γ̂j	NOUN
ma-99	497	21	,	,	PUNCT
ma-99	497	22	n	n	CCONJ
ma-99	497	23	,	,	PUNCT
ma-99	497	24	âj	âj	NOUN
ma-99	497	25	,	,	PUNCT
ma-99	497	26	n	n	NOUN
ma-99	497	27	=	=	PUNCT
ma-99	498	1	ρ̂nθ̂n	ρ̂nθ̂n	PROPN
ma-99	498	2	1−	1−	NUM
ma-99	498	3	γ̂n	γ̂n	NOUN
ma-99	498	4	.let	.let	PUNCT
ma-99	499	1	(	(	PUNCT
ma-99	499	2	s1	s1	NOUN
ma-99	499	3	,	,	PUNCT
ma-99	499	4	s2	s2	PROPN
ma-99	499	5	)	)	PUNCT
ma-99	499	6	have	have	VERB
ma-99	499	7	the	the	DET
ma-99	499	8	characteristic	characteristic	ADJ
ma-99	499	9	function	function	NOUN
ma-99	499	10	given	give	VERB
ma-99	499	11	by	by	ADP
ma-99	499	12	e[exp{iλ1s1	e[exp{iλ1s1	NOUN
ma-99	499	13	+	+	CCONJ
ma-99	499	14	iλ2s2	iλ2s2	PROPN
ma-99	499	15	}	}	PUNCT
ma-99	499	16	]	]	PUNCT
ma-99	499	17	:	:	PUNCT
ma-99	499	18	=	=	SYM
ma-99	499	19	exp	exp	NOUN
ma-99	499	20	{	{	PUNCT
ma-99	499	21	−	−	PROPN
ma-99	499	22	σα	σα	PROPN
ma-99	499	23	θ2γ(−α	θ2γ(−α	PROPN
ma-99	499	24	)	)	PUNCT
ma-99	499	25	∫	∫	PROPN
ma-99	500	1	∞	∞	PROPN
ma-99	500	2	0	0	PUNCT
ma-99	501	1	e	e	X
ma-99	501	2	(	(	PUNCT
ma-99	501	3	1−	1−	NUM
ma-99	501	4	exp{iλ1y	exp{iλ1y	NUM
ma-99	501	5	2	2	NUM
ma-99	501	6	+	+	CCONJ
ma-99	501	7	iλ2y	iλ2y	PROPN
ma-99	501	8	(	(	PUNCT
ma-99	501	9	α+1)/αvj,1	α+1)/αvj,1	NOUN
ma-99	501	10	}	}	PUNCT
ma-99	501	11	)	)	PUNCT
ma-99	501	12	×	×	NOUN
ma-99	501	13	e	e	NOUN
ma-99	501	14	(	(	PUNCT
ma-99	501	15	exp	exp	X
ma-99	501	16	{	{	PUNCT
ma-99	501	17	ie−2θλ1y	ie−2θλ1y	NUM
ma-99	501	18	2	2	NUM
ma-99	501	19	1−	1−	NUM
ma-99	501	20	e−2θ	e−2θ	NOUN
ma-99	502	1	+	+	CCONJ
ma-99	502	2	ie−θ(α+1)/αλ2y	ie−θ(α+1)/αλ2y	X
ma-99	502	3	(	(	PUNCT
ma-99	502	4	α+1)/αvj,2	α+1)/αvj,2	X
ma-99	502	5	(	(	PUNCT
ma-99	502	6	1−	1−	NUM
ma-99	502	7	eθ(α+1))1	eθ(α+1))1	NOUN
ma-99	502	8	/	/	SYM
ma-99	502	9	α	α	NOUN
ma-99	502	10	}	}	PUNCT
ma-99	502	11	)	)	PUNCT
ma-99	502	12	dy	dy	NOUN
ma-99	502	13	yα+1	yα+1	NOUN
ma-99	502	14	}	}	PUNCT
ma-99	502	15	(	(	PUNCT
ma-99	502	16	5.12	5.12	NUM
ma-99	502	17	)	)	PUNCT
ma-99	502	18	and	and	CCONJ
ma-99	502	19	vj	vj	INTJ
ma-99	502	20	,	,	PUNCT
ma-99	502	21	k	k	PROPN
ma-99	502	22	:	:	PUNCT
ma-99	502	23	=	=	SYM
ma-99	502	24	σ	σ	NUM
ma-99	502	25	∫	∫	PROPN
ma-99	503	1	k	k	PROPN
ma-99	503	2	k−1	k−1	PROPN
ma-99	503	3	e−θ(k−s)e−θ(s−k+1)/αdzj	e−θ(k−s)e−θ(s−k+1)/αdzj	PROPN
ma-99	503	4	,	,	PUNCT
ma-99	503	5	s	s	PART
ma-99	503	6	,	,	PUNCT
ma-99	503	7	k	k	PROPN
ma-99	504	1	=	=	SYM
ma-99	505	1	1	1	NUM
ma-99	505	2	,	,	PUNCT
ma-99	505	3	2	2	NUM
ma-99	505	4	,	,	PUNCT
ma-99	505	5	j	j	PROPN
ma-99	505	6	≥	≥	NUM
ma-99	505	7	1	1	NUM
ma-99	505	8	(	(	PUNCT
ma-99	505	9	5.13	5.13	NUM
ma-99	505	10	)	)	PUNCT
ma-99	505	11	which	which	PRON
ma-99	505	12	are	be	AUX
ma-99	505	13	i.i.d	i.i.d	ADJ
ma-99	505	14	.	.	PUNCT
ma-99	506	1	with	with	ADP
ma-99	506	2	the	the	DET
ma-99	506	3	same	same	ADJ
ma-99	506	4	distribution	distribution	NOUN
ma-99	506	5	as	as	ADP
ma-99	506	6	σ	σ	PROPN
ma-99	506	7	(	(	PUNCT
ma-99	506	8	e−θ	e−θ	PROPN
ma-99	506	9	−	−	PROPN
ma-99	506	10	1	1	NUM
ma-99	506	11	(	(	PUNCT
ma-99	506	12	α−	α−	ADP
ma-99	506	13	1)θ	1)θ	NUM
ma-99	506	14	)	)	PUNCT
ma-99	506	15	1	1	NUM
ma-99	506	16	/	/	SYM
ma-99	506	17	α	α	PROPN
ma-99	506	18	zj,1	zj,1	PROPN
ma-99	506	19	which	which	PRON
ma-99	506	20	is	be	AUX
ma-99	506	21	regularly	regularly	ADV
ma-99	506	22	varying	vary	VERB
ma-99	506	23	with	with	ADP
ma-99	506	24	index	index	NOUN
ma-99	506	25	α	α	NOUN
ma-99	506	26	.	.	PUNCT
ma-99	507	1	the	the	DET
ma-99	507	2	limit	limit	NOUN
ma-99	507	3	distribution	distribution	NOUN
ma-99	507	4	is	be	AUX
ma-99	507	5	normal	normal	ADJ
ma-99	507	6	only	only	ADV
ma-99	507	7	in	in	ADP
ma-99	507	8	the	the	DET
ma-99	507	9	gaussian	gaussian	ADJ
ma-99	507	10	case	case	NOUN
ma-99	507	11	α	α	X
ma-99	507	12	=	=	SYM
ma-99	507	13	2	2	X
ma-99	507	14	.	.	PUNCT
ma-99	507	15	following	follow	VERB
ma-99	507	16	li	li	PROPN
ma-99	507	17	and	and	CCONJ
ma-99	507	18	ma	ma	PROPN
ma-99	508	1	[	[	X
ma-99	508	2	31	31	NUM
ma-99	508	3	]	]	PUNCT
ma-99	508	4	it	it	PRON
ma-99	508	5	can	can	AUX
ma-99	508	6	be	be	AUX
ma-99	508	7	shown	show	VERB
ma-99	508	8	that	that	SCONJ
ma-99	508	9	for	for	ADP
ma-99	508	10	every	every	DET
ma-99	508	11	fixed	fix	VERB
ma-99	508	12	j	j	PROPN
ma-99	508	13	,	,	PUNCT
ma-99	508	14	if	if	SCONJ
ma-99	508	15	we	we	PRON
ma-99	508	16	have	have	VERB
ma-99	508	17	1	1	NUM
ma-99	508	18	<	<	X
ma-99	508	19	α	α	X
ma-99	508	20	<	<	X
ma-99	508	21	(	(	PUNCT
ma-99	508	22	1	1	NUM
ma-99	508	23	+	+	CCONJ
ma-99	508	24	√	√	ADJ
ma-99	508	25	5)/2,then	5)/2,then	ADV
ma-99	508	26	we	we	PRON
ma-99	508	27	have	have	VERB
ma-99	508	28	as	as	ADP
ma-99	508	29	n	n	X
ma-99	508	30	→∞	→∞	PROPN
ma-99	508	31	(	(	PUNCT
ma-99	508	32	d−2	d−2	PROPN
ma-99	508	33	n	n	PRON
ma-99	508	34	s1,j	s1,j	NOUN
ma-99	508	35	,	,	PUNCT
ma-99	508	36	n	n	CCONJ
ma-99	508	37	,	,	PUNCT
ma-99	508	38	c	c	NOUN
ma-99	508	39	−1	−1	NOUN
ma-99	508	40	n	n	PRON
ma-99	508	41	s2,j	s2,j	PROPN
ma-99	508	42	,	,	PUNCT
ma-99	508	43	n	n	CCONJ
ma-99	508	44	)	)	PUNCT
ma-99	508	45	d→(s1	d→(s1	PROPN
ma-99	508	46	,	,	PUNCT
ma-99	508	47	s2	s2	PROPN
ma-99	508	48	)	)	PUNCT
ma-99	508	49	on	on	ADP
ma-99	508	50	r2	r2	PROPN
ma-99	508	51	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	508	52	eur	eur	PROPN
ma-99	508	53	.	.	PUNCT
ma-99	509	1	j.	j.	PROPN
ma-99	509	2	math	math	PROPN
ma-99	509	3	.	.	PUNCT
ma-99	510	1	anal	anal	PROPN
ma-99	510	2	.	.	PUNCT
ma-99	511	1	10.28924	10.28924	NUM
ma-99	511	2	/	/	SYM
ma-99	511	3	ada	ada	PROPN
ma-99	511	4	/	/	SYM
ma-99	511	5	ma.3.4	ma.3.4	PROPN
ma-99	511	6	21	21	NUM
ma-99	511	7	where	where	SCONJ
ma-99	511	8	dn	dn	NOUN
ma-99	511	9	=	=	SYM
ma-99	511	10	n1	n1	PROPN
ma-99	511	11	/	/	SYM
ma-99	511	12	α	α	PROPN
ma-99	511	13	and	and	CCONJ
ma-99	511	14	cn	cn	PROPN
ma-99	511	15	=	=	NOUN
ma-99	511	16	n(α+1)/α2	n(α+1)/α2	NOUN
ma-99	512	1	=	=	SYM
ma-99	512	2	d	d	PROPN
ma-99	512	3	(	(	PUNCT
ma-99	512	4	α+1)/α	α+1)/α	PROPN
ma-99	512	5	n	n	PROPN
ma-99	512	6	.for	.for	PUNCT
ma-99	513	1	the	the	DET
ma-99	513	2	stable	stable	ADJ
ma-99	513	3	spde	spde	NOUN
ma-99	513	4	model	model	NOUN
ma-99	513	5	,	,	PUNCT
ma-99	513	6	we	we	PRON
ma-99	513	7	have	have	AUX
ma-99	513	8	the	the	DET
ma-99	513	9	following	following	ADJ
ma-99	513	10	result	result	NOUN
ma-99	513	11	on	on	ADP
ma-99	513	12	the	the	DET
ma-99	513	13	consistency	consistency	NOUN
ma-99	513	14	and	and	CCONJ
ma-99	513	15	the	the	DET
ma-99	513	16	limitdistribution	limitdistribution	NOUN
ma-99	513	17	of	of	ADP
ma-99	513	18	the	the	DET
ma-99	513	19	clse	clse	NOUN
ma-99	513	20	:	:	PUNCT
ma-99	513	21	theorem	theorem	VERB
ma-99	513	22	5.1	5.1	NUM
ma-99	513	23	if	if	SCONJ
ma-99	513	24	we	we	PRON
ma-99	513	25	have	have	VERB
ma-99	513	26	1	1	NUM
ma-99	513	27	<	<	X
ma-99	513	28	α	α	X
ma-99	513	29	<	<	X
ma-99	513	30	(	(	PUNCT
ma-99	513	31	1	1	NUM
ma-99	513	32	+	+	CCONJ
ma-99	513	33	√	√	NUM
ma-99	513	34	5)/2	5)/2	NUM
ma-99	513	35	,	,	PUNCT
ma-99	513	36	then	then	ADV
ma-99	513	37	for	for	ADP
ma-99	513	38	every	every	DET
ma-99	513	39	fixed	fix	VERB
ma-99	513	40	j	j	PROPN
ma-99	513	41	≥	≥	X
ma-99	513	42	1a	1a	PROPN
ma-99	513	43	)	)	PUNCT
ma-99	513	44	θ̂j	θ̂j	PROPN
ma-99	513	45	,	,	PUNCT
ma-99	513	46	n	n	CCONJ
ma-99	513	47	→p	→p	PROPN
ma-99	513	48	θ	θ	PROPN
ma-99	513	49	as	as	ADP
ma-99	513	50	n	n	PROPN
ma-99	513	51	→∞.b	→∞.b	NUM
ma-99	513	52	)	)	PUNCT
ma-99	513	53	n(α−1)/α2	n(α−1)/α2	NUM
ma-99	513	54	(	(	PUNCT
ma-99	513	55	θ̂j	θ̂j	PROPN
ma-99	513	56	,	,	PUNCT
ma-99	513	57	n	n	CCONJ
ma-99	513	58	−	−	PROPN
ma-99	513	59	θ)→d	θ)→d	NOUN
ma-99	513	60	(	(	PUNCT
ma-99	513	61	σ2	σ2	PROPN
ma-99	513	62	ν2	ν2	PROPN
ma-99	513	63	j	j	PROPN
ma-99	513	64	)	)	PUNCT
ma-99	513	65	1	1	NUM
ma-99	513	66	/	/	SYM
ma-99	513	67	α	α	NOUN
ma-99	513	68	s2	s2	NOUN
ma-99	513	69	s1	s1	NOUN
ma-99	513	70	as	as	ADP
ma-99	513	71	n	n	PROPN
ma-99	513	72	→∞.	→∞.	PROPN
ma-99	513	73	c	c	X
ma-99	513	74	)	)	PUNCT
ma-99	513	75	if	if	SCONJ
ma-99	513	76	in	in	ADP
ma-99	513	77	addition	addition	NOUN
ma-99	513	78	,	,	PUNCT
ma-99	513	79	limj→∞	limj→∞	PROPN
ma-99	513	80	∣∣νj	∣∣νj	PROPN
ma-99	513	81	∣∣	∣∣	NUM
ma-99	513	82	=	=	SYM
ma-99	513	83	∞	∞	PROPN
ma-99	513	84	,	,	PUNCT
ma-99	513	85	then	then	ADV
ma-99	513	86	for	for	ADP
ma-99	513	87	every	every	DET
ma-99	513	88	fixed	fix	VERB
ma-99	513	89	n	n	X
ma-99	513	90	≥	≥	NOUN
ma-99	513	91	1	1	NUM
ma-99	513	92	,	,	PUNCT
ma-99	513	93	θ̂j	θ̂j	PROPN
ma-99	513	94	,	,	PUNCT
ma-99	513	95	t	t	PROPN
ma-99	513	96	→p	→p	PROPN
ma-99	513	97	θ	θ	PROPN
ma-99	513	98	as	as	ADP
ma-99	513	99	j	j	PROPN
ma-99	513	100	→∞	→∞	PROPN
ma-99	513	101	and	and	CCONJ
ma-99	513	102	∣∣νj	∣∣νj	PROPN
ma-99	513	103	∣∣	∣∣	NUM
ma-99	513	104	(	(	PUNCT
ma-99	513	105	θ̂j	θ̂j	PROPN
ma-99	513	106	,	,	PUNCT
ma-99	513	107	n	n	CCONJ
ma-99	513	108	−	−	PROPN
ma-99	513	109	θ)→d	θ)→d	NOUN
ma-99	513	110	σ	σ	NOUN
ma-99	513	111	(	(	PUNCT
ma-99	513	112	n−(α−1)/α2	n−(α−1)/α2	NOUN
ma-99	513	113	)	)	PUNCT
ma-99	513	114	1	1	NUM
ma-99	513	115	/	/	SYM
ma-99	513	116	α	α	NOUN
ma-99	513	117	s2	s2	NOUN
ma-99	513	118	s1	s1	NOUN
ma-99	513	119	as	as	ADP
ma-99	513	120	j	j	PROPN
ma-99	513	121	→∞.where	→∞.where	X
ma-99	513	122	s2	s2	PROPN
ma-99	513	123	and	and	CCONJ
ma-99	513	124	s1	s1	NOUN
ma-99	513	125	are	be	AUX
ma-99	513	126	defined	define	VERB
ma-99	513	127	in	in	ADP
ma-99	513	128	(	(	PUNCT
ma-99	513	129	5.12	5.12	NUM
ma-99	513	130	)	)	PUNCT
ma-99	513	131	.	.	PUNCT
ma-99	514	1	remarks1	remarks1	NOUN
ma-99	514	2	)	)	PUNCT
ma-99	515	1	the	the	DET
ma-99	515	2	limit	limit	NOUN
ma-99	515	3	distribution	distribution	NOUN
ma-99	515	4	in	in	ADP
ma-99	515	5	the	the	DET
ma-99	515	6	case	case	NOUN
ma-99	515	7	(	(	PUNCT
ma-99	515	8	1	1	NUM
ma-99	515	9	+	+	CCONJ
ma-99	515	10	√	√	NUM
ma-99	515	11	5)/2	5)/2	NUM
ma-99	515	12	<	<	X
ma-99	515	13	α	α	X
ma-99	515	14	<	<	X
ma-99	515	15	2	2	NUM
ma-99	515	16	is	be	AUX
ma-99	515	17	still	still	ADV
ma-99	515	18	open.2	open.2	PRON
ma-99	515	19	)	)	PUNCT
ma-99	515	20	the	the	DET
ma-99	515	21	process	process	NOUN
ma-99	515	22	(	(	PUNCT
ma-99	515	23	xj	xj	NOUN
ma-99	515	24	)	)	PUNCT
ma-99	515	25	is	be	AUX
ma-99	515	26	exponentially	exponentially	ADV
ma-99	515	27	ergodic	ergodic	ADJ
ma-99	515	28	and	and	CCONJ
ma-99	515	29	hence	hence	ADV
ma-99	515	30	strongly	strongly	ADV
ma-99	515	31	mixing.3	mixing.3	PROPN
ma-99	515	32	)	)	PUNCT
ma-99	515	33	for	for	ADP
ma-99	515	34	the	the	DET
ma-99	515	35	gaussian	gaussian	ADJ
ma-99	515	36	case	case	NOUN
ma-99	515	37	(	(	PUNCT
ma-99	515	38	α	α	NOUN
ma-99	515	39	=	=	SYM
ma-99	515	40	2	2	NUM
ma-99	515	41	)	)	PUNCT
ma-99	515	42	,	,	PUNCT
ma-99	515	43	the	the	DET
ma-99	515	44	limit	limit	NOUN
ma-99	515	45	results	result	NOUN
ma-99	515	46	are	be	AUX
ma-99	515	47	based	base	VERB
ma-99	515	48	on	on	ADP
ma-99	515	49	ergodic	ergodic	ADJ
ma-99	515	50	theory	theory	NOUN
ma-99	515	51	and	and	CCONJ
ma-99	515	52	martingaleconvergence	martingaleconvergence	NOUN
ma-99	515	53	theorem	theorem	VERB
ma-99	515	54	.	.	PROPN
ma-99	516	1	for	for	ADP
ma-99	516	2	the	the	DET
ma-99	516	3	non	non	ADJ
ma-99	516	4	-	-	ADJ
ma-99	516	5	gaussian	gaussian	ADJ
ma-99	516	6	case	case	NOUN
ma-99	516	7	(	(	PUNCT
ma-99	516	8	1	1	NUM
ma-99	516	9	<	<	X
ma-99	516	10	α	α	X
ma-99	516	11	<	<	X
ma-99	516	12	2	2	NUM
ma-99	516	13	)	)	PUNCT
ma-99	516	14	,	,	PUNCT
ma-99	516	15	limit	limit	NOUN
ma-99	516	16	results	result	NOUN
ma-99	516	17	are	be	AUX
ma-99	516	18	obtained	obtain	VERB
ma-99	516	19	by	by	ADP
ma-99	516	20	thetheory	thetheory	NOUN
ma-99	516	21	of	of	ADP
ma-99	516	22	regular	regular	ADJ
ma-99	516	23	variation	variation	NOUN
ma-99	516	24	and	and	CCONJ
ma-99	516	25	convergence	convergence	NOUN
ma-99	516	26	of	of	ADP
ma-99	516	27	point	point	NOUN
ma-99	516	28	processes.4	processes.4	NOUN
ma-99	516	29	)	)	PUNCT
ma-99	517	1	let	let	VERB
ma-99	517	2	0	0	PUNCT
ma-99	517	3	<	<	X
ma-99	517	4	α	α	X
ma-99	517	5	<	<	X
ma-99	517	6	2	2	NUM
ma-99	517	7	and	and	CCONJ
ma-99	517	8	let	let	VERB
ma-99	517	9	zt	zt	PRON
ma-99	517	10	be	be	AUX
ma-99	517	11	a	a	DET
ma-99	517	12	one	one	NUM
ma-99	517	13	dimensional	dimensional	ADJ
ma-99	517	14	α	α	NOUN
ma-99	517	15	-	-	ADJ
ma-99	517	16	stable	stable	ADJ
ma-99	517	17	process	process	NOUN
ma-99	517	18	with	with	ADP
ma-99	517	19	levy	levy	NOUN
ma-99	517	20	measure	measure	NOUN
ma-99	517	21	ν(dz).then	ν(dz).then	ADV
ma-99	517	22	as	as	ADP
ma-99	517	23	n	n	PROPN
ma-99	517	24	→∞	→∞	PROPN
ma-99	517	25	,	,	PUNCT
ma-99	517	26	np	np	INTJ
ma-99	517	27	(	(	PUNCT
ma-99	517	28	n−1	n−1	PROPN
ma-99	517	29	/	/	SYM
ma-99	517	30	αzt	αzt	NOUN
ma-99	517	31	∈	∈	PROPN
ma-99	517	32	·	·	PUNCT
ma-99	517	33	)	)	PUNCT
ma-99	517	34	→v	→v	NUM
ma-99	517	35	tν	tν	NOUN
ma-99	517	36	(	(	PUNCT
ma-99	517	37	·	·	PUNCT
ma-99	517	38	)	)	PUNCT
ma-99	517	39	.	.	PUNCT
ma-99	518	1	6	6	X
ma-99	518	2	.	.	X
ma-99	518	3	examples	example	NOUN
ma-99	518	4	(	(	PUNCT
ma-99	518	5	a	a	X
ma-99	518	6	)	)	PUNCT
ma-99	518	7	consider	consider	VERB
ma-99	518	8	the	the	DET
ma-99	518	9	linear	linear	ADJ
ma-99	518	10	stochastic	stochastic	ADJ
ma-99	518	11	heat	heat	NOUN
ma-99	518	12	equation	equation	NOUN
ma-99	518	13	with	with	ADP
ma-99	518	14	additive	additive	ADJ
ma-99	518	15	noise	noise	NOUN
ma-99	518	16	du(t	du(t	NOUN
ma-99	518	17	,	,	PUNCT
ma-99	518	18	x	x	X
ma-99	518	19	)	)	PUNCT
ma-99	518	20	=	=	SYM
ma-99	518	21	θuxx(t	θuxx(t	PROPN
ma-99	518	22	,	,	PUNCT
ma-99	518	23	x)dt	x)dt	PROPN
ma-99	518	24	+	+	NUM
ma-99	518	25	dz(t	dz(t	NOUN
ma-99	518	26	,	,	PUNCT
ma-99	518	27	x	x	NOUN
ma-99	518	28	)	)	PUNCT
ma-99	518	29	for	for	ADP
ma-99	518	30	0	0	NUM
ma-99	518	31	≤	≤	NUM
ma-99	518	32	t	t	NOUN
ma-99	518	33	≤	≤	NOUN
ma-99	518	34	t	t	PROPN
ma-99	518	35	and	and	CCONJ
ma-99	518	36	x	x	PROPN
ma-99	518	37	∈	∈	PROPN
ma-99	518	38	(	(	PUNCT
ma-99	518	39	0	0	NUM
ma-99	518	40	,	,	PUNCT
ma-99	518	41	1	1	NUM
ma-99	518	42	)	)	PUNCT
ma-99	518	43	and	and	CCONJ
ma-99	518	44	θ	θ	X
ma-99	518	45	>	>	X
ma-99	518	46	0	0	PUNCT
ma-99	518	47	with	with	ADP
ma-99	518	48	periodic	periodic	ADJ
ma-99	518	49	boundary	boundary	ADJ
ma-99	518	50	conditions.here	conditions.here	NUM
ma-99	518	51	2	2	NUM
ma-99	518	52	m	m	NOUN
ma-99	518	53	=	=	NOUN
ma-99	518	54	m1	m1	NOUN
ma-99	518	55	=	=	SYM
ma-99	518	56	2	2	NUM
ma-99	518	57	and	and	CCONJ
ma-99	518	58	µj	µj	PROPN
ma-99	518	59	=	=	ADJ
ma-99	518	60	−θπ2j2	−θπ2j2	PROPN
ma-99	518	61	,	,	PUNCT
ma-99	518	62	γ	γ	X
ma-99	518	63	>	>	X
ma-99	518	64	1/2	1/2	NUM
ma-99	518	65	.	.	PUNCT
ma-99	519	1	the	the	DET
ma-99	519	2	eigenfunctions	eigenfunction	NOUN
ma-99	519	3	are	be	AUX
ma-99	519	4	hj(x1	hj(x1	ADJ
ma-99	519	5	,	,	PUNCT
ma-99	519	6	.	.	PUNCT
ma-99	519	7	.	.	PUNCT
ma-99	520	1	.	.	PUNCT
ma-99	521	1	,	,	PUNCT
ma-99	521	2	xn	xn	X
ma-99	521	3	)	)	PUNCT
ma-99	522	1	=	=	PRON
ma-99	522	2	(	(	PUNCT
ma-99	522	3	√	√	ADV
ma-99	522	4	2	2	NUM
ma-99	522	5	/	/	SYM
ma-99	522	6	π)d(sin(n1x1	π)d(sin(n1x1	NOUN
ma-99	522	7	)	)	PUNCT
ma-99	522	8	,	,	PUNCT
ma-99	522	9	.	.	PUNCT
ma-99	522	10	.	.	PUNCT
ma-99	523	1	.	.	PUNCT
ma-99	524	1	,	,	PUNCT
ma-99	524	2	sin(ndxd	sin(ndxd	PROPN
ma-99	524	3	)	)	PUNCT
ma-99	524	4	)	)	PUNCT
ma-99	524	5	,	,	PUNCT
ma-99	524	6	x	x	X
ma-99	524	7	=	=	PUNCT
ma-99	524	8	(	(	PUNCT
ma-99	524	9	x1	x1	PROPN
ma-99	524	10	,	,	PUNCT
ma-99	524	11	.	.	PUNCT
ma-99	524	12	.	.	PUNCT
ma-99	525	1	.	.	PUNCT
ma-99	526	1	,	,	PUNCT
ma-99	526	2	xn	xn	X
ma-99	526	3	)	)	PUNCT
ma-99	526	4	∈	∈	PROPN
ma-99	526	5	rd	rd	PROPN
ma-99	526	6	,	,	PUNCT
ma-99	526	7	j	j	PROPN
ma-99	526	8	=	=	PRON
ma-99	526	9	(	(	PUNCT
ma-99	526	10	n1	n1	PROPN
ma-99	526	11	,	,	PUNCT
ma-99	526	12	.	.	PUNCT
ma-99	526	13	.	.	PUNCT
ma-99	527	1	.	.	PUNCT
ma-99	528	1	,	,	PUNCT
ma-99	528	2	nd	nd	X
ma-99	528	3	)	)	PUNCT
ma-99	528	4	∈	∈	PROPN
ma-99	528	5	nd	nd	NOUN
ma-99	528	6	.	.	PUNCT
ma-99	529	1	the	the	DET
ma-99	529	2	corre	corre	NOUN
ma-99	529	3	-	-	PUNCT
ma-99	529	4	sponding	sponde	VERB
ma-99	529	5	eigenvalues	eigenvalue	NOUN
ma-99	529	6	are	be	AUX
ma-99	529	7	−νj	−νj	PRON
ma-99	529	8	where	where	SCONJ
ma-99	529	9	νj	νj	NOUN
ma-99	529	10	=	=	SYM
ma-99	529	11	(	(	PUNCT
ma-99	529	12	n2	n2	NOUN
ma-99	529	13	1	1	NUM
ma-99	529	14	+	+	CCONJ
ma-99	529	15	.	.	PUNCT
ma-99	529	16	.	.	PUNCT
ma-99	530	1	.+	.+	PROPN
ma-99	530	2	n2	n2	PROPN
ma-99	530	3	d).as	d).as	PROPN
ma-99	530	4	n	n	PRON
ma-99	530	5	→∞	→∞	PROPN
ma-99	530	6	,	,	PUNCT
ma-99	530	7	h	h	NOUN
ma-99	530	8	→	→	SYM
ma-99	530	9	0	0	NUM
ma-99	530	10	,	,	PUNCT
ma-99	530	11	nh1+α/	nh1+α/	NOUN
ma-99	530	12	log	log	VERB
ma-99	530	13	n	n	PROPN
ma-99	530	14	→	→	SYM
ma-99	530	15	0	0	NUM
ma-99	530	16	,	,	PUNCT
ma-99	530	17	nh2α−1	nh2α−1	NUM
ma-99	530	18	log	log	NOUN
ma-99	530	19	n	n	PRON
ma-99	530	20	→∞	→∞	NOUN
ma-99	530	21	,	,	PUNCT
ma-99	530	22	nh2−α/2+ρ	nh2−α/2+ρ	PRON
ma-99	530	23	→∞	→∞	NOUN
ma-99	530	24	for	for	ADP
ma-99	530	25	some	some	DET
ma-99	530	26	ρ	ρ	PROPN
ma-99	530	27	>	>	X
ma-99	530	28	0	0	NUM
ma-99	530	29	,	,	PUNCT
ma-99	530	30	(	(	PUNCT
ma-99	530	31	n	n	CCONJ
ma-99	530	32	log	log	VERB
ma-99	530	33	n	n	NOUN
ma-99	530	34	)	)	PUNCT
ma-99	530	35	1	1	NUM
ma-99	530	36	/	/	SYM
ma-99	530	37	α	α	PRON
ma-99	530	38	h1	h1	PROPN
ma-99	530	39	/	/	SYM
ma-99	531	1	α(θ̂n	α(θ̂n	NUM
ma-99	531	2	−	−	NOUN
ma-99	531	3	θ0)→d	θ0)→d	X
ma-99	531	4	2θ0(αθ0)−1	2θ0(αθ0)−1	NUM
ma-99	531	5	/	/	SYM
ma-99	531	6	αs4	αs4	NOUN
ma-99	531	7	s3	s3	PROPN
ma-99	531	8	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	531	9	eur	eur	PROPN
ma-99	531	10	.	.	PUNCT
ma-99	532	1	j.	j.	PROPN
ma-99	532	2	math	math	PROPN
ma-99	532	3	.	.	PUNCT
ma-99	533	1	anal	anal	PROPN
ma-99	533	2	.	.	PUNCT
ma-99	534	1	10.28924	10.28924	NUM
ma-99	534	2	/	/	SYM
ma-99	534	3	ada	ada	PROPN
ma-99	534	4	/	/	SYM
ma-99	534	5	ma.3.4	ma.3.4	PROPN
ma-99	534	6	22where	22where	PROPN
ma-99	535	1	s3	s3	PROPN
ma-99	535	2	and	and	CCONJ
ma-99	535	3	s4	s4	PROPN
ma-99	535	4	are	be	AUX
ma-99	535	5	independent	independent	ADJ
ma-99	535	6	stable	stable	ADJ
ma-99	535	7	random	random	ADJ
ma-99	535	8	variables	variable	NOUN
ma-99	535	9	,	,	PUNCT
ma-99	535	10	s3	s3	PROPN
ma-99	535	11	is	be	AUX
ma-99	535	12	positive	positive	ADJ
ma-99	535	13	α/2	α/2	NOUN
ma-99	535	14	-	-	PUNCT
ma-99	535	15	stable	stable	ADJ
ma-99	535	16	with	with	ADP
ma-99	535	17	distri	distri	NOUN
ma-99	535	18	-	-	NOUN
ma-99	535	19	bution	bution	NOUN
ma-99	535	20	sα/2(σ1	sα/2(σ1	NOUN
ma-99	535	21	,	,	PUNCT
ma-99	535	22	1	1	NUM
ma-99	535	23	,	,	PUNCT
ma-99	535	24	0	0	NUM
ma-99	535	25	)	)	PUNCT
ma-99	535	26	and	and	CCONJ
ma-99	535	27	s4	s4	PROPN
ma-99	535	28	is	be	AUX
ma-99	535	29	symmetric	symmetric	ADJ
ma-99	535	30	α	α	ADJ
ma-99	535	31	-	-	ADJ
ma-99	535	32	stable	stable	ADJ
ma-99	535	33	random	random	ADJ
ma-99	535	34	variable	variable	NOUN
ma-99	535	35	with	with	ADP
ma-99	535	36	distribution	distribution	NOUN
ma-99	535	37	sα(σ2	sα(σ2	NOUN
ma-99	535	38	,	,	PUNCT
ma-99	535	39	0	0	NUM
ma-99	535	40	,	,	PUNCT
ma-99	535	41	0	0	NUM
ma-99	535	42	)	)	PUNCT
ma-99	535	43	,	,	PUNCT
ma-99	535	44	σ1	σ1	NOUN
ma-99	535	45	=	=	PUNCT
ma-99	535	46	c	c	PROPN
ma-99	535	47	−2	−2	PROPN
ma-99	535	48	/	/	SYM
ma-99	535	49	α	α	PROPN
ma-99	535	50	α/2	α/2	NUM
ma-99	535	51	,	,	PUNCT
ma-99	535	52	σ2	σ2	PROPN
ma-99	535	53	=	=	SYM
ma-99	535	54	c	c	PROPN
ma-99	535	55	−1	−1	NOUN
ma-99	535	56	/	/	SYM
ma-99	535	57	α	α	NOUN
ma-99	535	58	α	α	NOUN
ma-99	535	59	,	,	PUNCT
ma-99	535	60	cα	cα	NOUN
ma-99	535	61	=	=	SYM
ma-99	535	62	(	(	PUNCT
ma-99	535	63	∫∞	∫∞	NOUN
ma-99	535	64	0	0	NUM
ma-99	535	65	x−α	x−α	PROPN
ma-99	535	66	sin	sin	VERB
ma-99	535	67	xdx)−1	xdx)−1	PROPN
ma-99	536	1	=	=	PUNCT
ma-99	537	1	[	[	X
ma-99	537	2	γ(1−	γ(1−	X
ma-99	537	3	α	α	X
ma-99	537	4	)	)	PUNCT
ma-99	537	5	cos(πα/2)]−1	cos(πα/2)]−1	PROPN
ma-99	537	6	.	.	PUNCT
ma-99	538	1	observe	observe	VERB
ma-99	538	2	the	the	DET
ma-99	538	3	rate	rate	NOUN
ma-99	538	4	of	of	ADP
ma-99	538	5	convergence	convergence	NOUN
ma-99	538	6	(	(	PUNCT
ma-99	538	7	nh)1	nh)1	NOUN
ma-99	538	8	/	/	SYM
ma-99	538	9	α(log	α(log	NOUN
ma-99	538	10	n)−1	n)−1	NOUN
ma-99	538	11	/	/	SYM
ma-99	538	12	α	α	NOUN
ma-99	538	13	=	=	SYM
ma-99	538	14	(	(	PUNCT
ma-99	538	15	t	t	PROPN
ma-99	538	16	)	)	PUNCT
ma-99	538	17	1	1	NUM
ma-99	538	18	/	/	SYM
ma-99	538	19	α(log	α(log	NOUN
ma-99	538	20	n)−1	n)−1	NOUN
ma-99	538	21	/	/	SYM
ma-99	538	22	α	α	NOUN
ma-99	538	23	.	.	PUNCT
ma-99	539	1	for	for	ADP
ma-99	539	2	α	α	NOUN
ma-99	539	3	=	=	SYM
ma-99	539	4	2	2	NUM
ma-99	539	5	,	,	PUNCT
ma-99	539	6	this	this	DET
ma-99	539	7	rate	rate	NOUN
ma-99	539	8	is	be	AUX
ma-99	539	9	t	t	PROPN
ma-99	539	10	1/2(log	1/2(log	PROPN
ma-99	539	11	n)−1/2	n)−1/2	PROPN
ma-99	539	12	.	.	PUNCT
ma-99	540	1	(	(	PUNCT
ma-99	540	2	b)consider	b)consider	NOUN
ma-99	540	3	the	the	DET
ma-99	540	4	linear	linear	ADJ
ma-99	540	5	stochastic	stochastic	ADJ
ma-99	540	6	heat	heat	NOUN
ma-99	540	7	equation	equation	NOUN
ma-99	540	8	with	with	ADP
ma-99	540	9	multiplicative	multiplicative	ADJ
ma-99	540	10	noise	noise	NOUN
ma-99	540	11	du(t	du(t	NOUN
ma-99	540	12	,	,	PUNCT
ma-99	540	13	x	x	X
ma-99	540	14	)	)	PUNCT
ma-99	540	15	=	=	SYM
ma-99	540	16	θuxx(t	θuxx(t	PROPN
ma-99	540	17	,	,	PUNCT
ma-99	540	18	x)dt	x)dt	PROPN
ma-99	540	19	+	+	CCONJ
ma-99	540	20	u(t	u(t	NOUN
ma-99	540	21	,	,	PUNCT
ma-99	540	22	x)dz(t	x)dz(t	PROPN
ma-99	540	23	,	,	PUNCT
ma-99	540	24	x	x	NOUN
ma-99	540	25	)	)	PUNCT
ma-99	540	26	for	for	ADP
ma-99	540	27	0	0	NUM
ma-99	540	28	≤	≤	NUM
ma-99	540	29	t	t	NOUN
ma-99	540	30	≤	≤	NOUN
ma-99	540	31	t	t	PROPN
ma-99	540	32	and	and	CCONJ
ma-99	540	33	x	x	PROPN
ma-99	540	34	∈	∈	PROPN
ma-99	540	35	(	(	PUNCT
ma-99	540	36	0	0	NUM
ma-99	540	37	,	,	PUNCT
ma-99	540	38	1	1	NUM
ma-99	540	39	)	)	PUNCT
ma-99	540	40	and	and	CCONJ
ma-99	540	41	θ	θ	X
ma-99	540	42	>	>	X
ma-99	540	43	0	0	PUNCT
ma-99	540	44	with	with	ADP
ma-99	540	45	zero	zero	NUM
ma-99	540	46	boundary	boundary	ADJ
ma-99	540	47	conditions	condition	NOUN
ma-99	540	48	and	and	CCONJ
ma-99	540	49	nonzero	nonzero	NOUN
ma-99	540	50	initial	initial	ADJ
ma-99	540	51	value	value	NOUN
ma-99	540	52	u(0	u(0	PROPN
ma-99	540	53	)	)	PUNCT
ma-99	540	54	∈	∈	PROPN
ma-99	540	55	l2(0	l2(0	NOUN
ma-99	540	56	,	,	PUNCT
ma-99	540	57	1	1	NUM
ma-99	540	58	)	)	PUNCT
ma-99	540	59	.	.	PUNCT
ma-99	541	1	here	here	ADV
ma-99	541	2	a1	a1	NOUN
ma-99	541	3	is	be	AUX
ma-99	541	4	the	the	DET
ma-99	541	5	laplace	laplace	NOUN
ma-99	541	6	operator	operator	NOUN
ma-99	541	7	on	on	ADP
ma-99	541	8	(	(	PUNCT
ma-99	541	9	0	0	NUM
ma-99	541	10	,	,	PUNCT
ma-99	541	11	1	1	NUM
ma-99	541	12	)	)	PUNCT
ma-99	541	13	with	with	ADP
ma-99	541	14	zero	zero	NUM
ma-99	541	15	boundary	boundary	ADJ
ma-99	541	16	conditions	condition	NOUN
ma-99	541	17	that	that	PRON
ma-99	541	18	hasthe	hasthe	DET
ma-99	541	19	eigenfunctions	eigenfunction	NOUN
ma-99	541	20	hk(x	hk(x	PUNCT
ma-99	541	21	)	)	PUNCT
ma-99	541	22	=	=	SYM
ma-99	541	23	√	√	ADP
ma-99	541	24	2	2	NUM
ma-99	541	25	/	/	SYM
ma-99	541	26	π	π	NOUN
ma-99	541	27	sin(kx	sin(kx	NOUN
ma-99	541	28	)	)	PUNCT
ma-99	541	29	,	,	PUNCT
ma-99	541	30	k	k	PROPN
ma-99	541	31	>	>	X
ma-99	541	32	0	0	PUNCT
ma-99	541	33	and	and	CCONJ
ma-99	541	34	the	the	DET
ma-99	541	35	eigenvalues	eigenvalue	NOUN
ma-99	541	36	νk	νk	NOUN
ma-99	541	37	=	=	SYM
ma-99	541	38	−k2	−k2	PROPN
ma-99	541	39	,	,	PUNCT
ma-99	541	40	ρk	ρk	ADP
ma-99	541	41	=	=	SYM
ma-99	541	42	0	0	PROPN
ma-99	541	43	,	,	PUNCT
ma-99	541	44	σk	σk	ADV
ma-99	541	45	=	=	NOUN
ma-99	541	46	1	1	NUM
ma-99	541	47	,	,	PUNCT
ma-99	541	48	k	k	PROPN
ma-99	541	49	>	>	X
ma-99	541	50	0	0	X
ma-99	541	51	.	.	PUNCT
ma-99	541	52	uk(t	uk(t	PUNCT
ma-99	541	53	)	)	PUNCT
ma-99	541	54	=	=	SYM
ma-99	542	1	∫	∫	PROPN
ma-99	542	2	1	1	NUM
ma-99	542	3	0	0	NUM
ma-99	542	4	hk(x)u(t	hk(x)u(t	NOUN
ma-99	542	5	,	,	PUNCT
ma-99	542	6	x)dx	x)dx	PROPN
ma-99	542	7	,	,	PUNCT
ma-99	542	8	duk(t	duk(t	PROPN
ma-99	542	9	)	)	PUNCT
ma-99	542	10	=	=	PUNCT
ma-99	542	11	(	(	PUNCT
ma-99	542	12	θνk	θνk	VERB
ma-99	542	13	+	+	CCONJ
ma-99	542	14	ρk)uk(t)dt	ρk)uk(t)dt	NOUN
ma-99	542	15	+	+	CCONJ
ma-99	542	16	σkuk(t)dzk(t).recall	σkuk(t)dzk(t).recall	NUM
ma-99	542	17	that	that	DET
ma-99	542	18	ṽk	ṽk	NOUN
ma-99	542	19	,	,	PUNCT
ma-99	542	20	t	t	PROPN
ma-99	542	21	:	:	PUNCT
ma-99	542	22	=	=	SYM
ma-99	542	23	ln(uk	ln(uk	PROPN
ma-99	542	24	,	,	PUNCT
ma-99	542	25	t	t	PROPN
ma-99	542	26	/uk,0).the	/uk,0).the	DET
ma-99	542	27	ccfe	ccfe	NOUN
ma-99	542	28	has	have	VERB
ma-99	542	29	the	the	DET
ma-99	542	30	form	form	NOUN
ma-99	542	31	θ̂k	θ̂k	NOUN
ma-99	542	32	,	,	PUNCT
ma-99	542	33	t	t	NOUN
ma-99	542	34	=	=	SYM
ma-99	542	35	ṽk	ṽk	NOUN
ma-99	542	36	,	,	PUNCT
ma-99	542	37	t	t	PROPN
ma-99	542	38	−	−	PROPN
ma-99	542	39	1	1	NUM
ma-99	542	40	k2	k2	PROPN
ma-99	542	41	.(c	.(c	NOUN
ma-99	542	42	)	)	PUNCT
ma-99	542	43	consider	consider	VERB
ma-99	542	44	the	the	DET
ma-99	542	45	following	follow	VERB
ma-99	542	46	spde	spde	NOUN
ma-99	542	47	du(t	du(t	PROPN
ma-99	542	48	,	,	PUNCT
ma-99	542	49	x	x	X
ma-99	542	50	)	)	PUNCT
ma-99	542	51	=	=	NOUN
ma-99	543	1	[	[	X
ma-99	543	2	∆u(t	∆u(t	PROPN
ma-99	543	3	,	,	PUNCT
ma-99	543	4	x	x	NOUN
ma-99	543	5	)	)	PUNCT
ma-99	543	6	+	+	CCONJ
ma-99	543	7	θu(t	θu(t	NOUN
ma-99	543	8	,	,	PUNCT
ma-99	543	9	x)]dt	x)]dt	X
ma-99	544	1	+	+	CCONJ
ma-99	544	2	(	(	PUNCT
ma-99	544	3	1−	1−	NUM
ma-99	544	4	∆)ru(t	∆)ru(t	PROPN
ma-99	544	5	,	,	PUNCT
ma-99	544	6	x)dz(t	x)dz(t	PROPN
ma-99	544	7	,	,	PUNCT
ma-99	544	8	x	x	NOUN
ma-99	544	9	)	)	PUNCT
ma-99	544	10	.	.	PUNCT
ma-99	545	1	in	in	ADP
ma-99	545	2	this	this	DET
ma-99	545	3	case	case	NOUN
ma-99	545	4	a0	a0	NOUN
ma-99	545	5	=	=	SYM
ma-99	545	6	∆	∆	PROPN
ma-99	545	7	,	,	PUNCT
ma-99	545	8	a1	a1	NOUN
ma-99	545	9	=	=	SYM
ma-99	545	10	i	i	PROPN
ma-99	545	11	,	,	PUNCT
ma-99	545	12	m	m	VERB
ma-99	545	13	=	=	X
ma-99	545	14	(	(	PUNCT
ma-99	545	15	1−	1−	NUM
ma-99	545	16	∆)r	∆)r	ADV
ma-99	545	17	with	with	ADP
ma-99	545	18	the	the	DET
ma-99	545	19	eigenvalues	eigenvalue	NOUN
ma-99	545	20	νk	νk	NOUN
ma-99	545	21	=	=	SYM
ma-99	545	22	1	1	NUM
ma-99	545	23	,	,	PUNCT
ma-99	545	24	ρk	ρk	ADP
ma-99	545	25	=	=	PUNCT
ma-99	545	26	σk	σk	PROPN
ma-99	545	27	,	,	PUNCT
ma-99	545	28	µk	µk	X
ma-99	545	29	=	=	SYM
ma-99	545	30	(	(	PUNCT
ma-99	545	31	1	1	NUM
ma-99	545	32	+	+	CCONJ
ma-99	545	33	σk)r	σk)r	PROPN
ma-99	545	34	.it	.it	PUNCT
ma-99	545	35	has	have	VERB
ma-99	545	36	a	a	DET
ma-99	545	37	unique	unique	ADJ
ma-99	545	38	solution	solution	NOUN
ma-99	545	39	for	for	ADP
ma-99	545	40	any	any	DET
ma-99	545	41	r	r	NOUN
ma-99	545	42	≤	≤	NOUN
ma-99	545	43	1/2.the	1/2.the	NUM
ma-99	545	44	ccfe	ccfe	NOUN
ma-99	545	45	has	have	VERB
ma-99	545	46	the	the	DET
ma-99	545	47	form̂	form̂	NOUN
ma-99	545	48	θk	θk	NOUN
ma-99	545	49	,	,	PUNCT
ma-99	545	50	t	t	NOUN
ma-99	545	51	=	=	SYM
ma-99	545	52	ṽk	ṽk	NOUN
ma-99	545	53	,	,	PUNCT
ma-99	545	54	t	t	PROPN
ma-99	545	55	k2	k2	PROPN
ma-99	545	56	t	t	PROPN
ma-99	545	57	2(α−1)/α2	2(α−1)/α2	NUM
ma-99	545	58	−	−	NOUN
ma-99	546	1	(	(	PUNCT
ma-99	546	2	1−	1−	NUM
ma-99	546	3	σk)2r	σk)2r	NOUN
ma-99	546	4	k2t−((α−1)2	k2t−((α−1)2	VERB
ma-99	547	1	+	+	NOUN
ma-99	547	2	1)/α2	1)/α2	NUM
ma-99	547	3	−	−	PROPN
ma-99	547	4	1	1	NUM
ma-99	547	5	σk(d	σk(d	NUM
ma-99	547	6	)	)	PUNCT
ma-99	547	7	stable	stable	ADJ
ma-99	547	8	cox	cox	PROPN
ma-99	547	9	-	-	PUNCT
ma-99	547	10	ingersoll	ingersoll	PROPN
ma-99	547	11	-	-	PUNCT
ma-99	547	12	ross	ross	PROPN
ma-99	547	13	model	model	PROPN
ma-99	547	14	xiong	xiong	PROPN
ma-99	547	15	and	and	CCONJ
ma-99	547	16	yang	yang	PROPN
ma-99	548	1	[	[	X
ma-99	548	2	44	44	NUM
ma-99	548	3	]	]	PUNCT
ma-99	548	4	studied	study	VERB
ma-99	548	5	existence	existence	NOUN
ma-99	548	6	and	and	CCONJ
ma-99	548	7	strong	strong	ADJ
ma-99	548	8	uniqueness	uniqueness	NOUN
ma-99	548	9	of	of	ADP
ma-99	548	10	the	the	DET
ma-99	548	11	following	follow	VERB
ma-99	548	12	spde	spde	NOUN
ma-99	548	13	:	:	PUNCT
ma-99	548	14	duk(t	duk(t	X
ma-99	548	15	)	)	PUNCT
ma-99	548	16	=	=	PUNCT
ma-99	548	17	(	(	PUNCT
ma-99	548	18	θνk	θνk	VERB
ma-99	548	19	+	+	CCONJ
ma-99	548	20	ρk)uk(t)dt	ρk)uk(t)dt	NOUN
ma-99	548	21	+	+	CCONJ
ma-99	548	22	σk(uk(t))1	σk(uk(t))1	PROPN
ma-99	548	23	/	/	SYM
ma-99	548	24	αdzk(t	αdzk(t	NOUN
ma-99	548	25	)	)	PUNCT
ma-99	548	26	,	,	PUNCT
ma-99	548	27	k	k	PROPN
ma-99	548	28	≥	≥	VERB
ma-99	548	29	1.the	1.the	DET
ma-99	548	30	existence	existence	NOUN
ma-99	548	31	of	of	ADP
ma-99	548	32	the	the	DET
ma-99	548	33	solution	solution	NOUN
ma-99	548	34	in	in	ADP
ma-99	548	35	the	the	DET
ma-99	548	36	case	case	NOUN
ma-99	548	37	of	of	ADP
ma-99	548	38	space	space	NOUN
ma-99	548	39	-	-	PUNCT
ma-99	548	40	time	time	NOUN
ma-99	548	41	white	white	ADJ
ma-99	548	42	noise	noise	NOUN
ma-99	548	43	is	be	AUX
ma-99	548	44	shown	show	VERB
ma-99	548	45	by	by	ADP
ma-99	548	46	consideringthe	consideringthe	ADJ
ma-99	548	47	weak	weak	ADJ
ma-99	548	48	limit	limit	NOUN
ma-99	548	49	of	of	ADP
ma-99	548	50	a	a	DET
ma-99	548	51	sequence	sequence	NOUN
ma-99	548	52	of	of	ADP
ma-99	548	53	sde	sde	PROPN
ma-99	548	54	systems	system	NOUN
ma-99	548	55	which	which	PRON
ma-99	548	56	is	be	AUX
ma-99	548	57	obtained	obtain	VERB
ma-99	548	58	by	by	ADP
ma-99	548	59	replacing	replace	VERB
ma-99	548	60	the	the	DET
ma-99	548	61	laplacianoperator	laplacianoperator	NOUN
ma-99	548	62	in	in	ADP
ma-99	548	63	the	the	DET
ma-99	548	64	spde	spde	NOUN
ma-99	548	65	by	by	ADP
ma-99	548	66	its	its	PRON
ma-99	548	67	discrete	discrete	ADJ
ma-99	548	68	version	version	NOUN
ma-99	548	69	.	.	PUNCT
ma-99	549	1	the	the	DET
ma-99	549	2	weak	weak	ADJ
ma-99	549	3	uniqueness	uniqueness	NOUN
ma-99	549	4	follows	follow	VERB
ma-99	549	5	from	from	ADP
ma-99	549	6	the	the	DET
ma-99	549	7	uniqueness	uniqueness	NOUN
ma-99	549	8	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	549	9	eur	eur	NOUN
ma-99	549	10	.	.	PUNCT
ma-99	550	1	j.	j.	PROPN
ma-99	550	2	math	math	PROPN
ma-99	550	3	.	.	PUNCT
ma-99	551	1	anal	anal	PROPN
ma-99	551	2	.	.	PUNCT
ma-99	552	1	10.28924	10.28924	NUM
ma-99	552	2	/	/	SYM
ma-99	552	3	ada	ada	PROPN
ma-99	552	4	/	/	SYM
ma-99	552	5	ma.3.4	ma.3.4	PROPN
ma-99	552	6	23of	23of	ADJ
ma-99	552	7	solution	solution	NOUN
ma-99	552	8	to	to	ADP
ma-99	552	9	the	the	DET
ma-99	552	10	martingale	martingale	ADJ
ma-99	552	11	problem	problem	NOUN
ma-99	552	12	for	for	ADP
ma-99	552	13	the	the	DET
ma-99	552	14	associated	associated	ADJ
ma-99	552	15	super	super	ADJ
ma-99	552	16	-	-	ADJ
ma-99	552	17	brownian	brownian	ADJ
ma-99	552	18	motion	motion	NOUN
ma-99	552	19	.	.	PUNCT
ma-99	553	1	in	in	ADP
ma-99	553	2	the	the	DET
ma-99	553	3	case	case	NOUN
ma-99	553	4	of	of	ADP
ma-99	553	5	α	α	NOUN
ma-99	553	6	-	-	ADJ
ma-99	553	7	stable	stable	ADJ
ma-99	553	8	noise	noise	NOUN
ma-99	553	9	the	the	DET
ma-99	553	10	existence	existence	NOUN
ma-99	553	11	and	and	CCONJ
ma-99	553	12	pathwise	pathwise	NOUN
ma-99	553	13	uniqueness	uniqueness	NOUN
ma-99	553	14	of	of	ADP
ma-99	553	15	the	the	DET
ma-99	553	16	solution	solution	NOUN
ma-99	553	17	is	be	AUX
ma-99	553	18	studied	study	VERB
ma-99	553	19	in	in	ADP
ma-99	553	20	xiong	xiong	PROPN
ma-99	553	21	and	and	CCONJ
ma-99	553	22	yang	yang	PROPN
ma-99	554	1	[	[	X
ma-99	554	2	44	44	NUM
ma-99	554	3	]	]	PUNCT
ma-99	554	4	.	.	PUNCT
ma-99	555	1	concluding	conclude	VERB
ma-99	555	2	remark	remark	NOUN
ma-99	555	3	we	we	PRON
ma-99	555	4	considered	consider	VERB
ma-99	555	5	levy	levy	NOUN
ma-99	555	6	process	process	NOUN
ma-99	555	7	driving	drive	VERB
ma-99	555	8	term	term	NOUN
ma-99	555	9	in	in	ADP
ma-99	555	10	this	this	DET
ma-99	555	11	paper	paper	NOUN
ma-99	555	12	.	.	PUNCT
ma-99	556	1	using	use	VERB
ma-99	556	2	fractionallevy	fractionallevy	NOUN
ma-99	556	3	process	process	NOUN
ma-99	556	4	as	as	ADP
ma-99	556	5	the	the	DET
ma-99	556	6	driving	drive	VERB
ma-99	556	7	term	term	NOUN
ma-99	556	8	,	,	PUNCT
ma-99	556	9	maximum	maximum	ADJ
ma-99	556	10	quasi	quasi	ADJ
ma-99	556	11	-	-	ADJ
ma-99	556	12	likelihood	likelihood	ADJ
ma-99	556	13	estimation	estimation	NOUN
ma-99	556	14	in	in	ADP
ma-99	556	15	fractional	fractional	ADJ
ma-99	556	16	levy	levy	NOUN
ma-99	556	17	stochasticvolatility	stochasticvolatility	NOUN
ma-99	556	18	model	model	NOUN
ma-99	556	19	was	be	AUX
ma-99	556	20	studied	study	VERB
ma-99	556	21	in	in	ADP
ma-99	556	22	bishwal	bishwal	NOUN
ma-99	556	23	[	[	X
ma-99	556	24	8	8	NUM
ma-99	556	25	]	]	PUNCT
ma-99	556	26	.	.	PUNCT
ma-99	557	1	recently	recently	ADV
ma-99	557	2	,	,	PUNCT
ma-99	557	3	sub	sub	ADJ
ma-99	557	4	-	-	ADJ
ma-99	557	5	fractional	fractional	ADJ
ma-99	557	6	brownian	brownian	NOUN
ma-99	557	7	(	(	PUNCT
ma-99	557	8	sub	sub	NOUN
ma-99	557	9	-	-	ADJ
ma-99	557	10	fbm	fbm	ADJ
ma-99	557	11	)	)	PUNCT
ma-99	557	12	motionwhich	motionwhich	NOUN
ma-99	557	13	is	be	AUX
ma-99	557	14	a	a	DET
ma-99	557	15	centered	center	VERB
ma-99	557	16	gaussian	gaussian	ADJ
ma-99	557	17	process	process	NOUN
ma-99	557	18	with	with	ADP
ma-99	557	19	covariance	covariance	NOUN
ma-99	557	20	function	function	NOUN
ma-99	557	21	ch(s	ch(s	PROPN
ma-99	557	22	,	,	PUNCT
ma-99	557	23	t	t	PROPN
ma-99	557	24	)	)	PUNCT
ma-99	557	25	=	=	PUNCT
ma-99	558	1	s2h	s2h	NOUN
ma-99	558	2	+	+	PROPN
ma-99	558	3	t2h	t2h	PROPN
ma-99	558	4	−	−	PROPN
ma-99	558	5	1	1	NUM
ma-99	558	6	2	2	NUM
ma-99	558	7	[	[	PUNCT
ma-99	558	8	(	(	PUNCT
ma-99	558	9	s	s	NOUN
ma-99	558	10	+	+	NOUN
ma-99	558	11	t)2h	t)2h	NOUN
ma-99	558	12	+	+	CCONJ
ma-99	558	13	|s	|s	PROPN
ma-99	558	14	−	−	PROPN
ma-99	558	15	t|2h	t|2h	NOUN
ma-99	558	16	]	]	PUNCT
ma-99	558	17	,	,	PUNCT
ma-99	558	18	s	s	X
ma-99	558	19	,	,	PUNCT
ma-99	558	20	t	t	X
ma-99	558	21	>	>	X
ma-99	558	22	0	0	PUNCT
ma-99	559	1	for	for	ADP
ma-99	559	2	0	0	NUM
ma-99	559	3	<	<	X
ma-99	559	4	h	h	X
ma-99	559	5	<	<	X
ma-99	559	6	1	1	NUM
ma-99	559	7	introduced	introduce	VERB
ma-99	559	8	by	by	ADP
ma-99	559	9	bojdecki	bojdecki	ADJ
ma-99	559	10	,	,	PUNCT
ma-99	559	11	gorostiza	gorostiza	ADJ
ma-99	559	12	and	and	CCONJ
ma-99	559	13	talarczyk	talarczyk	X
ma-99	559	14	[	[	X
ma-99	559	15	13	13	NUM
ma-99	559	16	]	]	PUNCT
ma-99	559	17	has	have	AUX
ma-99	559	18	received	receive	VERB
ma-99	559	19	some	some	PRON
ma-99	559	20	attentionrecently	attentionrecently	ADV
ma-99	559	21	in	in	ADP
ma-99	559	22	finite	finite	ADJ
ma-99	559	23	dimensional	dimensional	ADJ
ma-99	559	24	models	model	NOUN
ma-99	559	25	.	.	PUNCT
ma-99	560	1	the	the	DET
ma-99	560	2	interesting	interesting	ADJ
ma-99	560	3	feature	feature	NOUN
ma-99	560	4	of	of	ADP
ma-99	560	5	this	this	DET
ma-99	560	6	process	process	NOUN
ma-99	560	7	is	be	AUX
ma-99	560	8	that	that	SCONJ
ma-99	560	9	this	this	PRON
ma-99	560	10	processhas	processha	VERB
ma-99	560	11	some	some	PRON
ma-99	560	12	of	of	ADP
ma-99	560	13	the	the	DET
ma-99	560	14	main	main	ADJ
ma-99	560	15	properties	property	NOUN
ma-99	560	16	of	of	ADP
ma-99	560	17	fbm	fbm	NOUN
ma-99	560	18	,	,	PUNCT
ma-99	560	19	but	but	CCONJ
ma-99	560	20	the	the	DET
ma-99	560	21	increments	increment	NOUN
ma-99	560	22	of	of	ADP
ma-99	560	23	the	the	DET
ma-99	560	24	process	process	NOUN
ma-99	560	25	are	be	AUX
ma-99	560	26	nonstationary	nonstationary	ADJ
ma-99	560	27	,	,	PUNCT
ma-99	560	28	more	more	ADV
ma-99	560	29	weakly	weakly	ADV
ma-99	560	30	correlated	correlate	VERB
ma-99	560	31	on	on	ADP
ma-99	560	32	non	non	ADJ
ma-99	560	33	-	-	ADJ
ma-99	560	34	overlapping	overlapping	ADJ
ma-99	560	35	time	time	NOUN
ma-99	560	36	intervals	interval	NOUN
ma-99	560	37	than	than	ADP
ma-99	560	38	that	that	PRON
ma-99	560	39	of	of	ADP
ma-99	560	40	fbm	fbm	NOUN
ma-99	560	41	,	,	PUNCT
ma-99	560	42	and	and	CCONJ
ma-99	560	43	its	its	PRON
ma-99	560	44	covariancedecays	covariancedecay	NOUN
ma-99	560	45	polynomially	polynomially	ADV
ma-99	560	46	at	at	ADP
ma-99	560	47	a	a	DET
ma-99	560	48	higher	high	ADJ
ma-99	560	49	rate	rate	NOUN
ma-99	560	50	as	as	ADP
ma-99	560	51	the	the	DET
ma-99	560	52	distance	distance	NOUN
ma-99	560	53	between	between	ADP
ma-99	560	54	the	the	DET
ma-99	560	55	intervals	interval	NOUN
ma-99	560	56	tends	tend	VERB
ma-99	560	57	to	to	PART
ma-99	560	58	infinity	infinity	VERB
ma-99	560	59	.	.	PUNCT
ma-99	561	1	itwould	itwould	AUX
ma-99	561	2	be	be	AUX
ma-99	561	3	interesting	interesting	ADJ
ma-99	561	4	to	to	PART
ma-99	561	5	see	see	VERB
ma-99	561	6	extension	extension	NOUN
ma-99	561	7	of	of	ADP
ma-99	561	8	this	this	DET
ma-99	561	9	paper	paper	NOUN
ma-99	561	10	to	to	ADP
ma-99	561	11	sub	sub	VERB
ma-99	561	12	-	-	ADJ
ma-99	561	13	fbm	fbm	ADJ
ma-99	561	14	case	case	NOUN
ma-99	561	15	.	.	PUNCT
ma-99	562	1	we	we	PRON
ma-99	562	2	generalize	generalize	VERB
ma-99	562	3	sub	sub	ADJ
ma-99	562	4	-	-	ADJ
ma-99	562	5	fbm	fbm	ADJ
ma-99	562	6	tosub	tosub	NOUN
ma-99	562	7	-	-	PUNCT
ma-99	562	8	fractional	fractional	ADJ
ma-99	562	9	levy	levy	NOUN
ma-99	562	10	process	process	NOUN
ma-99	562	11	(	(	PUNCT
ma-99	562	12	sub	sub	ADJ
ma-99	562	13	-	-	ADJ
ma-99	562	14	flp).sub	flp).sub	ADJ
ma-99	562	15	-	-	PUNCT
ma-99	562	16	fractional	fractional	ADJ
ma-99	562	17	levy	levy	NOUN
ma-99	562	18	process	process	NOUN
ma-99	562	19	(	(	PUNCT
ma-99	562	20	sflp	sflp	PROPN
ma-99	562	21	)	)	PUNCT
ma-99	562	22	is	be	AUX
ma-99	562	23	defined	define	VERB
ma-99	562	24	as	as	ADP
ma-99	562	25	sh	sh	PROPN
ma-99	562	26	,	,	PUNCT
ma-99	562	27	t	t	NOUN
ma-99	562	28	=	=	SYM
ma-99	562	29	1	1	NUM
ma-99	562	30	γ(h	γ(h	NOUN
ma-99	562	31	+	+	CCONJ
ma-99	562	32	1	1	NUM
ma-99	562	33	2	2	NUM
ma-99	562	34	)	)	PUNCT
ma-99	562	35	∫	∫	NOUN
ma-99	563	1	r	r	NOUN
ma-99	563	2	[	[	X
ma-99	563	3	(	(	PUNCT
ma-99	563	4	t	t	PROPN
ma-99	563	5	−	−	PROPN
ma-99	563	6	s	s	PART
ma-99	563	7	)	)	PUNCT
ma-99	563	8	h−1/2	h−1/2	PROPN
ma-99	563	9	+	+	CCONJ
ma-99	563	10	−	−	PROPN
ma-99	563	11	(	(	PUNCT
ma-99	563	12	−s	−s	NOUN
ma-99	563	13	)	)	PUNCT
ma-99	563	14	h−1/2	h−1/2	NOUN
ma-99	564	1	+	+	NUM
ma-99	564	2	]	]	X
ma-99	564	3	dms	dms	NOUN
ma-99	564	4	,	,	PUNCT
ma-99	564	5	t	t	PROPN
ma-99	564	6	∈	∈	PROPN
ma-99	564	7	r	r	NOUN
ma-99	564	8	where	where	SCONJ
ma-99	564	9	mt	mt	PROPN
ma-99	564	10	,	,	PUNCT
ma-99	564	11	t	t	PROPN
ma-99	564	12	∈	∈	PROPN
ma-99	564	13	r	r	NOUN
ma-99	564	14	is	be	AUX
ma-99	564	15	a	a	DET
ma-99	564	16	levy	levy	NOUN
ma-99	564	17	process	process	NOUN
ma-99	564	18	on	on	ADP
ma-99	564	19	r	r	NOUN
ma-99	564	20	with	with	ADP
ma-99	564	21	e(m1	e(m1	NOUN
ma-99	564	22	)	)	PUNCT
ma-99	564	23	=	=	SYM
ma-99	564	24	0	0	NUM
ma-99	564	25	,	,	PUNCT
ma-99	564	26	e(m2	e(m2	X
ma-99	564	27	1	1	NUM
ma-99	564	28	)	)	PUNCT
ma-99	564	29	<	<	X
ma-99	564	30	∞	∞	PROPN
ma-99	564	31	and	and	CCONJ
ma-99	564	32	without	without	ADP
ma-99	564	33	browniancomponent	browniancomponent	ADJ
ma-99	564	34	.	.	PUNCT
ma-99	565	1	sflp	sflp	PROPN
ma-99	565	2	has	have	VERB
ma-99	565	3	the	the	DET
ma-99	565	4	following	following	NOUN
ma-99	565	5	properties:1	properties:1	VERB
ma-99	565	6	)	)	PUNCT
ma-99	565	7	the	the	DET
ma-99	565	8	covariance	covariance	NOUN
ma-99	565	9	of	of	ADP
ma-99	565	10	the	the	DET
ma-99	565	11	process	process	NOUN
ma-99	565	12	is	be	AUX
ma-99	565	13	given	give	VERB
ma-99	565	14	by	by	ADP
ma-99	565	15	cov(sh	cov(sh	NOUN
ma-99	565	16	,	,	PUNCT
ma-99	565	17	t	t	PROPN
ma-99	565	18	,	,	PUNCT
ma-99	565	19	sh	sh	PROPN
ma-99	565	20	,	,	PUNCT
ma-99	565	21	s	s	PART
ma-99	565	22	)	)	PUNCT
ma-99	565	23	=	=	SYM
ma-99	566	1	s2h	s2h	NOUN
ma-99	566	2	+	+	PROPN
ma-99	566	3	t2h	t2h	PROPN
ma-99	566	4	+	+	CCONJ
ma-99	566	5	e[l(1)2	e[l(1)2	ADJ
ma-99	566	6	]	]	X
ma-99	566	7	2γ(2h	2γ(2h	NUM
ma-99	566	8	+	+	SYM
ma-99	566	9	1	1	NUM
ma-99	566	10	)	)	PUNCT
ma-99	566	11	sin(πh	sin(πh	NOUN
ma-99	566	12	)	)	PUNCT
ma-99	567	1	[	[	X
ma-99	567	2	|t|2h	|t|2h	ADJ
ma-99	567	3	+	+	CCONJ
ma-99	567	4	|s|2h	|s|2h	ADJ
ma-99	567	5	−	−	PROPN
ma-99	567	6	|t	|t	NOUN
ma-99	567	7	−	−	PROPN
ma-99	567	8	s|2h	s|2h	ADJ
ma-99	567	9	]	]	PUNCT
ma-99	567	10	.	.	PUNCT
ma-99	568	1	2	2	X
ma-99	568	2	)	)	PUNCT
ma-99	568	3	sh	sh	NOUN
ma-99	568	4	is	be	AUX
ma-99	568	5	not	not	PART
ma-99	568	6	a	a	DET
ma-99	568	7	martingale	martingale	NOUN
ma-99	568	8	.	.	PUNCT
ma-99	569	1	for	for	ADP
ma-99	569	2	a	a	DET
ma-99	569	3	large	large	ADJ
ma-99	569	4	class	class	NOUN
ma-99	569	5	of	of	ADP
ma-99	569	6	levy	levy	NOUN
ma-99	569	7	processes	process	NOUN
ma-99	569	8	,	,	PUNCT
ma-99	569	9	sh	sh	PROPN
ma-99	569	10	is	be	AUX
ma-99	569	11	neither	neither	CCONJ
ma-99	569	12	a	a	DET
ma-99	569	13	semimartingalenor	semimartingalenor	NOUN
ma-99	569	14	a	a	DET
ma-99	569	15	markov	markov	NOUN
ma-99	569	16	process	process	NOUN
ma-99	569	17	.	.	PUNCT
ma-99	570	1	3	3	X
ma-99	570	2	)	)	PUNCT
ma-99	570	3	sh	sh	PROPN
ma-99	570	4	is	be	AUX
ma-99	570	5	hölder	hölder	NOUN
ma-99	570	6	continuous	continuous	ADJ
ma-99	570	7	of	of	ADP
ma-99	570	8	any	any	DET
ma-99	570	9	order	order	NOUN
ma-99	570	10	β	β	X
ma-99	570	11	less	less	ADJ
ma-99	570	12	than	than	ADP
ma-99	570	13	h	h	NOUN
ma-99	570	14	−	−	NOUN
ma-99	570	15	1	1	NUM
ma-99	570	16	2	2	NUM
ma-99	570	17	.	.	PUNCT
ma-99	571	1	4	4	X
ma-99	571	2	)	)	PUNCT
ma-99	571	3	sh	sh	PROPN
ma-99	571	4	hasnonstationary	hasnonstationary	ADJ
ma-99	571	5	increments	increment	NOUN
ma-99	571	6	.	.	PUNCT
ma-99	572	1	5	5	X
ma-99	572	2	)	)	PUNCT
ma-99	572	3	sh	sh	PROPN
ma-99	572	4	is	be	AUX
ma-99	572	5	symmetric	symmetric	ADJ
ma-99	572	6	.	.	PUNCT
ma-99	573	1	6	6	X
ma-99	573	2	)	)	PUNCT
ma-99	573	3	sh	sh	PROPN
ma-99	573	4	is	be	AUX
ma-99	573	5	self	self	NOUN
ma-99	573	6	similar	similar	ADJ
ma-99	573	7	.	.	PUNCT
ma-99	574	1	7	7	X
ma-99	574	2	)	)	PUNCT
ma-99	574	3	sh	sh	NOUN
ma-99	574	4	has	have	AUX
ma-99	574	5	infinite	infinite	VERB
ma-99	574	6	totalvariation	totalvariation	NOUN
ma-99	574	7	on	on	ADP
ma-99	574	8	compacts.it	compacts.it	PRON
ma-99	574	9	would	would	AUX
ma-99	574	10	be	be	AUX
ma-99	574	11	interesting	interesting	ADJ
ma-99	574	12	to	to	PART
ma-99	574	13	investigate	investigate	VERB
ma-99	574	14	qml	qml	NOUN
ma-99	574	15	estimation	estimation	NOUN
ma-99	574	16	in	in	ADP
ma-99	574	17	spde	spde	NOUN
ma-99	574	18	driven	drive	VERB
ma-99	574	19	by	by	ADP
ma-99	574	20	subfractional	subfractional	ADJ
ma-99	574	21	levyprocesses	levyprocesse	NOUN
ma-99	574	22	which	which	PRON
ma-99	574	23	incorporate	incorporate	VERB
ma-99	574	24	both	both	PRON
ma-99	574	25	jumps	jump	VERB
ma-99	574	26	and	and	CCONJ
ma-99	574	27	long	long	ADJ
ma-99	574	28	memory	memory	NOUN
ma-99	574	29	apart	apart	ADV
ma-99	574	30	from	from	ADP
ma-99	574	31	nonstationarity	nonstationarity	NOUN
ma-99	574	32	.	.	PUNCT
ma-99	575	1	references	reference	NOUN
ma-99	575	2	[	[	X
ma-99	575	3	1	1	NUM
ma-99	575	4	]	]	X
ma-99	575	5	d.	d.	PROPN
ma-99	575	6	applebaum	applebaum	PROPN
ma-99	575	7	,	,	PUNCT
ma-99	575	8	levy	levy	NOUN
ma-99	575	9	processes	process	NOUN
ma-99	575	10	and	and	CCONJ
ma-99	575	11	stochastic	stochastic	ADJ
ma-99	575	12	calculus	calculus	NOUN
ma-99	575	13	,	,	PUNCT
ma-99	575	14	second	second	ADJ
ma-99	575	15	edition	edition	NOUN
ma-99	575	16	,	,	PUNCT
ma-99	575	17	cambridge	cambridge	PROPN
ma-99	575	18	university	university	PROPN
ma-99	575	19	press	press	NOUN
ma-99	575	20	,	,	PUNCT
ma-99	575	21	new	new	ADJ
ma-99	575	22	york,(2009).[2	york,(2009).[2	NOUN
ma-99	575	23	]	]	X
ma-99	575	24	b.m	b.m	PROPN
ma-99	575	25	.	.	PROPN
ma-99	575	26	bibby	bibby	PROPN
ma-99	575	27	,	,	PUNCT
ma-99	575	28	m.	m.	NOUN
ma-99	575	29	sørensen	sørensen	NOUN
ma-99	575	30	,	,	PUNCT
ma-99	575	31	m.	m.	PROPN
ma-99	575	32	sorensen	sorensen	PROPN
ma-99	575	33	,	,	PUNCT
ma-99	575	34	martingale	martingale	ADJ
ma-99	575	35	estimation	estimation	NOUN
ma-99	575	36	functions	function	NOUN
ma-99	575	37	for	for	ADP
ma-99	575	38	discretely	discretely	ADV
ma-99	575	39	observed	observe	VERB
ma-99	575	40	diffusion	diffusion	NOUN
ma-99	575	41	pro	pro	ADJ
ma-99	575	42	-	-	NOUN
ma-99	575	43	cesses	cesse	NOUN
ma-99	575	44	,	,	PUNCT
ma-99	575	45	bernoulli	bernoulli	PROPN
ma-99	575	46	.	.	PUNCT
ma-99	576	1	1	1	NUM
ma-99	576	2	(	(	PUNCT
ma-99	576	3	1995	1995	NUM
ma-99	576	4	)	)	PUNCT
ma-99	576	5	17	17	NUM
ma-99	576	6	-	-	SYM
ma-99	576	7	39	39	NUM
ma-99	576	8	.	.	PUNCT
ma-99	577	1	https://doi.org/10.2307/3318679.[3	https://doi.org/10.2307/3318679.[3	PRON
ma-99	577	2	]	]	PUNCT
ma-99	577	3	j.p.n	j.p.n	PROPN
ma-99	577	4	.	.	PROPN
ma-99	577	5	bishwal	bishwal	PROPN
ma-99	577	6	,	,	PUNCT
ma-99	577	7	bayes	bayes	PROPN
ma-99	577	8	and	and	CCONJ
ma-99	577	9	sequential	sequential	ADJ
ma-99	577	10	estimation	estimation	NOUN
ma-99	577	11	in	in	ADP
ma-99	577	12	hilbert	hilbert	NOUN
ma-99	577	13	space	space	NOUN
ma-99	577	14	valued	value	VERB
ma-99	577	15	stochastic	stochastic	ADJ
ma-99	577	16	differential	differential	ADJ
ma-99	577	17	equations	equation	NOUN
ma-99	577	18	,	,	PUNCT
ma-99	577	19	j.	j.	PROPN
ma-99	577	20	koreanstat	koreanstat	PROPN
ma-99	577	21	.	.	PUNCT
ma-99	578	1	soc	soc	PROPN
ma-99	578	2	.	.	PUNCT
ma-99	579	1	28	28	NUM
ma-99	579	2	(	(	PUNCT
ma-99	579	3	1999	1999	NUM
ma-99	579	4	)	)	PUNCT
ma-99	579	5	93	93	NUM
ma-99	579	6	-	-	SYM
ma-99	579	7	106	106	NUM
ma-99	579	8	.	.	PUNCT
ma-99	580	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	580	2	https://doi.org/10.2307/3318679	https://doi.org/10.2307/3318679	PROPN
ma-99	580	3	eur	eur	NOUN
ma-99	580	4	.	.	PUNCT
ma-99	581	1	j.	j.	PROPN
ma-99	581	2	math	math	PROPN
ma-99	581	3	.	.	PUNCT
ma-99	582	1	anal	anal	PROPN
ma-99	582	2	.	.	PUNCT
ma-99	583	1	10.28924	10.28924	NUM
ma-99	583	2	/	/	SYM
ma-99	583	3	ada	ada	PROPN
ma-99	583	4	/	/	SYM
ma-99	583	5	ma.3.4	ma.3.4	PROPN
ma-99	583	6	24	24	NUM
ma-99	583	7	[	[	SYM
ma-99	583	8	4	4	NUM
ma-99	583	9	]	]	PUNCT
ma-99	583	10	j.p.n	j.p.n	PROPN
ma-99	583	11	.	.	PROPN
ma-99	583	12	bishwal	bishwal	NOUN
ma-99	583	13	,	,	PUNCT
ma-99	583	14	rates	rate	NOUN
ma-99	583	15	of	of	ADP
ma-99	583	16	convergence	convergence	NOUN
ma-99	583	17	of	of	ADP
ma-99	583	18	the	the	DET
ma-99	583	19	posterior	posterior	ADJ
ma-99	583	20	distributions	distribution	NOUN
ma-99	583	21	and	and	CCONJ
ma-99	583	22	the	the	DET
ma-99	583	23	bayes	bayes	PROPN
ma-99	583	24	estimations	estimation	NOUN
ma-99	583	25	in	in	ADP
ma-99	583	26	the	the	DET
ma-99	583	27	ornstein	ornstein	PROPN
ma-99	583	28	-	-	PUNCT
ma-99	583	29	uhlenbeck	uhlenbeck	PROPN
ma-99	583	30	process	process	NOUN
ma-99	583	31	,	,	PUNCT
ma-99	583	32	rand	rand	NOUN
ma-99	583	33	.	.	PUNCT
ma-99	584	1	oper	oper	PROPN
ma-99	584	2	.	.	PROPN
ma-99	584	3	stoch	stoch	PROPN
ma-99	584	4	.	.	PUNCT
ma-99	585	1	equ	equ	PROPN
ma-99	585	2	.	.	PROPN
ma-99	585	3	8	8	NUM
ma-99	585	4	(	(	PUNCT
ma-99	585	5	2000	2000	NUM
ma-99	585	6	)	)	PUNCT
ma-99	585	7	51	51	NUM
ma-99	585	8	-	-	SYM
ma-99	585	9	70	70	NUM
ma-99	585	10	.	.	PUNCT
ma-99	586	1	https://doi.org/10.1515/rose.2000.8.1.51.[5	https://doi.org/10.1515/rose.2000.8.1.51.[5	PROPN
ma-99	586	2	]	]	PUNCT
ma-99	586	3	j.p.n	j.p.n	PROPN
ma-99	586	4	.	.	PROPN
ma-99	586	5	bishwal	bishwal	PROPN
ma-99	586	6	,	,	PUNCT
ma-99	586	7	the	the	DET
ma-99	586	8	bernstein	bernstein	PROPN
ma-99	586	9	-	-	PUNCT
ma-99	586	10	von	von	PROPN
ma-99	586	11	mises	mises	PROPN
ma-99	586	12	theorem	theorem	VERB
ma-99	586	13	and	and	CCONJ
ma-99	586	14	spectral	spectral	ADJ
ma-99	586	15	asymptotics	asymptotic	NOUN
ma-99	586	16	of	of	ADP
ma-99	586	17	bayes	bayes	NOUN
ma-99	586	18	estimators	estimator	NOUN
ma-99	586	19	for	for	ADP
ma-99	586	20	parabolic	parabolic	ADJ
ma-99	586	21	spdes	spde	NOUN
ma-99	586	22	,	,	PUNCT
ma-99	586	23	j.	j.	PROPN
ma-99	586	24	aust	aust	PROPN
ma-99	586	25	.	.	PUNCT
ma-99	586	26	math	math	PROPN
ma-99	586	27	.	.	PUNCT
ma-99	587	1	soc	soc	PROPN
ma-99	587	2	.	.	PUNCT
ma-99	588	1	72	72	NUM
ma-99	588	2	(	(	PUNCT
ma-99	588	3	2002	2002	NUM
ma-99	588	4	)	)	PUNCT
ma-99	589	1	287–298	287–298	NUM
ma-99	589	2	.	.	PUNCT
ma-99	590	1	https://doi.org/10.1017/s1446788700003906.[6	https://doi.org/10.1017/s1446788700003906.[6	NOUN
ma-99	590	2	]	]	PUNCT
ma-99	590	3	j.p.n	j.p.n	PROPN
ma-99	590	4	.	.	PROPN
ma-99	590	5	bishwal	bishwal	PROPN
ma-99	590	6	,	,	PUNCT
ma-99	590	7	a	a	DET
ma-99	590	8	new	new	ADJ
ma-99	590	9	estimating	estimating	NOUN
ma-99	590	10	function	function	NOUN
ma-99	590	11	for	for	ADP
ma-99	590	12	discretely	discretely	ADV
ma-99	590	13	sampled	sample	VERB
ma-99	590	14	diffusions	diffusion	NOUN
ma-99	590	15	,	,	PUNCT
ma-99	590	16	rand	rand	NOUN
ma-99	590	17	.	.	PUNCT
ma-99	591	1	oper	oper	PROPN
ma-99	591	2	.	.	PROPN
ma-99	591	3	stoch	stoch	PROPN
ma-99	591	4	.	.	PUNCT
ma-99	592	1	equ	equ	PROPN
ma-99	592	2	.	.	PROPN
ma-99	592	3	15	15	NUM
ma-99	592	4	(	(	PUNCT
ma-99	592	5	2007)65	2007)65	NUM
ma-99	592	6	-	-	SYM
ma-99	592	7	88	88	NUM
ma-99	592	8	.	.	PUNCT
ma-99	592	9	https://doi.org/10.1515/rose.2007.005.[7	https://doi.org/10.1515/rose.2007.005.[7	NOUN
ma-99	592	10	]	]	X
ma-99	592	11	j.p.n	j.p.n	PROPN
ma-99	592	12	.	.	PROPN
ma-99	592	13	bishwal	bishwal	PROPN
ma-99	592	14	,	,	PUNCT
ma-99	592	15	parameter	parameter	NOUN
ma-99	592	16	estimation	estimation	NOUN
ma-99	592	17	in	in	ADP
ma-99	592	18	stochastic	stochastic	ADJ
ma-99	592	19	differential	differential	ADJ
ma-99	592	20	equations	equation	NOUN
ma-99	592	21	,	,	PUNCT
ma-99	592	22	lecture	lecture	NOUN
ma-99	592	23	notes	note	NOUN
ma-99	592	24	in	in	ADP
ma-99	592	25	mathematics	mathematic	NOUN
ma-99	592	26	,	,	PUNCT
ma-99	592	27	1923,springer	1923,springer	NUM
ma-99	592	28	-	-	PUNCT
ma-99	592	29	verlag	verlag	NOUN
ma-99	592	30	,	,	PUNCT
ma-99	592	31	(	(	PUNCT
ma-99	592	32	2008).[8	2008).[8	NOUN
ma-99	592	33	]	]	X
ma-99	592	34	j.p.n	j.p.n	PROPN
ma-99	592	35	.	.	PROPN
ma-99	592	36	bishwal	bishwal	PROPN
ma-99	592	37	,	,	PUNCT
ma-99	592	38	maximum	maximum	ADJ
ma-99	592	39	quasi	quasi	ADJ
ma-99	592	40	-	-	ADJ
ma-99	592	41	likelihood	likelihood	ADJ
ma-99	592	42	estimation	estimation	NOUN
ma-99	592	43	in	in	ADP
ma-99	592	44	fractional	fractional	ADJ
ma-99	592	45	levy	levy	NOUN
ma-99	592	46	stochastic	stochastic	ADJ
ma-99	592	47	volatility	volatility	NOUN
ma-99	592	48	model	model	NOUN
ma-99	592	49	,	,	PUNCT
ma-99	592	50	j.	j.	PROPN
ma-99	592	51	math	math	PROPN
ma-99	592	52	.	.	PUNCT
ma-99	593	1	finance.1	finance.1	PROPN
ma-99	593	2	(	(	PUNCT
ma-99	593	3	2011	2011	NUM
ma-99	593	4	)	)	PUNCT
ma-99	593	5	12	12	NUM
ma-99	593	6	-	-	SYM
ma-99	593	7	15	15	NUM
ma-99	593	8	.	.	PUNCT
ma-99	594	1	https://doi.org/10.4236/jmf.2011.13008.[9	https://doi.org/10.4236/jmf.2011.13008.[9	NOUN
ma-99	594	2	]	]	PUNCT
ma-99	594	3	j.p.n	j.p.n	PROPN
ma-99	594	4	.	.	PROPN
ma-99	594	5	bishwal	bishwal	PROPN
ma-99	594	6	,	,	PUNCT
ma-99	594	7	hypothesis	hypothesis	NOUN
ma-99	594	8	testing	testing	NOUN
ma-99	594	9	for	for	ADP
ma-99	594	10	fractional	fractional	ADJ
ma-99	594	11	stochastic	stochastic	ADJ
ma-99	594	12	partial	partial	ADJ
ma-99	594	13	differential	differential	NOUN
ma-99	594	14	equations	equation	NOUN
ma-99	594	15	with	with	ADP
ma-99	594	16	applications	application	NOUN
ma-99	594	17	to	to	ADP
ma-99	594	18	neu	neu	NOUN
ma-99	594	19	-	-	PUNCT
ma-99	594	20	rophysiology	rophysiology	NOUN
ma-99	594	21	and	and	CCONJ
ma-99	594	22	finance	finance	NOUN
ma-99	594	23	,	,	PUNCT
ma-99	594	24	asian	asian	ADJ
ma-99	594	25	res	re	NOUN
ma-99	594	26	.	.	PUNCT
ma-99	595	1	j.	j.	PROPN
ma-99	595	2	math	math	PROPN
ma-99	595	3	.	.	PUNCT
ma-99	596	1	4	4	NUM
ma-99	596	2	(	(	PUNCT
ma-99	596	3	2017	2017	NUM
ma-99	596	4	)	)	PUNCT
ma-99	596	5	,	,	PUNCT
ma-99	596	6	1–24	1–24	PROPN
ma-99	596	7	.	.	PUNCT
ma-99	597	1	https://doi.org/10.9734/arjom/2017/33094.[10	https://doi.org/10.9734/arjom/2017/33094.[10	PROPN
ma-99	597	2	]	]	PUNCT
ma-99	597	3	j.p.n	j.p.n	PROPN
ma-99	597	4	.	.	PROPN
ma-99	597	5	bishwal	bishwal	PROPN
ma-99	597	6	,	,	PUNCT
ma-99	597	7	benstein	benstein	PROPN
ma-99	597	8	-	-	PUNCT
ma-99	597	9	von	von	PROPN
ma-99	597	10	mises	mises	PROPN
ma-99	597	11	theorem	theorem	VERB
ma-99	597	12	and	and	CCONJ
ma-99	597	13	small	small	ADJ
ma-99	597	14	noise	noise	NOUN
ma-99	597	15	bayesian	bayesian	NOUN
ma-99	597	16	asymptotics	asymptotic	NOUN
ma-99	597	17	for	for	ADP
ma-99	597	18	parabolic	parabolic	ADJ
ma-99	597	19	stochastic	stochastic	ADJ
ma-99	597	20	partialdifferential	partialdifferential	ADJ
ma-99	597	21	equations	equation	NOUN
ma-99	597	22	,	,	PUNCT
ma-99	597	23	theory	theory	NOUN
ma-99	597	24	stoch	stoch	NOUN
ma-99	597	25	.	.	PUNCT
ma-99	598	1	processes	process	NOUN
ma-99	598	2	.	.	PUNCT
ma-99	599	1	23	23	NUM
ma-99	599	2	(	(	PUNCT
ma-99	599	3	2018	2018	NUM
ma-99	599	4	)	)	PUNCT
ma-99	599	5	6	6	NUM
ma-99	599	6	-	-	SYM
ma-99	599	7	17.[11	17.[11	NUM
ma-99	599	8	]	]	PUNCT
ma-99	599	9	j.p.n	j.p.n	PROPN
ma-99	599	10	.	.	PROPN
ma-99	599	11	bishwal	bishwal	NOUN
ma-99	599	12	,	,	PUNCT
ma-99	599	13	sequential	sequential	ADJ
ma-99	599	14	maximum	maximum	ADJ
ma-99	599	15	likelihood	likelihood	NOUN
ma-99	599	16	estimation	estimation	NOUN
ma-99	599	17	in	in	ADP
ma-99	599	18	nonlinear	nonlinear	ADJ
ma-99	599	19	non	non	ADJ
ma-99	599	20	-	-	ADJ
ma-99	599	21	markov	markov	ADJ
ma-99	599	22	diffusion	diffusion	NOUN
ma-99	599	23	type	type	NOUN
ma-99	599	24	processes	process	NOUN
ma-99	599	25	,	,	PUNCT
ma-99	599	26	dyn.syst	dyn.syst	NOUN
ma-99	599	27	.	.	PUNCT
ma-99	600	1	appl	appl	PROPN
ma-99	600	2	.	.	PROPN
ma-99	601	1	27	27	NUM
ma-99	601	2	(	(	PUNCT
ma-99	601	3	2018	2018	NUM
ma-99	601	4	)	)	PUNCT
ma-99	601	5	107	107	NUM
ma-99	601	6	-	-	SYM
ma-99	601	7	124.[12	124.[12	NUM
ma-99	601	8	]	]	PUNCT
ma-99	601	9	j.p.n	j.p.n	PROPN
ma-99	601	10	.	.	PROPN
ma-99	601	11	bishwal	bishwal	PROPN
ma-99	601	12	,	,	PUNCT
ma-99	601	13	parameter	parameter	NOUN
ma-99	601	14	estimation	estimation	NOUN
ma-99	601	15	in	in	ADP
ma-99	601	16	stochastic	stochastic	ADJ
ma-99	601	17	volatility	volatility	NOUN
ma-99	601	18	models	model	NOUN
ma-99	601	19	,	,	PUNCT
ma-99	601	20	springer	springer	NOUN
ma-99	601	21	nature	nature	NOUN
ma-99	601	22	,	,	PUNCT
ma-99	601	23	cham	cham	PROPN
ma-99	601	24	(	(	PUNCT
ma-99	601	25	in	in	ADP
ma-99	601	26	press	press	NOUN
ma-99	601	27	)	)	PUNCT
ma-99	601	28	,	,	PUNCT
ma-99	601	29	(	(	PUNCT
ma-99	601	30	2022).[13	2022).[13	NOUN
ma-99	601	31	]	]	X
ma-99	601	32	t.	t.	PROPN
ma-99	601	33	bojdecki	bojdecki	PROPN
ma-99	601	34	,	,	PUNCT
ma-99	601	35	l.g	l.g	PROPN
ma-99	601	36	.	.	PROPN
ma-99	601	37	gorostiza	gorostiza	PROPN
ma-99	601	38	,	,	PUNCT
ma-99	601	39	a.	a.	NOUN
ma-99	601	40	talarczyk	talarczyk	NOUN
ma-99	601	41	,	,	PUNCT
ma-99	601	42	sub	sub	ADJ
ma-99	601	43	-	-	ADJ
ma-99	601	44	fractional	fractional	ADJ
ma-99	601	45	brownian	brownian	ADJ
ma-99	601	46	motion	motion	NOUN
ma-99	601	47	and	and	CCONJ
ma-99	601	48	its	its	PRON
ma-99	601	49	relation	relation	NOUN
ma-99	601	50	to	to	ADP
ma-99	601	51	occupation	occupation	PROPN
ma-99	601	52	times	time	NOUN
ma-99	601	53	,	,	PUNCT
ma-99	601	54	stat.probab	stat.probab	PROPN
ma-99	601	55	.	.	PUNCT
ma-99	601	56	lett	lett	PROPN
ma-99	601	57	.	.	PUNCT
ma-99	602	1	69	69	NUM
ma-99	602	2	(	(	PUNCT
ma-99	602	3	2004	2004	NUM
ma-99	602	4	)	)	PUNCT
ma-99	603	1	405–419	405–419	NUM
ma-99	603	2	.	.	PUNCT
ma-99	604	1	https://doi.org/10.1016/j.spl.2004.06.035.[14	https://doi.org/10.1016/j.spl.2004.06.035.[14	PROPN
ma-99	604	2	]	]	PUNCT
ma-99	604	3	p.	p.	PROPN
ma-99	604	4	carr	carr	PROPN
ma-99	604	5	,	,	PUNCT
ma-99	604	6	h.	h.	PROPN
ma-99	604	7	geman	geman	PROPN
ma-99	604	8	,	,	PUNCT
ma-99	604	9	d.b	d.b	PROPN
ma-99	604	10	.	.	PROPN
ma-99	604	11	madan	madan	PROPN
ma-99	604	12	,	,	PUNCT
ma-99	604	13	m.	m.	NOUN
ma-99	604	14	yor	yor	PROPN
ma-99	604	15	,	,	PUNCT
ma-99	604	16	the	the	DET
ma-99	604	17	fine	fine	ADJ
ma-99	604	18	structure	structure	NOUN
ma-99	604	19	of	of	ADP
ma-99	604	20	asset	asset	NOUN
ma-99	604	21	returns	return	NOUN
ma-99	604	22	:	:	PUNCT
ma-99	604	23	an	an	DET
ma-99	604	24	empirical	empirical	ADJ
ma-99	604	25	investigation	investigation	NOUN
ma-99	604	26	,	,	PUNCT
ma-99	604	27	j.	j.	PROPN
ma-99	604	28	bus	bus	PROPN
ma-99	604	29	.	.	PUNCT
ma-99	605	1	75(2002	75(2002	NUM
ma-99	605	2	)	)	PUNCT
ma-99	606	1	305–333	305–333	NUM
ma-99	606	2	.	.	PUNCT
ma-99	607	1	https://doi.org/10.1086/338705.[15	https://doi.org/10.1086/338705.[15	PROPN
ma-99	607	2	]	]	PUNCT
ma-99	607	3	i.	i.	NOUN
ma-99	607	4	cialenco	cialenco	PROPN
ma-99	607	5	,	,	PUNCT
ma-99	607	6	parameter	parameter	NOUN
ma-99	607	7	estimation	estimation	NOUN
ma-99	607	8	for	for	ADP
ma-99	607	9	spdes	spde	NOUN
ma-99	607	10	with	with	ADP
ma-99	607	11	multiplicative	multiplicative	ADJ
ma-99	607	12	fractional	fractional	ADJ
ma-99	607	13	noise	noise	NOUN
ma-99	607	14	,	,	PUNCT
ma-99	607	15	stoch	stoch	NOUN
ma-99	607	16	.	.	PUNCT
ma-99	608	1	dyn	dyn	PROPN
ma-99	608	2	.	.	PUNCT
ma-99	609	1	10	10	NUM
ma-99	609	2	(	(	PUNCT
ma-99	609	3	2010	2010	NUM
ma-99	609	4	)	)	PUNCT
ma-99	610	1	561–576	561–576	NUM
ma-99	610	2	.	.	PUNCT
ma-99	611	1	https://doi.org/10.1142/s0219493710003091.[16	https://doi.org/10.1142/s0219493710003091.[16	X
ma-99	611	2	]	]	X
ma-99	611	3	g.	g.	PROPN
ma-99	611	4	da	da	PROPN
ma-99	611	5	prato	prato	PROPN
ma-99	611	6	,	,	PUNCT
ma-99	611	7	j.	j.	PROPN
ma-99	611	8	zabczyk	zabczyk	PROPN
ma-99	611	9	,	,	PUNCT
ma-99	611	10	stochastic	stochastic	ADJ
ma-99	611	11	equations	equation	NOUN
ma-99	611	12	in	in	ADP
ma-99	611	13	infinite	infinite	ADJ
ma-99	611	14	dimensions	dimension	NOUN
ma-99	611	15	,	,	PUNCT
ma-99	611	16	second	second	ADJ
ma-99	611	17	ed	ed	NOUN
ma-99	611	18	.	.	PROPN
ma-99	611	19	,	,	PUNCT
ma-99	611	20	cambridge	cambridge	PROPN
ma-99	611	21	university	university	PROPN
ma-99	611	22	press,(2014).[17	press,(2014).[17	PROPN
ma-99	611	23	]	]	PUNCT
ma-99	611	24	z.	z.	PROPN
ma-99	611	25	fu	fu	PROPN
ma-99	611	26	,	,	PUNCT
ma-99	611	27	z.	z.	PROPN
ma-99	611	28	li	li	PROPN
ma-99	611	29	,	,	PUNCT
ma-99	611	30	stochastic	stochastic	ADJ
ma-99	611	31	equations	equation	NOUN
ma-99	611	32	of	of	ADP
ma-99	611	33	non	non	ADJ
ma-99	611	34	-	-	ADJ
ma-99	611	35	negative	negative	ADJ
ma-99	611	36	processes	process	NOUN
ma-99	611	37	with	with	ADP
ma-99	611	38	jumps	jump	NOUN
ma-99	611	39	,	,	PUNCT
ma-99	611	40	stoch	stoch	NOUN
ma-99	611	41	.	.	PUNCT
ma-99	612	1	processes	process	VERB
ma-99	612	2	appl	appl	NOUN
ma-99	612	3	.	.	PUNCT
ma-99	613	1	120	120	NUM
ma-99	613	2	(	(	PUNCT
ma-99	613	3	2010	2010	NUM
ma-99	613	4	)	)	PUNCT
ma-99	613	5	306–330	306–330	NUM
ma-99	613	6	.	.	PUNCT
ma-99	614	1	https://doi.org/10.1016/j.spa.2009.11.005.[18	https://doi.org/10.1016/j.spa.2009.11.005.[18	PROPN
ma-99	614	2	]	]	PUNCT
ma-99	614	3	h.	h.	PROPN
ma-99	615	1	he	he	PRON
ma-99	615	2	,	,	PUNCT
ma-99	615	3	z.	z.	PROPN
ma-99	615	4	li	li	PROPN
ma-99	615	5	,	,	PUNCT
ma-99	615	6	x.	x.	PROPN
ma-99	615	7	yang	yang	PROPN
ma-99	615	8	,	,	PUNCT
ma-99	615	9	stochastic	stochastic	ADJ
ma-99	615	10	equations	equation	NOUN
ma-99	615	11	of	of	ADP
ma-99	615	12	super	super	ADJ
ma-99	615	13	-	-	ADJ
ma-99	615	14	lévy	lévy	ADJ
ma-99	615	15	processes	process	NOUN
ma-99	615	16	with	with	ADP
ma-99	615	17	general	general	ADJ
ma-99	615	18	branching	branching	NOUN
ma-99	615	19	mechanism	mechanism	NOUN
ma-99	615	20	,	,	PUNCT
ma-99	615	21	stoch.processes	stoch.processe	VERB
ma-99	615	22	appl	appl	NOUN
ma-99	615	23	.	.	PUNCT
ma-99	616	1	124	124	NUM
ma-99	616	2	(	(	PUNCT
ma-99	616	3	2014	2014	NUM
ma-99	616	4	)	)	PUNCT
ma-99	616	5	1519–1565	1519–1565	NUM
ma-99	616	6	.	.	PUNCT
ma-99	617	1	https://doi.org/10.1016/j.spa.2013.12.007.[19	https://doi.org/10.1016/j.spa.2013.12.007.[19	PROPN
ma-99	617	2	]	]	PUNCT
ma-99	618	1	y.	y.	PROPN
ma-99	618	2	hu	hu	PROPN
ma-99	618	3	,	,	PUNCT
ma-99	618	4	h.	h.	PROPN
ma-99	618	5	long	long	PROPN
ma-99	618	6	,	,	PUNCT
ma-99	618	7	parameter	parameter	NOUN
ma-99	618	8	estimation	estimation	NOUN
ma-99	618	9	for	for	ADP
ma-99	618	10	ornstein	ornstein	PROPN
ma-99	618	11	-	-	PUNCT
ma-99	618	12	uhlenbeck	uhlenbeck	PROPN
ma-99	618	13	processes	process	NOUN
ma-99	618	14	driven	drive	VERB
ma-99	618	15	by	by	ADP
ma-99	618	16	α	α	VERB
ma-99	618	17	-	-	ADJ
ma-99	618	18	stable	stable	ADJ
ma-99	618	19	levy	levy	NOUN
ma-99	618	20	motions	motion	NOUN
ma-99	618	21	,	,	PUNCT
ma-99	618	22	commun.stoch	commun.stoch	NOUN
ma-99	618	23	.	.	PUNCT
ma-99	618	24	anal	anal	NOUN
ma-99	618	25	.	.	PUNCT
ma-99	619	1	1	1	NUM
ma-99	619	2	(	(	PUNCT
ma-99	619	3	2007	2007	NUM
ma-99	619	4	)	)	PUNCT
ma-99	619	5	175	175	NUM
ma-99	619	6	-	-	SYM
ma-99	619	7	192.[20	192.[20	NUM
ma-99	619	8	]	]	X
ma-99	619	9	y.	y.	PROPN
ma-99	619	10	hu	hu	PROPN
ma-99	619	11	,	,	PUNCT
ma-99	619	12	h.	h.	PROPN
ma-99	619	13	long	long	ADV
ma-99	619	14	,	,	PUNCT
ma-99	619	15	least	least	ADJ
ma-99	619	16	squares	square	NOUN
ma-99	619	17	estimator	estimator	NOUN
ma-99	619	18	for	for	ADP
ma-99	619	19	ornstein	ornstein	PROPN
ma-99	619	20	-	-	PUNCT
ma-99	619	21	uhlenbeck	uhlenbeck	PROPN
ma-99	619	22	processes	process	NOUN
ma-99	619	23	driven	drive	VERB
ma-99	619	24	by	by	ADP
ma-99	619	25	α	α	VERB
ma-99	619	26	-	-	ADJ
ma-99	619	27	stable	stable	ADJ
ma-99	619	28	levy	levy	NOUN
ma-99	619	29	motions	motion	NOUN
ma-99	619	30	,	,	PUNCT
ma-99	619	31	stoch.processes	stoch.processe	VERB
ma-99	619	32	appl	appl	NOUN
ma-99	619	33	.	.	PUNCT
ma-99	620	1	119	119	NUM
ma-99	620	2	(	(	PUNCT
ma-99	620	3	2009	2009	NUM
ma-99	620	4	)	)	PUNCT
ma-99	620	5	2465	2465	NUM
ma-99	620	6	-	-	SYM
ma-99	620	7	2480	2480	NUM
ma-99	620	8	.	.	PUNCT
ma-99	621	1	https://doi.org/10.1016/j.spa.2008.12.006.[21	https://doi.org/10.1016/j.spa.2008.12.006.[21	PROPN
ma-99	621	2	]	]	PUNCT
ma-99	621	3	m.	m.	PROPN
ma-99	621	4	huebner	huebner	PROPN
ma-99	621	5	,	,	PUNCT
ma-99	621	6	a	a	DET
ma-99	621	7	characterization	characterization	NOUN
ma-99	621	8	of	of	ADP
ma-99	621	9	asymptotic	asymptotic	ADJ
ma-99	621	10	behaviour	behaviour	NOUN
ma-99	621	11	of	of	ADP
ma-99	621	12	maximum	maximum	ADJ
ma-99	621	13	likelihood	likelihood	NOUN
ma-99	621	14	estimators	estimator	NOUN
ma-99	621	15	for	for	ADP
ma-99	621	16	stochastic	stochastic	ADJ
ma-99	621	17	pde’s	pde’s	NOUN
ma-99	621	18	,	,	PUNCT
ma-99	621	19	math	math	NOUN
ma-99	621	20	.	.	PUNCT
ma-99	622	1	meth	meth	NOUN
ma-99	622	2	.	.	PUNCT
ma-99	623	1	stat	stat	PROPN
ma-99	623	2	.	.	PUNCT
ma-99	624	1	6	6	NUM
ma-99	624	2	(	(	PUNCT
ma-99	624	3	1997	1997	NUM
ma-99	624	4	)	)	PUNCT
ma-99	624	5	395	395	NUM
ma-99	624	6	-	-	SYM
ma-99	624	7	415.[22	415.[22	PROPN
ma-99	624	8	]	]	X
ma-99	624	9	m.	m.	NOUN
ma-99	624	10	huebner	huebner	PROPN
ma-99	624	11	,	,	PUNCT
ma-99	624	12	asymptotic	asymptotic	ADJ
ma-99	624	13	properties	property	NOUN
ma-99	624	14	of	of	ADP
ma-99	624	15	the	the	DET
ma-99	624	16	maximum	maximum	ADJ
ma-99	624	17	likelihood	likelihood	NOUN
ma-99	624	18	estimator	estimator	NOUN
ma-99	624	19	for	for	ADP
ma-99	624	20	stochastic	stochastic	ADJ
ma-99	624	21	pdes	pde	NOUN
ma-99	624	22	disturbed	disturb	VERB
ma-99	624	23	by	by	ADP
ma-99	624	24	smallnoise	smallnoise	ADJ
ma-99	624	25	,	,	PUNCT
ma-99	624	26	stat	stat	PROPN
ma-99	624	27	.	.	PUNCT
ma-99	625	1	infer	infer	VERB
ma-99	625	2	.	.	PUNCT
ma-99	626	1	stoch	stoch	NOUN
ma-99	626	2	.	.	PUNCT
ma-99	627	1	processes	process	NOUN
ma-99	627	2	.	.	PUNCT
ma-99	628	1	2	2	NUM
ma-99	628	2	(	(	PUNCT
ma-99	628	3	1999	1999	NUM
ma-99	628	4	)	)	PUNCT
ma-99	628	5	57–68	57–68	NUM
ma-99	628	6	.	.	PUNCT
ma-99	629	1	https://doi.org/10.1023/a:1009990504925.[23	https://doi.org/10.1023/a:1009990504925.[23	NOUN
ma-99	629	2	]	]	PUNCT
ma-99	629	3	m.	m.	NOUN
ma-99	629	4	hübner	hübner	NOUN
ma-99	629	5	,	,	PUNCT
ma-99	629	6	r.	r.	PROPN
ma-99	629	7	khasminskii	khasminskii	PROPN
ma-99	629	8	,	,	PUNCT
ma-99	629	9	b.l	b.l	PROPN
ma-99	629	10	.	.	PROPN
ma-99	629	11	rozovskii	rozovskii	PROPN
ma-99	629	12	,	,	PUNCT
ma-99	629	13	two	two	NUM
ma-99	629	14	examples	example	NOUN
ma-99	629	15	of	of	ADP
ma-99	629	16	parameter	parameter	NOUN
ma-99	629	17	estimation	estimation	NOUN
ma-99	629	18	for	for	ADP
ma-99	629	19	stochastic	stochastic	ADJ
ma-99	629	20	partial	partial	ADJ
ma-99	629	21	differentialequations	differentialequation	NOUN
ma-99	629	22	,	,	PUNCT
ma-99	629	23	in	in	ADP
ma-99	629	24	:	:	PUNCT
ma-99	629	25	s.	s.	PROPN
ma-99	629	26	cambanis	cambanis	PROPN
ma-99	629	27	,	,	PUNCT
ma-99	629	28	j.k	j.k	PROPN
ma-99	629	29	.	.	PROPN
ma-99	629	30	ghosh	ghosh	PROPN
ma-99	629	31	,	,	PUNCT
ma-99	629	32	r.l	r.l	PROPN
ma-99	629	33	.	.	PROPN
ma-99	629	34	karandikar	karandikar	PROPN
ma-99	629	35	,	,	PUNCT
ma-99	629	36	p.k	p.k	PROPN
ma-99	629	37	.	.	PROPN
ma-99	629	38	sen	sen	PROPN
ma-99	629	39	(	(	PUNCT
ma-99	629	40	eds	eds	PROPN
ma-99	629	41	.	.	PUNCT
ma-99	629	42	)	)	PUNCT
ma-99	629	43	,	,	PUNCT
ma-99	629	44	stochastic	stochastic	NOUN
ma-99	629	45	processes	process	NOUN
ma-99	629	46	,	,	PUNCT
ma-99	629	47	springer	springer	NOUN
ma-99	629	48	new	new	PROPN
ma-99	629	49	york	york	PROPN
ma-99	629	50	,	,	PUNCT
ma-99	629	51	new	new	PROPN
ma-99	629	52	york	york	PROPN
ma-99	629	53	,	,	PUNCT
ma-99	629	54	ny	ny	PROPN
ma-99	629	55	,	,	PUNCT
ma-99	629	56	1993	1993	NUM
ma-99	629	57	:	:	PUNCT
ma-99	630	1	pp	pp	ADP
ma-99	630	2	.	.	PUNCT
ma-99	631	1	149–160	149–160	NUM
ma-99	631	2	.	.	PUNCT
ma-99	632	1	https://doi.org/10.1007/978-1-4615-7909-0_18.[24	https://doi.org/10.1007/978-1-4615-7909-0_18.[24	NOUN
ma-99	632	2	]	]	PUNCT
ma-99	632	3	m.	m.	NOUN
ma-99	632	4	huebner	huebner	PROPN
ma-99	632	5	,	,	PUNCT
ma-99	632	6	b.l	b.l	PROPN
ma-99	632	7	.	.	PROPN
ma-99	632	8	rozovskii	rozovskii	PROPN
ma-99	632	9	,	,	PUNCT
ma-99	632	10	on	on	ADP
ma-99	632	11	asymptotic	asymptotic	ADJ
ma-99	632	12	properties	property	NOUN
ma-99	632	13	of	of	ADP
ma-99	632	14	maximum	maximum	ADJ
ma-99	632	15	likelihood	likelihood	NOUN
ma-99	632	16	estimators	estimator	NOUN
ma-99	632	17	for	for	ADP
ma-99	632	18	parabolic	parabolic	ADJ
ma-99	632	19	stochasticpde	stochasticpde	NOUN
ma-99	632	20	’s	’s	PART
ma-99	632	21	,	,	PUNCT
ma-99	632	22	probab	probab	PROPN
ma-99	632	23	.	.	PUNCT
ma-99	633	1	theory	theory	NOUN
ma-99	633	2	related	relate	VERB
ma-99	633	3	fields	field	NOUN
ma-99	633	4	.	.	PUNCT
ma-99	634	1	103	103	NUM
ma-99	634	2	(	(	PUNCT
ma-99	634	3	1995	1995	NUM
ma-99	634	4	)	)	PUNCT
ma-99	634	5	143–163	143–163	NUM
ma-99	634	6	.	.	PUNCT
ma-99	635	1	https://doi.org/10.1007/bf01204212.[25	https://doi.org/10.1007/bf01204212.[25	NOUN
ma-99	635	2	]	]	X
ma-99	636	1	y.s	y.s	PROPN
ma-99	636	2	.	.	PROPN
ma-99	636	3	kim	kim	PROPN
ma-99	636	4	,	,	PUNCT
ma-99	636	5	s.t	s.t	PROPN
ma-99	636	6	.	.	PROPN
ma-99	636	7	rachev	rachev	PROPN
ma-99	636	8	,	,	PUNCT
ma-99	636	9	d.m	d.m	PROPN
ma-99	636	10	.	.	PROPN
ma-99	636	11	chung	chung	PROPN
ma-99	636	12	,	,	PUNCT
ma-99	636	13	m.l	m.l	PROPN
ma-99	636	14	.	.	PROPN
ma-99	636	15	bianichi	bianichi	PROPN
ma-99	636	16	,	,	PUNCT
ma-99	636	17	a	a	DET
ma-99	636	18	modified	modify	VERB
ma-99	636	19	tempered	temper	VERB
ma-99	636	20	stable	stable	ADJ
ma-99	636	21	distribution	distribution	NOUN
ma-99	636	22	with	with	ADP
ma-99	636	23	volatility	volatility	NOUN
ma-99	636	24	cluster	cluster	NOUN
ma-99	636	25	-	-	PUNCT
ma-99	636	26	ing	ing	NOUN
ma-99	636	27	,	,	PUNCT
ma-99	636	28	in	in	ADP
ma-99	636	29	:	:	PUNCT
ma-99	636	30	j.o	j.o	PROPN
ma-99	636	31	.	.	PROPN
ma-99	636	32	soares	soares	PROPN
ma-99	636	33	,	,	PUNCT
ma-99	636	34	j.	j.	PROPN
ma-99	636	35	pina	pina	PROPN
ma-99	636	36	,	,	PUNCT
ma-99	636	37	m.	m.	NOUN
ma-99	636	38	catalao	catalao	PROPN
ma-99	636	39	-	-	PUNCT
ma-99	636	40	lopes	lope	NOUN
ma-99	636	41	,	,	PUNCT
ma-99	636	42	new	new	ADJ
ma-99	636	43	developments	development	NOUN
ma-99	636	44	in	in	ADP
ma-99	636	45	financial	financial	ADJ
ma-99	636	46	modelling	modelling	NOUN
ma-99	636	47	,	,	PUNCT
ma-99	636	48	cambridge	cambridge	PROPN
ma-99	636	49	scholarspublishing	scholarspublishing	PROPN
ma-99	636	50	,	,	PUNCT
ma-99	636	51	newcastle	newcastle	PROPN
ma-99	636	52	upon	upon	SCONJ
ma-99	636	53	tyne	tyne	PROPN
ma-99	636	54	,	,	PUNCT
ma-99	636	55	uk	uk	PROPN
ma-99	636	56	,	,	PUNCT
ma-99	636	57	(	(	PUNCT
ma-99	636	58	2008	2008	NUM
ma-99	636	59	)	)	PUNCT
ma-99	636	60	.	.	PUNCT
ma-99	637	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	PROPN
ma-99	637	2	https://doi.org/10.1515/rose.2000.8.1.51	https://doi.org/10.1515/rose.2000.8.1.51	PROPN
ma-99	637	3	https://doi.org/10.1017/s1446788700003906	https://doi.org/10.1017/s1446788700003906	NUM
ma-99	637	4	https://doi.org/10.1515/rose.2007.005	https://doi.org/10.1515/rose.2007.005	PROPN
ma-99	637	5	https://doi.org/10.4236/jmf.2011.13008	https://doi.org/10.4236/jmf.2011.13008	NOUN
ma-99	637	6	https://doi.org/10.9734/arjom/2017/33094	https://doi.org/10.9734/arjom/2017/33094	X
ma-99	637	7	https://doi.org/10.1016/j.spl.2004.06.035	https://doi.org/10.1016/j.spl.2004.06.035	NOUN
ma-99	637	8	https://doi.org/10.1086/338705	https://doi.org/10.1086/338705	ADJ
ma-99	637	9	https://doi.org/10.1142/s0219493710003091	https://doi.org/10.1142/s0219493710003091	NUM
ma-99	637	10	https://doi.org/10.1016/j.spa.2009.11.005	https://doi.org/10.1016/j.spa.2009.11.005	NOUN
ma-99	637	11	https://doi.org/10.1016/j.spa.2013.12.007	https://doi.org/10.1016/j.spa.2013.12.007	PROPN
ma-99	637	12	https://doi.org/10.1016/j.spa.2008.12.006	https://doi.org/10.1016/j.spa.2008.12.006	ADJ
ma-99	637	13	https://doi.org/10.1023/a:1009990504925	https://doi.org/10.1023/a:1009990504925	NOUN
ma-99	637	14	https://doi.org/10.1007/978-1-4615-7909-0_18	https://doi.org/10.1007/978-1-4615-7909-0_18	NOUN
ma-99	637	15	https://doi.org/10.1007/bf01204212	https://doi.org/10.1007/bf01204212	NUM
ma-99	637	16	eur	eur	NOUN
ma-99	637	17	.	.	PUNCT
ma-99	638	1	j.	j.	PROPN
ma-99	638	2	math	math	PROPN
ma-99	638	3	.	.	PUNCT
ma-99	639	1	anal	anal	PROPN
ma-99	639	2	.	.	PUNCT
ma-99	640	1	10.28924	10.28924	NUM
ma-99	640	2	/	/	SYM
ma-99	640	3	ada	ada	PROPN
ma-99	640	4	/	/	SYM
ma-99	640	5	ma.3.4	ma.3.4	PROPN
ma-99	640	6	25	25	NUM
ma-99	640	7	[	[	X
ma-99	640	8	26	26	NUM
ma-99	640	9	]	]	X
ma-99	640	10	n.	n.	NOUN
ma-99	640	11	konno	konno	NOUN
ma-99	640	12	,	,	PUNCT
ma-99	640	13	t.	t.	PROPN
ma-99	640	14	shiga	shiga	PROPN
ma-99	640	15	,	,	PUNCT
ma-99	640	16	stochastic	stochastic	ADJ
ma-99	640	17	partial	partial	ADJ
ma-99	640	18	differential	differential	NOUN
ma-99	640	19	equations	equation	NOUN
ma-99	640	20	for	for	ADP
ma-99	640	21	some	some	DET
ma-99	640	22	measure	measure	NOUN
ma-99	640	23	-	-	PUNCT
ma-99	640	24	valued	value	VERB
ma-99	640	25	diffusions	diffusion	NOUN
ma-99	640	26	,	,	PUNCT
ma-99	640	27	probab	probab	PROPN
ma-99	640	28	.	.	PUNCT
ma-99	641	1	th	th	X
ma-99	641	2	.	.	PUNCT
ma-99	641	3	rel.fields	rel.fields	PROPN
ma-99	641	4	.	.	PROPN
ma-99	642	1	79	79	NUM
ma-99	642	2	(	(	PUNCT
ma-99	642	3	1988	1988	NUM
ma-99	642	4	)	)	PUNCT
ma-99	642	5	201–225	201–225	NUM
ma-99	642	6	.	.	PUNCT
ma-99	643	1	https://doi.org/10.1007/bf00320919.[27	https://doi.org/10.1007/bf00320919.[27	NOUN
ma-99	643	2	]	]	PUNCT
ma-99	643	3	t.	t.	PROPN
ma-99	643	4	koski	koski	PROPN
ma-99	643	5	,	,	PUNCT
ma-99	643	6	w.	w.	PROPN
ma-99	643	7	loges	loges	PROPN
ma-99	643	8	,	,	PUNCT
ma-99	643	9	asymptotic	asymptotic	ADJ
ma-99	643	10	statistical	statistical	ADJ
ma-99	643	11	inference	inference	NOUN
ma-99	643	12	for	for	ADP
ma-99	643	13	a	a	DET
ma-99	643	14	stochastic	stochastic	ADJ
ma-99	643	15	heat	heat	NOUN
ma-99	643	16	flow	flow	NOUN
ma-99	643	17	problem	problem	NOUN
ma-99	643	18	,	,	PUNCT
ma-99	643	19	stat	stat	PROPN
ma-99	643	20	.	.	PUNCT
ma-99	644	1	probab	probab	PROPN
ma-99	644	2	.	.	PUNCT
ma-99	645	1	lett	lett	PROPN
ma-99	645	2	.	.	PROPN
ma-99	646	1	3	3	NUM
ma-99	646	2	(	(	PUNCT
ma-99	646	3	1985)185–189	1985)185–189	NUM
ma-99	646	4	.	.	PUNCT
ma-99	647	1	https://doi.org/10.1016/0167-7152(85)90015-x.[28	https://doi.org/10.1016/0167-7152(85)90015-x.[28	PROPN
ma-99	647	2	]	]	PUNCT
ma-99	647	3	t.	t.	PROPN
ma-99	647	4	koski	koski	PROPN
ma-99	647	5	,	,	PUNCT
ma-99	647	6	w.	w.	PROPN
ma-99	647	7	loges	loges	PROPN
ma-99	647	8	,	,	PUNCT
ma-99	647	9	on	on	ADP
ma-99	647	10	minimum	minimum	ADJ
ma-99	647	11	-	-	PUNCT
ma-99	647	12	contrast	contrast	NOUN
ma-99	647	13	estimation	estimation	NOUN
ma-99	647	14	for	for	ADP
ma-99	647	15	hilbert	hilbert	PROPN
ma-99	647	16	space	space	NOUN
ma-99	647	17	-	-	PUNCT
ma-99	647	18	valued	value	VERB
ma-99	647	19	stochastic	stochastic	ADJ
ma-99	647	20	differential	differential	ADJ
ma-99	647	21	equations	equation	NOUN
ma-99	647	22	,	,	PUNCT
ma-99	647	23	stochastics	stochastic	NOUN
ma-99	647	24	.	.	PUNCT
ma-99	648	1	16	16	NUM
ma-99	648	2	(	(	PUNCT
ma-99	648	3	1986	1986	NUM
ma-99	648	4	)	)	PUNCT
ma-99	649	1	217–225	217–225	NUM
ma-99	649	2	.	.	PUNCT
ma-99	650	1	https://doi.org/10.1080/17442508608833374.[29	https://doi.org/10.1080/17442508608833374.[29	PROPN
ma-99	650	2	]	]	X
ma-99	650	3	i.a	i.a	PROPN
ma-99	650	4	.	.	PROPN
ma-99	650	5	ibragimov	ibragimov	PROPN
ma-99	650	6	,	,	PUNCT
ma-99	650	7	r.z	r.z	PROPN
ma-99	650	8	.	.	PROPN
ma-99	650	9	khas’minskii	khas’minskii	PROPN
ma-99	650	10	,	,	PUNCT
ma-99	650	11	some	some	DET
ma-99	650	12	estimation	estimation	NOUN
ma-99	650	13	problems	problem	NOUN
ma-99	650	14	for	for	ADP
ma-99	650	15	stochastic	stochastic	ADJ
ma-99	650	16	partial	partial	ADJ
ma-99	650	17	differential	differential	NOUN
ma-99	650	18	equations	equation	NOUN
ma-99	650	19	,	,	PUNCT
ma-99	650	20	dokl	dokl	NOUN
ma-99	650	21	.	.	PUNCT
ma-99	651	1	akad.nauk	akad.nauk	NUM
ma-99	651	2	,	,	PUNCT
ma-99	651	3	353	353	NUM
ma-99	651	4	(	(	PUNCT
ma-99	651	5	1997	1997	NUM
ma-99	651	6	)	)	PUNCT
ma-99	651	7	300–302.[30	300–302.[30	NUM
ma-99	651	8	]	]	PUNCT
ma-99	651	9	janicki	janicki	NOUN
ma-99	651	10	,	,	PUNCT
ma-99	651	11	a.	a.	NOUN
ma-99	651	12	and	and	CCONJ
ma-99	651	13	weron	weron	NOUN
ma-99	651	14	,	,	PUNCT
ma-99	651	15	a.	a.	NOUN
ma-99	651	16	(	(	PUNCT
ma-99	651	17	1994	1994	NUM
ma-99	651	18	)	)	PUNCT
ma-99	651	19	:	:	PUNCT
ma-99	652	1	simulation	simulation	NOUN
ma-99	652	2	and	and	CCONJ
ma-99	652	3	chaotic	chaotic	ADJ
ma-99	652	4	behavior	behavior	NOUN
ma-99	652	5	of	of	ADP
ma-99	652	6	α	α	NOUN
ma-99	652	7	-	-	ADJ
ma-99	652	8	stable	stable	ADJ
ma-99	652	9	stochastic	stochastic	NOUN
ma-99	652	10	processes	process	NOUN
ma-99	652	11	,	,	PUNCT
ma-99	652	12	marceldekker	marceldekker	NOUN
ma-99	652	13	,	,	PUNCT
ma-99	652	14	new	new	ADJ
ma-99	652	15	york.[31	york.[31	PROPN
ma-99	652	16	]	]	X
ma-99	652	17	z.	z.	PROPN
ma-99	652	18	li	li	PROPN
ma-99	652	19	,	,	PUNCT
ma-99	652	20	c.	c.	PROPN
ma-99	652	21	ma	ma	PROPN
ma-99	652	22	,	,	PUNCT
ma-99	652	23	asymptotic	asymptotic	ADJ
ma-99	652	24	properties	property	NOUN
ma-99	652	25	of	of	ADP
ma-99	652	26	estimators	estimator	NOUN
ma-99	652	27	in	in	ADP
ma-99	652	28	a	a	DET
ma-99	652	29	stable	stable	ADJ
ma-99	652	30	cox	cox	PROPN
ma-99	652	31	–	–	PUNCT
ma-99	652	32	ingersoll	ingersoll	PROPN
ma-99	652	33	–	–	PUNCT
ma-99	652	34	ross	ross	PROPN
ma-99	652	35	model	model	PROPN
ma-99	652	36	,	,	PUNCT
ma-99	652	37	stoch	stoch	NOUN
ma-99	652	38	.	.	PUNCT
ma-99	652	39	processes	process	VERB
ma-99	652	40	appl	appl	NOUN
ma-99	652	41	.	.	PUNCT
ma-99	653	1	125(2015	125(2015	NUM
ma-99	653	2	)	)	PUNCT
ma-99	653	3	3196–3233	3196–3233	NUM
ma-99	653	4	.	.	PUNCT
ma-99	654	1	https://doi.org/10.1016/j.spa.2015.03.002.[32	https://doi.org/10.1016/j.spa.2015.03.002.[32	PROPN
ma-99	654	2	]	]	PUNCT
ma-99	654	3	w.	w.	PROPN
ma-99	654	4	loges	loges	PROPN
ma-99	654	5	,	,	PUNCT
ma-99	654	6	girsanov	girsanov	PROPN
ma-99	654	7	’s	’s	PART
ma-99	654	8	theorem	theorem	NOUN
ma-99	654	9	in	in	ADP
ma-99	654	10	hilbert	hilbert	NOUN
ma-99	654	11	space	space	NOUN
ma-99	654	12	and	and	CCONJ
ma-99	654	13	an	an	DET
ma-99	654	14	application	application	NOUN
ma-99	654	15	to	to	ADP
ma-99	654	16	the	the	DET
ma-99	654	17	statistics	statistic	NOUN
ma-99	654	18	of	of	ADP
ma-99	654	19	hilbert	hilbert	PROPN
ma-99	654	20	spacevalued	spacevalue	VERB
ma-99	654	21	stochasticdifferential	stochasticdifferential	ADJ
ma-99	654	22	equations	equation	NOUN
ma-99	654	23	,	,	PUNCT
ma-99	654	24	stoch	stoch	NOUN
ma-99	654	25	.	.	PUNCT
ma-99	655	1	processes	process	VERB
ma-99	655	2	appl	appl	NOUN
ma-99	655	3	.	.	PUNCT
ma-99	656	1	17	17	NUM
ma-99	656	2	(	(	PUNCT
ma-99	656	3	1984	1984	NUM
ma-99	656	4	)	)	PUNCT
ma-99	656	5	243–263	243–263	NUM
ma-99	656	6	.	.	PUNCT
ma-99	656	7	https://doi.org/10.1016/0304-4149(84	https://doi.org/10.1016/0304-4149(84	NOUN
ma-99	656	8	)	)	PUNCT
ma-99	656	9	90004	90004	NUM
ma-99	657	1	-	-	SYM
ma-99	657	2	8.[33	8.[33	NUM
ma-99	657	3	]	]	X
ma-99	657	4	s.v	s.v	PROPN
ma-99	657	5	.	.	PROPN
ma-99	657	6	lototsky	lototsky	PROPN
ma-99	657	7	,	,	PUNCT
ma-99	657	8	b.l	b.l	PROPN
ma-99	657	9	.	.	PROPN
ma-99	657	10	rosovskii	rosovskii	PROPN
ma-99	657	11	,	,	PUNCT
ma-99	657	12	spectral	spectral	ADJ
ma-99	657	13	asymptotics	asymptotic	NOUN
ma-99	657	14	of	of	ADP
ma-99	657	15	some	some	DET
ma-99	657	16	functionals	functional	NOUN
ma-99	657	17	arising	arise	VERB
ma-99	657	18	in	in	ADP
ma-99	657	19	statistical	statistical	ADJ
ma-99	657	20	inference	inference	NOUN
ma-99	657	21	for	for	ADP
ma-99	657	22	spdes	spde	NOUN
ma-99	657	23	,	,	PUNCT
ma-99	657	24	stoch	stoch	NOUN
ma-99	657	25	.	.	PUNCT
ma-99	658	1	processes	process	VERB
ma-99	658	2	appl	appl	NOUN
ma-99	658	3	.	.	PUNCT
ma-99	659	1	79	79	NUM
ma-99	659	2	(	(	PUNCT
ma-99	659	3	1999	1999	NUM
ma-99	659	4	)	)	PUNCT
ma-99	659	5	69–94	69–94	NOUN
ma-99	659	6	.	.	PUNCT
ma-99	660	1	https://doi.org/10.1016/s0304-4149(98)00079-9.[34	https://doi.org/10.1016/s0304-4149(98)00079-9.[34	PROPN
ma-99	660	2	]	]	X
ma-99	660	3	h.	h.	PROPN
ma-99	660	4	masuda	masuda	PROPN
ma-99	660	5	,	,	PUNCT
ma-99	660	6	classical	classical	ADJ
ma-99	660	7	method	method	NOUN
ma-99	660	8	of	of	ADP
ma-99	660	9	moments	moment	NOUN
ma-99	660	10	for	for	ADP
ma-99	660	11	partially	partially	ADV
ma-99	660	12	and	and	CCONJ
ma-99	660	13	discretely	discretely	ADV
ma-99	660	14	observed	observe	VERB
ma-99	660	15	ergodic	ergodic	ADJ
ma-99	660	16	models	model	NOUN
ma-99	660	17	,	,	PUNCT
ma-99	660	18	stat	stat	PROPN
ma-99	660	19	.	.	PUNCT
ma-99	660	20	infer	infer	VERB
ma-99	660	21	.	.	PUNCT
ma-99	661	1	stoch.processes	stoch.processe	NOUN
ma-99	661	2	.	.	PROPN
ma-99	661	3	8	8	NUM
ma-99	661	4	(	(	PUNCT
ma-99	661	5	2005	2005	NUM
ma-99	661	6	)	)	PUNCT
ma-99	661	7	25–50	25–50	NUM
ma-99	661	8	.	.	PUNCT
ma-99	662	1	https://doi.org/10.1023/b:sisp.0000049120.83388.89.[35	https://doi.org/10.1023/b:sisp.0000049120.83388.89.[35	PROPN
ma-99	662	2	]	]	X
ma-99	662	3	h.	h.	PROPN
ma-99	662	4	masuda	masuda	PROPN
ma-99	662	5	,	,	PUNCT
ma-99	662	6	non	non	ADJ
ma-99	662	7	-	-	ADJ
ma-99	662	8	gaussian	gaussian	ADJ
ma-99	662	9	quasi	quasi	ADJ
ma-99	662	10	-	-	ADJ
ma-99	662	11	likelihood	likelihood	ADJ
ma-99	662	12	estimation	estimation	NOUN
ma-99	662	13	of	of	ADP
ma-99	662	14	sde	sde	PROPN
ma-99	662	15	driven	drive	VERB
ma-99	662	16	by	by	ADP
ma-99	662	17	locally	locally	ADV
ma-99	662	18	stable	stable	ADJ
ma-99	662	19	lévy	lévy	ADJ
ma-99	662	20	process	process	NOUN
ma-99	662	21	,	,	PUNCT
ma-99	662	22	stoch	stoch	NOUN
ma-99	662	23	.	.	PUNCT
ma-99	663	1	pro	pro	ADJ
ma-99	663	2	-	-	ADJ
ma-99	663	3	cesses	cesse	NOUN
ma-99	663	4	appl	appl	NOUN
ma-99	663	5	.	.	PUNCT
ma-99	664	1	129	129	NUM
ma-99	664	2	(	(	PUNCT
ma-99	664	3	2019	2019	NUM
ma-99	664	4	)	)	PUNCT
ma-99	664	5	1013–1059	1013–1059	NUM
ma-99	664	6	.	.	PUNCT
ma-99	665	1	https://doi.org/10.1016/j.spa.2018.04.004.[36	https://doi.org/10.1016/j.spa.2018.04.004.[36	PROPN
ma-99	665	2	]	]	PUNCT
ma-99	665	3	h.	h.	PROPN
ma-99	665	4	masuda	masuda	PROPN
ma-99	665	5	,	,	PUNCT
ma-99	665	6	y.	y.	PROPN
ma-99	665	7	uehara	uehara	PROPN
ma-99	665	8	,	,	PUNCT
ma-99	665	9	two	two	NUM
ma-99	665	10	-	-	PUNCT
ma-99	665	11	step	step	NOUN
ma-99	665	12	estimation	estimation	NOUN
ma-99	665	13	of	of	ADP
ma-99	665	14	ergodic	ergodic	ADJ
ma-99	665	15	lévy	lévy	PROPN
ma-99	665	16	driven	drive	VERB
ma-99	665	17	sde	sde	PROPN
ma-99	665	18	,	,	PUNCT
ma-99	665	19	stat	stat	PROPN
ma-99	665	20	.	.	PUNCT
ma-99	666	1	infer	infer	VERB
ma-99	666	2	.	.	PUNCT
ma-99	667	1	stoch	stoch	NOUN
ma-99	667	2	.	.	PUNCT
ma-99	668	1	processes	process	NOUN
ma-99	668	2	.	.	PUNCT
ma-99	669	1	20	20	NUM
ma-99	669	2	(	(	PUNCT
ma-99	669	3	2016)105–137	2016)105–137	PROPN
ma-99	669	4	.	.	PUNCT
ma-99	670	1	https://doi.org/10.1007/s11203-016-9133-5.[37	https://doi.org/10.1007/s11203-016-9133-5.[37	PROPN
ma-99	670	2	]	]	X
ma-99	670	3	s.	s.	PROPN
ma-99	670	4	peszat	peszat	PROPN
ma-99	670	5	,	,	PUNCT
ma-99	670	6	j.	j.	PROPN
ma-99	670	7	zabczyk	zabczyk	PROPN
ma-99	670	8	,	,	PUNCT
ma-99	670	9	stochastic	stochastic	ADJ
ma-99	670	10	partial	partial	ADJ
ma-99	670	11	differential	differential	ADJ
ma-99	670	12	equations	equation	NOUN
ma-99	670	13	with	with	ADP
ma-99	670	14	levy	levy	NOUN
ma-99	670	15	noise	noise	NOUN
ma-99	670	16	:	:	PUNCT
ma-99	670	17	evolution	evolution	NOUN
ma-99	670	18	equations	equation	NOUN
ma-99	670	19	approach	approach	PROPN
ma-99	670	20	,	,	PUNCT
ma-99	670	21	cambridge	cambridge	PROPN
ma-99	670	22	university	university	PROPN
ma-99	670	23	press	press	PROPN
ma-99	670	24	,	,	PUNCT
ma-99	670	25	cambridge	cambridge	PROPN
ma-99	670	26	,	,	PUNCT
ma-99	670	27	england	england	PROPN
ma-99	670	28	,	,	PUNCT
ma-99	670	29	(	(	PUNCT
ma-99	670	30	2007).[38	2007).[38	NUM
ma-99	670	31	]	]	X
ma-99	670	32	e.	e.	PROPN
ma-99	670	33	priola	priola	PROPN
ma-99	670	34	,	,	PUNCT
ma-99	670	35	a.	a.	PROPN
ma-99	670	36	shirikyan	shirikyan	PROPN
ma-99	670	37	,	,	PUNCT
ma-99	670	38	l.	l.	PROPN
ma-99	670	39	xu	xu	PROPN
ma-99	670	40	,	,	PUNCT
ma-99	670	41	j.	j.	PROPN
ma-99	670	42	zabczyk	zabczyk	PROPN
ma-99	670	43	,	,	PUNCT
ma-99	670	44	exponential	exponential	ADJ
ma-99	670	45	ergodicity	ergodicity	NOUN
ma-99	670	46	and	and	CCONJ
ma-99	670	47	regularity	regularity	NOUN
ma-99	670	48	for	for	ADP
ma-99	670	49	equations	equation	NOUN
ma-99	670	50	with	with	ADP
ma-99	670	51	lévy	lévy	ADJ
ma-99	670	52	noise	noise	NOUN
ma-99	670	53	,	,	PUNCT
ma-99	670	54	stoch.processes	stoch.processe	VERB
ma-99	670	55	appl	appl	NOUN
ma-99	670	56	.	.	PUNCT
ma-99	671	1	122	122	NUM
ma-99	671	2	(	(	PUNCT
ma-99	671	3	2012	2012	NUM
ma-99	671	4	)	)	PUNCT
ma-99	672	1	106–133	106–133	NUM
ma-99	672	2	.	.	PUNCT
ma-99	673	1	https://doi.org/10.1016/j.spa.2011.10.003.[39	https://doi.org/10.1016/j.spa.2011.10.003.[39	PROPN
ma-99	673	2	]	]	PUNCT
ma-99	673	3	e.	e.	PROPN
ma-99	673	4	priola	priola	PROPN
ma-99	673	5	,	,	PUNCT
ma-99	673	6	j.	j.	PROPN
ma-99	673	7	zabczyk	zabczyk	PROPN
ma-99	673	8	,	,	PUNCT
ma-99	673	9	structural	structural	ADJ
ma-99	673	10	properties	property	NOUN
ma-99	673	11	of	of	ADP
ma-99	673	12	semilinear	semilinear	ADJ
ma-99	673	13	spdes	spde	NOUN
ma-99	673	14	driven	drive	VERB
ma-99	673	15	by	by	ADP
ma-99	673	16	cylindrical	cylindrical	ADJ
ma-99	673	17	stable	stable	ADJ
ma-99	673	18	processes	process	NOUN
ma-99	673	19	,	,	PUNCT
ma-99	673	20	probab.theory	probab.theory	NOUN
ma-99	673	21	relat	relat	NOUN
ma-99	673	22	.	.	PUNCT
ma-99	674	1	fields	field	NOUN
ma-99	674	2	.	.	PUNCT
ma-99	675	1	149	149	NUM
ma-99	675	2	(	(	PUNCT
ma-99	675	3	2009	2009	NUM
ma-99	675	4	)	)	PUNCT
ma-99	675	5	97–137	97–137	NUM
ma-99	675	6	.	.	PUNCT
ma-99	676	1	https://doi.org/10.1007/s00440-009-0243-5.[40	https://doi.org/10.1007/s00440-009-0243-5.[40	PROPN
ma-99	676	2	]	]	PUNCT
ma-99	676	3	k.	k.	PROPN
ma-99	676	4	sato	sato	PROPN
ma-99	676	5	,	,	PUNCT
ma-99	676	6	levy	levy	NOUN
ma-99	676	7	processes	process	NOUN
ma-99	676	8	and	and	CCONJ
ma-99	676	9	infinitely	infinitely	ADV
ma-99	676	10	divisible	divisible	ADJ
ma-99	676	11	distributions	distribution	NOUN
ma-99	676	12	,	,	PUNCT
ma-99	676	13	cambridge	cambridge	PROPN
ma-99	676	14	university	university	PROPN
ma-99	676	15	press	press	PROPN
ma-99	676	16	,	,	PUNCT
ma-99	676	17	cambridge	cambridge	PROPN
ma-99	676	18	,	,	PUNCT
ma-99	676	19	(	(	PUNCT
ma-99	676	20	1999).[41	1999).[41	PROPN
ma-99	676	21	]	]	X
ma-99	676	22	a.w	a.w	PROPN
ma-99	676	23	.	.	PROPN
ma-99	676	24	van	van	PROPN
ma-99	676	25	der	der	PROPN
ma-99	676	26	vaart	vaart	PROPN
ma-99	676	27	,	,	PUNCT
ma-99	676	28	asymptotic	asymptotic	ADJ
ma-99	676	29	statistics	statistic	NOUN
ma-99	676	30	,	,	PUNCT
ma-99	676	31	cambridge	cambridge	PROPN
ma-99	676	32	university	university	PROPN
ma-99	676	33	press	press	PROPN
ma-99	676	34	,	,	PUNCT
ma-99	676	35	cambridge	cambridge	PROPN
ma-99	676	36	,	,	PUNCT
ma-99	676	37	(	(	PUNCT
ma-99	676	38	2000).[42	2000).[42	NUM
ma-99	676	39	]	]	X
ma-99	676	40	l.	l.	PROPN
ma-99	676	41	wang	wang	PROPN
ma-99	676	42	,	,	PUNCT
ma-99	676	43	x.	x.	PROPN
ma-99	676	44	yang	yang	PROPN
ma-99	676	45	,	,	PUNCT
ma-99	676	46	x.	x.	PROPN
ma-99	676	47	zhou	zhou	PROPN
ma-99	676	48	,	,	PUNCT
ma-99	676	49	a	a	DET
ma-99	676	50	distribution	distribution	NOUN
ma-99	676	51	-	-	PUNCT
ma-99	676	52	function	function	NOUN
ma-99	676	53	-	-	PUNCT
ma-99	676	54	valued	value	VERB
ma-99	676	55	spde	spde	NOUN
ma-99	676	56	and	and	CCONJ
ma-99	676	57	its	its	PRON
ma-99	676	58	applications	application	NOUN
ma-99	676	59	,	,	PUNCT
ma-99	676	60	j.	j.	PROPN
ma-99	676	61	differ	differ	VERB
ma-99	676	62	.	.	PUNCT
ma-99	677	1	equ	equ	PROPN
ma-99	677	2	.	.	PROPN
ma-99	678	1	262	262	NUM
ma-99	678	2	(	(	PUNCT
ma-99	678	3	2017)1085–1118	2017)1085–1118	NUM
ma-99	678	4	.	.	PUNCT
ma-99	679	1	https://doi.org/10.1016/j.jde.2016.10.009.[43	https://doi.org/10.1016/j.jde.2016.10.009.[43	ADV
ma-99	679	2	]	]	PUNCT
ma-99	679	3	j.	j.	PROPN
ma-99	679	4	xiong	xiong	PROPN
ma-99	679	5	,	,	PUNCT
ma-99	679	6	super	super	ADJ
ma-99	679	7	-	-	ADJ
ma-99	679	8	brownian	brownian	ADJ
ma-99	679	9	motion	motion	NOUN
ma-99	679	10	as	as	ADP
ma-99	679	11	the	the	DET
ma-99	679	12	unique	unique	ADJ
ma-99	679	13	strong	strong	ADJ
ma-99	679	14	solution	solution	NOUN
ma-99	679	15	to	to	ADP
ma-99	679	16	an	an	DET
ma-99	679	17	spde	spde	NOUN
ma-99	679	18	,	,	PUNCT
ma-99	679	19	ann	ann	PROPN
ma-99	679	20	.	.	PROPN
ma-99	680	1	probab	probab	PROPN
ma-99	680	2	.	.	PUNCT
ma-99	681	1	41	41	NUM
ma-99	681	2	(	(	PUNCT
ma-99	681	3	2013	2013	NUM
ma-99	681	4	)	)	PUNCT
ma-99	681	5	1030	1030	NUM
ma-99	681	6	-	-	SYM
ma-99	681	7	1054	1054	NUM
ma-99	681	8	.	.	PUNCT
ma-99	682	1	https://doi.org/10.1214/12-aop789.[44	https://doi.org/10.1214/12-aop789.[44	PROPN
ma-99	682	2	]	]	PUNCT
ma-99	682	3	j.	j.	PROPN
ma-99	682	4	xiong	xiong	PROPN
ma-99	682	5	,	,	PUNCT
ma-99	682	6	x.	x.	PROPN
ma-99	682	7	yang	yang	PROPN
ma-99	682	8	,	,	PUNCT
ma-99	682	9	existence	existence	NOUN
ma-99	682	10	and	and	CCONJ
ma-99	682	11	pathwise	pathwise	NOUN
ma-99	682	12	uniqueness	uniqueness	NOUN
ma-99	682	13	to	to	ADP
ma-99	682	14	an	an	DET
ma-99	682	15	spde	spde	NOUN
ma-99	682	16	driven	drive	VERB
ma-99	682	17	by	by	ADP
ma-99	682	18	α	α	VERB
ma-99	682	19	-	-	ADJ
ma-99	682	20	stable	stable	ADJ
ma-99	682	21	colored	colored	ADJ
ma-99	682	22	noise	noise	NOUN
ma-99	682	23	,	,	PUNCT
ma-99	682	24	stoch.processes	stoch.processes	PROPN
ma-99	682	25	.	.	PROPN
ma-99	682	26	appl	appl	PROPN
ma-99	682	27	.	.	PUNCT
ma-99	683	1	129	129	NUM
ma-99	683	2	(	(	PUNCT
ma-99	683	3	2019	2019	NUM
ma-99	683	4	)	)	PUNCT
ma-99	683	5	2681–2722	2681–2722	NUM
ma-99	683	6	.	.	PUNCT
ma-99	684	1	https://doi.org/10.1016/j.spa.2018.08.003.[45	https://doi.org/10.1016/j.spa.2018.08.003.[45	PROPN
ma-99	684	2	]	]	PUNCT
ma-99	684	3	x.	x.	PROPN
ma-99	684	4	yang	yang	PROPN
ma-99	684	5	,	,	PUNCT
ma-99	684	6	x.	x.	PROPN
ma-99	684	7	zhou	zhou	PROPN
ma-99	684	8	,	,	PUNCT
ma-99	684	9	pathwise	pathwise	NOUN
ma-99	684	10	uniqueness	uniqueness	NOUN
ma-99	684	11	for	for	ADP
ma-99	684	12	an	an	DET
ma-99	684	13	spde	spde	NOUN
ma-99	684	14	with	with	ADP
ma-99	684	15	hölder	hölder	PROPN
ma-99	684	16	continuous	continuous	ADJ
ma-99	684	17	coefficient	coefficient	NOUN
ma-99	684	18	driven	drive	VERB
ma-99	684	19	by	by	ADP
ma-99	684	20	α	α	NOUN
ma-99	684	21	-	-	ADJ
ma-99	684	22	stable	stable	ADJ
ma-99	684	23	noise	noise	NOUN
ma-99	684	24	,	,	PUNCT
ma-99	684	25	electron	electron	NOUN
ma-99	684	26	.	.	PUNCT
ma-99	685	1	j.	j.	PROPN
ma-99	685	2	probab	probab	PROPN
ma-99	685	3	.	.	PUNCT
ma-99	686	1	22	22	NUM
ma-99	686	2	(	(	PUNCT
ma-99	686	3	2017	2017	NUM
ma-99	686	4	)	)	PUNCT
ma-99	686	5	1	1	NUM
ma-99	686	6	-	-	SYM
ma-99	686	7	48	48	NUM
ma-99	686	8	.	.	PUNCT
ma-99	687	1	https://doi.org/10.1214/16-ejp23	https://doi.org/10.1214/16-ejp23	NOUN
ma-99	687	2	.	.	PUNCT
ma-99	688	1	https://doi.org/10.28924/ada/ma.3.4	https://doi.org/10.28924/ada/ma.3.4	NOUN
ma-99	688	2	https://doi.org/10.1007/bf00320919	https://doi.org/10.1007/bf00320919	NOUN
ma-99	688	3	https://doi.org/10.1016/0167-7152(85)90015-x	https://doi.org/10.1016/0167-7152(85)90015-x	NOUN
ma-99	688	4	https://doi.org/10.1080/17442508608833374	https://doi.org/10.1080/17442508608833374	PUNCT
ma-99	688	5	https://doi.org/10.1016/j.spa.2015.03.002	https://doi.org/10.1016/j.spa.2015.03.002	NOUN
ma-99	688	6	https://doi.org/10.1016/0304-4149(84)90004-8	https://doi.org/10.1016/0304-4149(84)90004-8	PROPN
ma-99	688	7	https://doi.org/10.1016/0304-4149(84)90004-8	https://doi.org/10.1016/0304-4149(84)90004-8	PROPN
ma-99	689	1	https://doi.org/10.1016/s0304-4149(98)00079-9	https://doi.org/10.1016/s0304-4149(98)00079-9	PROPN
ma-99	689	2	https://doi.org/10.1023/b:sisp.0000049120.83388.89	https://doi.org/10.1023/b:sisp.0000049120.83388.89	INTJ
ma-99	689	3	https://doi.org/10.1016/j.spa.2018.04.004	https://doi.org/10.1016/j.spa.2018.04.004	VERB
ma-99	689	4	https://doi.org/10.1007/s11203-016-9133-5	https://doi.org/10.1007/s11203-016-9133-5	NUM
ma-99	690	1	https://doi.org/10.1016/j.spa.2011.10.003	https://doi.org/10.1016/j.spa.2011.10.003	PROPN
ma-99	691	1	https://doi.org/10.1007/s00440-009-0243-5	https://doi.org/10.1007/s00440-009-0243-5	NUM
ma-99	692	1	https://doi.org/10.1016/j.jde.2016.10.009	https://doi.org/10.1016/j.jde.2016.10.009	NOUN
ma-99	692	2	https://doi.org/10.1214/12-aop789	https://doi.org/10.1214/12-aop789	ADV
ma-99	692	3	https://doi.org/10.1016/j.spa.2018.08.003	https://doi.org/10.1016/j.spa.2018.08.003	PROPN
ma-99	692	4	https://doi.org/10.1214/16-ejp23	https://doi.org/10.1214/16-ejp23	NOUN
ma-99	692	5	references	reference	NOUN