id	sid	tid	token	lemma	pos
ma-86	1	1	2022	2022	NUM
ma-86	1	2	ada	ada	PROPN
ma-86	1	3	academica	academica	PROPN
ma-86	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-86	1	5	.	.	PUNCT
ma-86	2	1	j.	j.	PROPN
ma-86	2	2	math	math	PROPN
ma-86	2	3	.	.	PUNCT
ma-86	3	1	anal	anal	ADJ
ma-86	3	2	.	.	PUNCT
ma-86	3	3	2	2	NUM
ma-86	3	4	(	(	PUNCT
ma-86	3	5	2022	2022	NUM
ma-86	3	6	)	)	PUNCT
ma-86	3	7	15doi	15doi	NOUN
ma-86	3	8	:	:	PUNCT
ma-86	3	9	10.28924	10.28924	NUM
ma-86	3	10	/	/	SYM
ma-86	3	11	ada	ada	NOUN
ma-86	3	12	/	/	SYM
ma-86	3	13	ma.2.15	ma.2.15	NOUN
ma-86	3	14	quasi	quasi	ADJ
ma-86	3	15	-	-	ADJ
ma-86	3	16	likelihood	likelihood	ADJ
ma-86	3	17	estimation	estimation	NOUN
ma-86	3	18	in	in	ADP
ma-86	3	19	fractional	fractional	ADJ
ma-86	3	20	levy	levy	NOUN
ma-86	3	21	spdes	spde	NOUN
ma-86	3	22	from	from	ADP
ma-86	3	23	poisson	poisson	NOUN
ma-86	3	24	sampling	sample	VERB
ma-86	3	25	jaya	jaya	PROPN
ma-86	3	26	p.	p.	PROPN
ma-86	3	27	n.	n.	PROPN
ma-86	3	28	bishwal	bishwal	PROPN
ma-86	3	29	department	department	PROPN
ma-86	3	30	of	of	ADP
ma-86	3	31	mathematics	mathematics	PROPN
ma-86	3	32	and	and	CCONJ
ma-86	3	33	statistics	statistic	NOUN
ma-86	3	34	,	,	PUNCT
ma-86	3	35	university	university	PROPN
ma-86	3	36	of	of	ADP
ma-86	3	37	north	north	PROPN
ma-86	3	38	carolina	carolina	PROPN
ma-86	3	39	at	at	ADP
ma-86	3	40	charlotte,376	charlotte,376	PROPN
ma-86	3	41	fretwell	fretwell	NOUN
ma-86	3	42	bldg	bldg	PROPN
ma-86	3	43	,	,	PUNCT
ma-86	3	44	9201	9201	NUM
ma-86	3	45	university	university	NOUN
ma-86	3	46	city	city	NOUN
ma-86	3	47	blvd	blvd	PROPN
ma-86	3	48	.	.	PUNCT
ma-86	4	1	charlotte	charlotte	PROPN
ma-86	4	2	,	,	PUNCT
ma-86	4	3	nc	nc	PROPN
ma-86	4	4	28223	28223	NUM
ma-86	4	5	-	-	PUNCT
ma-86	4	6	0001	0001	NUM
ma-86	4	7	,	,	PUNCT
ma-86	4	8	usacorrespondence	usacorrespondence	NOUN
ma-86	4	9	:	:	PUNCT
ma-86	4	10	j.bishwal@uncc.edu	j.bishwal@uncc.edu	PROPN
ma-86	4	11	abstract	abstract	ADJ
ma-86	4	12	.	.	PUNCT
ma-86	5	1	we	we	PRON
ma-86	5	2	study	study	VERB
ma-86	5	3	the	the	DET
ma-86	5	4	quasi	quasi	ADJ
ma-86	5	5	-	-	ADJ
ma-86	5	6	likelihood	likelihood	ADJ
ma-86	5	7	estimator	estimator	NOUN
ma-86	5	8	of	of	ADP
ma-86	5	9	the	the	DET
ma-86	5	10	drift	drift	NOUN
ma-86	5	11	parameter	parameter	NOUN
ma-86	5	12	in	in	ADP
ma-86	5	13	the	the	DET
ma-86	5	14	stochastic	stochastic	ADJ
ma-86	5	15	partialdifferential	partialdifferential	ADJ
ma-86	5	16	equations	equation	NOUN
ma-86	5	17	driven	drive	VERB
ma-86	5	18	by	by	ADP
ma-86	5	19	a	a	DET
ma-86	5	20	cylindrical	cylindrical	ADJ
ma-86	5	21	fractional	fractional	ADJ
ma-86	5	22	levy	levy	NOUN
ma-86	5	23	process	process	NOUN
ma-86	5	24	when	when	SCONJ
ma-86	5	25	the	the	DET
ma-86	5	26	process	process	NOUN
ma-86	5	27	is	be	AUX
ma-86	5	28	observed	observe	VERB
ma-86	5	29	atthe	atthe	ADJ
ma-86	5	30	arrival	arrival	NOUN
ma-86	5	31	times	time	NOUN
ma-86	5	32	of	of	ADP
ma-86	5	33	a	a	DET
ma-86	5	34	poisson	poisson	NOUN
ma-86	5	35	process	process	NOUN
ma-86	5	36	.	.	PUNCT
ma-86	6	1	we	we	PRON
ma-86	6	2	use	use	VERB
ma-86	6	3	a	a	DET
ma-86	6	4	two	two	NUM
ma-86	6	5	stage	stage	NOUN
ma-86	6	6	estimation	estimation	NOUN
ma-86	6	7	procedure	procedure	NOUN
ma-86	6	8	.	.	PUNCT
ma-86	7	1	we	we	PRON
ma-86	7	2	first	first	ADV
ma-86	7	3	estimatethe	estimatethe	ADJ
ma-86	7	4	intensity	intensity	NOUN
ma-86	7	5	of	of	ADP
ma-86	7	6	the	the	DET
ma-86	7	7	poisson	poisson	NOUN
ma-86	7	8	process	process	NOUN
ma-86	7	9	.	.	PUNCT
ma-86	8	1	then	then	ADV
ma-86	8	2	we	we	PRON
ma-86	8	3	plug	plug	VERB
ma-86	8	4	-	-	PUNCT
ma-86	8	5	in	in	ADP
ma-86	8	6	this	this	DET
ma-86	8	7	estimate	estimate	NOUN
ma-86	8	8	in	in	ADP
ma-86	8	9	the	the	DET
ma-86	8	10	quasi	quasi	NOUN
ma-86	8	11	-	-	NOUN
ma-86	8	12	likelihood	likelihood	NOUN
ma-86	8	13	to	to	PART
ma-86	8	14	estimatethe	estimatethe	VERB
ma-86	8	15	drift	drift	NOUN
ma-86	8	16	parameter	parameter	NOUN
ma-86	8	17	.	.	PUNCT
ma-86	9	1	we	we	PRON
ma-86	9	2	obtain	obtain	VERB
ma-86	9	3	the	the	DET
ma-86	9	4	strong	strong	ADJ
ma-86	9	5	consistency	consistency	NOUN
ma-86	9	6	and	and	CCONJ
ma-86	9	7	the	the	DET
ma-86	9	8	asymptotic	asymptotic	ADJ
ma-86	9	9	normality	normality	NOUN
ma-86	9	10	of	of	ADP
ma-86	9	11	the	the	DET
ma-86	9	12	estimators	estimator	NOUN
ma-86	9	13	.	.	PUNCT
ma-86	10	1	1	1	X
ma-86	10	2	.	.	X
ma-86	10	3	introduction	introduction	NOUN
ma-86	10	4	parameter	parameter	NOUN
ma-86	10	5	estimation	estimation	NOUN
ma-86	10	6	in	in	ADP
ma-86	10	7	infinite	infinite	ADJ
ma-86	10	8	dimensional	dimensional	ADJ
ma-86	10	9	stochastic	stochastic	ADJ
ma-86	10	10	differential	differential	ADJ
ma-86	10	11	equations	equation	NOUN
ma-86	10	12	was	be	AUX
ma-86	10	13	first	first	ADV
ma-86	10	14	studied	study	VERB
ma-86	10	15	byloges	byloge	NOUN
ma-86	10	16	[	[	X
ma-86	10	17	20	20	NUM
ma-86	10	18	]	]	PUNCT
ma-86	10	19	.	.	PUNCT
ma-86	11	1	when	when	SCONJ
ma-86	11	2	the	the	DET
ma-86	11	3	length	length	NOUN
ma-86	11	4	of	of	ADP
ma-86	11	5	the	the	DET
ma-86	11	6	observation	observation	NOUN
ma-86	11	7	time	time	NOUN
ma-86	11	8	becomes	become	VERB
ma-86	11	9	large	large	ADJ
ma-86	11	10	,	,	PUNCT
ma-86	11	11	he	he	PRON
ma-86	11	12	obtained	obtain	VERB
ma-86	11	13	consistency	consistency	NOUN
ma-86	11	14	andasymptotic	andasymptotic	ADJ
ma-86	11	15	normality	normality	NOUN
ma-86	11	16	of	of	ADP
ma-86	11	17	the	the	DET
ma-86	11	18	maximum	maximum	ADJ
ma-86	11	19	likelihood	likelihood	NOUN
ma-86	11	20	estimator	estimator	NOUN
ma-86	11	21	(	(	PUNCT
ma-86	11	22	mle	mle	PROPN
ma-86	11	23	)	)	PUNCT
ma-86	11	24	of	of	ADP
ma-86	11	25	a	a	DET
ma-86	11	26	real	real	ADV
ma-86	11	27	valued	value	VERB
ma-86	11	28	drift	drift	NOUN
ma-86	11	29	parameterin	parameterin	PROPN
ma-86	11	30	a	a	DET
ma-86	11	31	hilbert	hilbert	NOUN
ma-86	11	32	space	space	NOUN
ma-86	11	33	valued	value	VERB
ma-86	11	34	sde	sde	PROPN
ma-86	11	35	.	.	PUNCT
ma-86	12	1	koski	koski	PROPN
ma-86	12	2	and	and	CCONJ
ma-86	12	3	loges	loge	NOUN
ma-86	13	1	[	[	X
ma-86	13	2	18	18	NUM
ma-86	13	3	]	]	PUNCT
ma-86	13	4	extended	extend	VERB
ma-86	13	5	the	the	DET
ma-86	13	6	work	work	NOUN
ma-86	13	7	of	of	ADP
ma-86	13	8	loges	loge	NOUN
ma-86	13	9	[	[	X
ma-86	13	10	20	20	NUM
ma-86	13	11	]	]	PUNCT
ma-86	13	12	to	to	ADP
ma-86	13	13	minimumcontrast	minimumcontrast	ADJ
ma-86	13	14	estimators	estimator	NOUN
ma-86	13	15	.	.	PUNCT
ma-86	14	1	koski	koski	PROPN
ma-86	14	2	and	and	CCONJ
ma-86	14	3	loges	loge	NOUN
ma-86	15	1	[	[	X
ma-86	15	2	17	17	NUM
ma-86	15	3	]	]	PUNCT
ma-86	15	4	applied	apply	VERB
ma-86	15	5	the	the	DET
ma-86	15	6	work	work	NOUN
ma-86	15	7	to	to	ADP
ma-86	15	8	a	a	DET
ma-86	15	9	stochastic	stochastic	ADJ
ma-86	15	10	heat	heat	NOUN
ma-86	15	11	flow	flow	NOUN
ma-86	15	12	problem	problem	NOUN
ma-86	15	13	.	.	PUNCT
ma-86	16	1	seethe	seethe	ADJ
ma-86	16	2	monograph	monograph	PROPN
ma-86	16	3	bishwal	bishwal	NOUN
ma-86	17	1	[	[	X
ma-86	17	2	5	5	NUM
ma-86	17	3	]	]	PUNCT
ma-86	17	4	for	for	ADP
ma-86	17	5	asymptotic	asymptotic	ADJ
ma-86	17	6	results	result	NOUN
ma-86	17	7	on	on	ADP
ma-86	17	8	likelihood	likelihood	NOUN
ma-86	17	9	inference	inference	NOUN
ma-86	17	10	and	and	CCONJ
ma-86	17	11	bayesian	bayesian	NOUN
ma-86	17	12	inferencefor	inferencefor	PROPN
ma-86	17	13	drift	drift	NOUN
ma-86	17	14	estimation	estimation	NOUN
ma-86	17	15	of	of	ADP
ma-86	17	16	finite	finite	NOUN
ma-86	17	17	and	and	CCONJ
ma-86	17	18	infinite	infinite	ADJ
ma-86	17	19	dimensional	dimensional	ADJ
ma-86	17	20	stochastic	stochastic	ADJ
ma-86	17	21	differential	differential	NOUN
ma-86	17	22	equations.huebner	equations.huebner	PROPN
ma-86	17	23	,	,	PUNCT
ma-86	17	24	khasminskii	khasminskii	ADJ
ma-86	17	25	and	and	CCONJ
ma-86	17	26	rozovskii	rozovskii	PROPN
ma-86	17	27	[	[	X
ma-86	17	28	12	12	NUM
ma-86	17	29	]	]	PUNCT
ma-86	17	30	started	start	VERB
ma-86	17	31	statistical	statistical	ADJ
ma-86	17	32	investigation	investigation	NOUN
ma-86	17	33	in	in	ADP
ma-86	17	34	spdes	spde	NOUN
ma-86	17	35	.	.	PUNCT
ma-86	18	1	they	they	PRON
ma-86	18	2	gavetwo	gavetwo	VERB
ma-86	18	3	contrast	contrast	NOUN
ma-86	18	4	examples	example	NOUN
ma-86	18	5	of	of	ADP
ma-86	18	6	parabolic	parabolic	ADJ
ma-86	18	7	spdes	spde	NOUN
ma-86	18	8	in	in	ADP
ma-86	18	9	one	one	NUM
ma-86	18	10	of	of	ADP
ma-86	18	11	which	which	PRON
ma-86	18	12	they	they	PRON
ma-86	18	13	obtained	obtain	VERB
ma-86	18	14	consistency	consistency	NOUN
ma-86	18	15	,	,	PUNCT
ma-86	18	16	asymptoticnormality	asymptoticnormality	NOUN
ma-86	18	17	and	and	CCONJ
ma-86	18	18	asymptotic	asymptotic	ADJ
ma-86	18	19	efficiency	efficiency	NOUN
ma-86	18	20	of	of	ADP
ma-86	18	21	the	the	DET
ma-86	18	22	mle	mle	NOUN
ma-86	18	23	as	as	SCONJ
ma-86	18	24	noise	noise	NOUN
ma-86	18	25	intensity	intensity	NOUN
ma-86	18	26	decreases	decrease	VERB
ma-86	18	27	to	to	ADP
ma-86	18	28	zero	zero	NUM
ma-86	18	29	under	under	ADP
ma-86	18	30	thecondition	thecondition	NOUN
ma-86	18	31	of	of	ADP
ma-86	18	32	absolute	absolute	ADJ
ma-86	18	33	continuity	continuity	NOUN
ma-86	18	34	of	of	ADP
ma-86	18	35	measures	measure	NOUN
ma-86	18	36	generated	generate	VERB
ma-86	18	37	by	by	ADP
ma-86	18	38	the	the	DET
ma-86	18	39	process	process	NOUN
ma-86	18	40	for	for	ADP
ma-86	18	41	different	different	ADJ
ma-86	18	42	parameters	parameter	NOUN
ma-86	18	43	(	(	PUNCT
ma-86	18	44	thesituation	thesituation	NOUN
ma-86	18	45	is	be	AUX
ma-86	18	46	similar	similar	ADJ
ma-86	18	47	to	to	ADP
ma-86	18	48	the	the	DET
ma-86	18	49	classical	classical	ADJ
ma-86	18	50	finite	finite	ADJ
ma-86	18	51	dimensional	dimensional	ADJ
ma-86	18	52	case	case	NOUN
ma-86	18	53	)	)	PUNCT
ma-86	18	54	and	and	CCONJ
ma-86	18	55	in	in	ADP
ma-86	18	56	the	the	DET
ma-86	18	57	other	other	ADJ
ma-86	18	58	they	they	PRON
ma-86	18	59	obtained	obtain	VERB
ma-86	18	60	theseproperties	thesepropertie	NOUN
ma-86	18	61	as	as	SCONJ
ma-86	18	62	the	the	DET
ma-86	18	63	finite	finite	ADJ
ma-86	18	64	dimensional	dimensional	ADJ
ma-86	18	65	projection	projection	NOUN
ma-86	18	66	becomes	become	VERB
ma-86	18	67	large	large	ADJ
ma-86	18	68	under	under	ADP
ma-86	18	69	the	the	DET
ma-86	18	70	condition	condition	NOUN
ma-86	18	71	of	of	ADP
ma-86	18	72	singularity	singularity	NOUN
ma-86	18	73	ofthe	ofthe	NOUN
ma-86	18	74	measures	measure	NOUN
ma-86	18	75	generated	generate	VERB
ma-86	18	76	by	by	ADP
ma-86	18	77	the	the	DET
ma-86	18	78	process	process	NOUN
ma-86	18	79	for	for	ADP
ma-86	18	80	different	different	ADJ
ma-86	18	81	parameters	parameter	NOUN
ma-86	18	82	.	.	PUNCT
ma-86	19	1	the	the	DET
ma-86	19	2	second	second	ADJ
ma-86	19	3	example	example	NOUN
ma-86	19	4	was	be	AUX
ma-86	19	5	extendedby	extendedby	PROPN
ma-86	19	6	huebner	huebner	NOUN
ma-86	19	7	and	and	CCONJ
ma-86	19	8	rozovskii	rozovskii	PROPN
ma-86	19	9	[	[	X
ma-86	19	10	13	13	NUM
ma-86	19	11	]	]	PUNCT
ma-86	19	12	and	and	CCONJ
ma-86	19	13	the	the	DET
ma-86	19	14	first	first	ADJ
ma-86	19	15	example	example	NOUN
ma-86	19	16	was	be	AUX
ma-86	19	17	extended	extend	VERB
ma-86	19	18	by	by	ADP
ma-86	19	19	huebner	huebner	NOUN
ma-86	20	1	[	[	X
ma-86	20	2	11	11	NUM
ma-86	20	3	]	]	PUNCT
ma-86	20	4	to	to	ADP
ma-86	20	5	mle	mle	PROPN
ma-86	20	6	forgeneral	forgeneral	PROPN
ma-86	20	7	parabolic	parabolic	PROPN
ma-86	20	8	spdes	spde	NOUN
ma-86	20	9	where	where	SCONJ
ma-86	20	10	the	the	DET
ma-86	20	11	partial	partial	ADJ
ma-86	20	12	differential	differential	NOUN
ma-86	20	13	operators	operator	NOUN
ma-86	20	14	commute	commute	VERB
ma-86	20	15	and	and	CCONJ
ma-86	20	16	satisfy	satisfy	NOUN
ma-86	20	17	differentorder	differentorder	NOUN
ma-86	20	18	conditions	condition	NOUN
ma-86	20	19	in	in	ADP
ma-86	20	20	the	the	DET
ma-86	20	21	two	two	NUM
ma-86	20	22	cases	case	NOUN
ma-86	20	23	.	.	PUNCT
ma-86	21	1	received	receive	VERB
ma-86	21	2	:	:	PUNCT
ma-86	21	3	19	19	NUM
ma-86	21	4	feb	feb	PROPN
ma-86	21	5	2022	2022	NUM
ma-86	21	6	.	.	PUNCT
ma-86	22	1	key	key	ADJ
ma-86	22	2	words	word	NOUN
ma-86	22	3	and	and	CCONJ
ma-86	22	4	phrases	phrase	NOUN
ma-86	22	5	.	.	PUNCT
ma-86	23	1	cylindrical	cylindrical	ADJ
ma-86	23	2	fractional	fractional	ADJ
ma-86	23	3	levy	levy	NOUN
ma-86	23	4	process	process	NOUN
ma-86	23	5	,	,	PUNCT
ma-86	23	6	stochastic	stochastic	ADJ
ma-86	23	7	partial	partial	ADJ
ma-86	23	8	differential	differential	NOUN
ma-86	23	9	equations	equation	NOUN
ma-86	23	10	,	,	PUNCT
ma-86	23	11	space	space	NOUN
ma-86	23	12	-	-	PUNCT
ma-86	23	13	time	time	NOUN
ma-86	23	14	colornoise	colornoise	NOUN
ma-86	23	15	,	,	PUNCT
ma-86	23	16	convoluted	convoluted	ADJ
ma-86	23	17	levy	levy	NOUN
ma-86	23	18	field	field	NOUN
ma-86	23	19	,	,	PUNCT
ma-86	23	20	infinite	infinite	ADJ
ma-86	23	21	divisibility	divisibility	NOUN
ma-86	23	22	,	,	PUNCT
ma-86	23	23	poisson	poisson	NOUN
ma-86	23	24	sampling	sampling	NOUN
ma-86	23	25	,	,	PUNCT
ma-86	23	26	quasi	quasi	ADJ
ma-86	23	27	maximum	maximum	ADJ
ma-86	23	28	likelihood	likelihood	NOUN
ma-86	23	29	estimator	estimator	NOUN
ma-86	23	30	,	,	PUNCT
ma-86	23	31	consistency	consistency	NOUN
ma-86	23	32	,	,	PUNCT
ma-86	23	33	asymptotic	asymptotic	ADJ
ma-86	23	34	normality	normality	NOUN
ma-86	23	35	.	.	PUNCT
ma-86	24	1	1	1	NUM
ma-86	24	2	https://adac.ee	https://adac.ee	PROPN
ma-86	24	3	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	PROPN
ma-86	24	4	eur	eur	PROPN
ma-86	24	5	.	.	PUNCT
ma-86	25	1	j.	j.	PROPN
ma-86	25	2	math	math	PROPN
ma-86	25	3	.	.	PUNCT
ma-86	26	1	anal	anal	PROPN
ma-86	26	2	.	.	PUNCT
ma-86	27	1	10.28924	10.28924	NUM
ma-86	27	2	/	/	SYM
ma-86	27	3	ada	ada	NOUN
ma-86	27	4	/	/	SYM
ma-86	27	5	ma.2.15	ma.2.15	NOUN
ma-86	27	6	2huebner	2huebner	NUM
ma-86	28	1	[	[	X
ma-86	28	2	10	10	NUM
ma-86	28	3	]	]	PUNCT
ma-86	28	4	extended	extend	VERB
ma-86	28	5	the	the	DET
ma-86	28	6	problem	problem	NOUN
ma-86	28	7	to	to	ADP
ma-86	28	8	the	the	DET
ma-86	28	9	ml	ml	X
ma-86	28	10	estimation	estimation	NOUN
ma-86	28	11	of	of	ADP
ma-86	28	12	multidimensional	multidimensional	ADJ
ma-86	28	13	parameter	parameter	NOUN
ma-86	28	14	.	.	PUNCT
ma-86	29	1	lototskyand	lototskyand	NOUN
ma-86	29	2	rozovskii	rozovskii	PROPN
ma-86	30	1	[	[	X
ma-86	30	2	21	21	NUM
ma-86	30	3	]	]	PUNCT
ma-86	30	4	studied	study	VERB
ma-86	30	5	the	the	DET
ma-86	30	6	same	same	ADJ
ma-86	30	7	problem	problem	NOUN
ma-86	30	8	without	without	ADP
ma-86	30	9	the	the	DET
ma-86	30	10	commutativity	commutativity	NOUN
ma-86	30	11	condition	condition	NOUN
ma-86	30	12	.	.	PUNCT
ma-86	31	1	small	small	ADJ
ma-86	31	2	noiseasymptotics	noiseasymptotic	NOUN
ma-86	31	3	of	of	ADP
ma-86	31	4	the	the	DET
ma-86	31	5	nonparmetric	nonparmetric	ADJ
ma-86	31	6	estimation	estimation	NOUN
ma-86	31	7	of	of	ADP
ma-86	31	8	the	the	DET
ma-86	31	9	drift	drift	NOUN
ma-86	31	10	coefficient	coefficient	NOUN
ma-86	31	11	was	be	AUX
ma-86	31	12	studies	study	NOUN
ma-86	31	13	by	by	ADP
ma-86	31	14	ibragimov	ibragimov	ADJ
ma-86	31	15	andkhasminskii	andkhasminskii	NOUN
ma-86	31	16	[	[	X
ma-86	31	17	14].bishwal	14].bishwal	NUM
ma-86	31	18	[	[	X
ma-86	31	19	3	3	NUM
ma-86	31	20	]	]	PUNCT
ma-86	31	21	proved	prove	VERB
ma-86	31	22	the	the	DET
ma-86	31	23	bernstein	bernstein	PROPN
ma-86	31	24	-	-	PUNCT
ma-86	31	25	von	von	PROPN
ma-86	31	26	mises	mises	PROPN
ma-86	31	27	theorem	theorem	PROPN
ma-86	31	28	(	(	PUNCT
ma-86	31	29	bvt	bvt	PROPN
ma-86	31	30	)	)	PUNCT
ma-86	31	31	and	and	CCONJ
ma-86	31	32	obtained	obtain	VERB
ma-86	31	33	asymptotic	asymptotic	ADJ
ma-86	31	34	properties	property	NOUN
ma-86	31	35	ofregular	ofregular	VERB
ma-86	31	36	bayes	bayes	PROPN
ma-86	31	37	estimator	estimator	NOUN
ma-86	31	38	of	of	ADP
ma-86	31	39	the	the	DET
ma-86	31	40	drift	drift	NOUN
ma-86	31	41	parameter	parameter	NOUN
ma-86	31	42	in	in	ADP
ma-86	31	43	a	a	DET
ma-86	31	44	hilbert	hilbert	NOUN
ma-86	31	45	space	space	NOUN
ma-86	31	46	valued	value	VERB
ma-86	31	47	sde	sde	PROPN
ma-86	31	48	when	when	SCONJ
ma-86	31	49	the	the	DET
ma-86	31	50	correspond	correspond	VERB
ma-86	31	51	-	-	PUNCT
ma-86	31	52	ing	ing	ADJ
ma-86	31	53	ergodic	ergodic	ADJ
ma-86	31	54	diffusion	diffusion	NOUN
ma-86	31	55	process	process	NOUN
ma-86	31	56	is	be	AUX
ma-86	31	57	observed	observe	VERB
ma-86	31	58	continuously	continuously	ADV
ma-86	31	59	over	over	ADP
ma-86	31	60	a	a	DET
ma-86	31	61	time	time	NOUN
ma-86	31	62	interval	interval	NOUN
ma-86	31	63	[	[	X
ma-86	31	64	0	0	NUM
ma-86	31	65	,	,	PUNCT
ma-86	31	66	t	t	X
ma-86	31	67	]	]	PUNCT
ma-86	31	68	.	.	PUNCT
ma-86	32	1	the	the	DET
ma-86	32	2	asymptoticsare	asymptoticsare	NOUN
ma-86	32	3	studied	study	VERB
ma-86	32	4	as	as	ADP
ma-86	32	5	t	t	PROPN
ma-86	32	6	→	→	SYM
ma-86	32	7	∞	∞	PROPN
ma-86	32	8	under	under	ADP
ma-86	32	9	the	the	DET
ma-86	32	10	condition	condition	NOUN
ma-86	32	11	of	of	ADP
ma-86	32	12	absolute	absolute	ADJ
ma-86	32	13	continuity	continuity	NOUN
ma-86	32	14	of	of	ADP
ma-86	32	15	measures	measure	NOUN
ma-86	32	16	generated	generate	VERB
ma-86	32	17	by	by	ADP
ma-86	32	18	theprocess	theprocess	NOUN
ma-86	32	19	.	.	PUNCT
ma-86	33	1	results	result	NOUN
ma-86	33	2	are	be	AUX
ma-86	33	3	illustrated	illustrate	VERB
ma-86	33	4	for	for	ADP
ma-86	33	5	the	the	DET
ma-86	33	6	example	example	NOUN
ma-86	33	7	of	of	ADP
ma-86	33	8	an	an	DET
ma-86	33	9	spde.bishwal	spde.bishwal	NOUN
ma-86	33	10	[	[	X
ma-86	33	11	4	4	NUM
ma-86	33	12	]	]	PUNCT
ma-86	33	13	obtained	obtain	VERB
ma-86	33	14	bvt	bvt	PROPN
ma-86	33	15	and	and	CCONJ
ma-86	33	16	spectral	spectral	ADJ
ma-86	33	17	asymptotics	asymptotic	NOUN
ma-86	33	18	of	of	ADP
ma-86	33	19	bayes	bayes	NOUN
ma-86	33	20	estimators	estimator	NOUN
ma-86	33	21	for	for	ADP
ma-86	33	22	parabolic	parabolic	ADJ
ma-86	33	23	spdeswhen	spdeswhen	NOUN
ma-86	33	24	the	the	DET
ma-86	33	25	number	number	NOUN
ma-86	33	26	of	of	ADP
ma-86	33	27	fourier	fourier	ADJ
ma-86	33	28	coefficients	coefficient	NOUN
ma-86	33	29	becomes	become	VERB
ma-86	33	30	large	large	ADJ
ma-86	33	31	.	.	PUNCT
ma-86	34	1	in	in	ADP
ma-86	34	2	that	that	DET
ma-86	34	3	case	case	NOUN
ma-86	34	4	,	,	PUNCT
ma-86	34	5	the	the	DET
ma-86	34	6	measures	measure	NOUN
ma-86	34	7	generatedby	generatedby	NOUN
ma-86	34	8	the	the	DET
ma-86	34	9	process	process	NOUN
ma-86	34	10	for	for	ADP
ma-86	34	11	different	different	ADJ
ma-86	34	12	parameters	parameter	NOUN
ma-86	34	13	are	be	AUX
ma-86	34	14	singular	singular	ADJ
ma-86	34	15	.	.	PUNCT
ma-86	35	1	here	here	ADV
ma-86	35	2	we	we	PRON
ma-86	35	3	treat	treat	VERB
ma-86	35	4	the	the	DET
ma-86	35	5	case	case	NOUN
ma-86	35	6	when	when	SCONJ
ma-86	35	7	the	the	DET
ma-86	35	8	measuresgenerated	measuresgenerate	VERB
ma-86	35	9	by	by	ADP
ma-86	35	10	the	the	DET
ma-86	35	11	process	process	NOUN
ma-86	35	12	for	for	ADP
ma-86	35	13	different	different	ADJ
ma-86	35	14	parameters	parameter	NOUN
ma-86	35	15	are	be	AUX
ma-86	35	16	absolutely	absolutely	ADV
ma-86	35	17	continuous	continuous	ADJ
ma-86	35	18	under	under	ADP
ma-86	35	19	some	some	DET
ma-86	35	20	conditionson	conditionson	NOUN
ma-86	35	21	the	the	DET
ma-86	35	22	order	order	NOUN
ma-86	35	23	of	of	ADP
ma-86	35	24	the	the	DET
ma-86	35	25	partial	partial	ADJ
ma-86	35	26	differential	differential	NOUN
ma-86	35	27	operators	operator	NOUN
ma-86	35	28	.	.	PUNCT
ma-86	36	1	bishwal	bishwal	NOUN
ma-86	37	1	[	[	X
ma-86	37	2	9	9	NUM
ma-86	37	3	]	]	PUNCT
ma-86	37	4	studied	study	VERB
ma-86	37	5	the	the	DET
ma-86	37	6	asymptotic	asymptotic	ADJ
ma-86	37	7	properties	property	NOUN
ma-86	37	8	ofthe	ofthe	VERB
ma-86	37	9	posterior	posterior	ADJ
ma-86	37	10	distributions	distribution	NOUN
ma-86	37	11	and	and	CCONJ
ma-86	37	12	bayes	bayes	NOUN
ma-86	37	13	estimators	estimator	NOUN
ma-86	37	14	when	when	SCONJ
ma-86	37	15	one	one	PRON
ma-86	37	16	has	have	AUX
ma-86	37	17	either	either	CCONJ
ma-86	37	18	fully	fully	ADV
ma-86	37	19	observed	observe	VERB
ma-86	37	20	process	process	NOUN
ma-86	37	21	orfinite	orfinite	ADJ
ma-86	37	22	-	-	PUNCT
ma-86	37	23	dimensional	dimensional	ADJ
ma-86	37	24	projections	projection	NOUN
ma-86	37	25	.	.	PUNCT
ma-86	38	1	the	the	DET
ma-86	38	2	asymptotic	asymptotic	ADJ
ma-86	38	3	parameter	parameter	NOUN
ma-86	38	4	is	be	AUX
ma-86	38	5	only	only	ADV
ma-86	38	6	the	the	DET
ma-86	38	7	intensity	intensity	NOUN
ma-86	38	8	of	of	ADP
ma-86	38	9	noise	noise	NOUN
ma-86	38	10	.	.	PUNCT
ma-86	39	1	in	in	ADP
ma-86	39	2	thispaper	thispaper	NOUN
ma-86	39	3	we	we	PRON
ma-86	39	4	treat	treat	VERB
ma-86	39	5	the	the	DET
ma-86	39	6	more	more	ADV
ma-86	39	7	general	general	ADJ
ma-86	39	8	model	model	NOUN
ma-86	39	9	with	with	ADP
ma-86	39	10	non	non	ADJ
ma-86	39	11	-	-	ADJ
ma-86	39	12	gaussian	gaussian	ADJ
ma-86	39	13	noise	noise	NOUN
ma-86	39	14	with	with	ADP
ma-86	39	15	long	long	ADJ
ma-86	39	16	memory.on	memory.on	NOUN
ma-86	39	17	the	the	DET
ma-86	39	18	other	other	ADJ
ma-86	39	19	hand	hand	NOUN
ma-86	39	20	,	,	PUNCT
ma-86	39	21	recently	recently	ADV
ma-86	39	22	long	long	ADJ
ma-86	39	23	memory	memory	NOUN
ma-86	39	24	processes	process	NOUN
ma-86	39	25	,	,	PUNCT
ma-86	39	26	i.e.	i.e.	X
ma-86	39	27	processes	process	NOUN
ma-86	39	28	with	with	ADP
ma-86	39	29	slowly	slowly	ADV
ma-86	39	30	decaying	decay	VERB
ma-86	39	31	auto	auto	NOUN
ma-86	39	32	-	-	PUNCT
ma-86	39	33	correlation	correlation	NOUN
ma-86	39	34	and	and	CCONJ
ma-86	39	35	processes	process	NOUN
ma-86	39	36	with	with	ADP
ma-86	39	37	jumps	jump	NOUN
ma-86	39	38	have	have	AUX
ma-86	39	39	received	receive	VERB
ma-86	39	40	attention	attention	NOUN
ma-86	39	41	in	in	ADP
ma-86	39	42	finance	finance	NOUN
ma-86	39	43	,	,	PUNCT
ma-86	39	44	engineering	engineering	NOUN
ma-86	39	45	and	and	CCONJ
ma-86	39	46	physics.the	physics.the	DET
ma-86	39	47	simplest	simple	ADJ
ma-86	39	48	continuous	continuous	ADJ
ma-86	39	49	time	time	NOUN
ma-86	39	50	long	long	ADJ
ma-86	39	51	memory	memory	NOUN
ma-86	39	52	process	process	NOUN
ma-86	39	53	is	be	AUX
ma-86	39	54	the	the	DET
ma-86	39	55	fractional	fractional	ADJ
ma-86	39	56	brownian	brownian	ADJ
ma-86	39	57	motion	motion	NOUN
ma-86	39	58	discovered	discover	VERB
ma-86	39	59	bykolmogorov	bykolmogorov	ADJ
ma-86	39	60	[	[	X
ma-86	39	61	15	15	NUM
ma-86	39	62	]	]	PUNCT
ma-86	39	63	and	and	CCONJ
ma-86	39	64	later	later	ADV
ma-86	39	65	on	on	SCONJ
ma-86	39	66	studied	study	VERB
ma-86	39	67	by	by	ADP
ma-86	39	68	levy	levy	NOUN
ma-86	39	69	[	[	X
ma-86	39	70	19	19	NUM
ma-86	39	71	]	]	PUNCT
ma-86	39	72	and	and	CCONJ
ma-86	39	73	mandelbrot	mandelbrot	PROPN
ma-86	39	74	and	and	CCONJ
ma-86	39	75	van	van	PROPN
ma-86	39	76	ness	ness	NOUN
ma-86	39	77	[	[	X
ma-86	39	78	27	27	NUM
ma-86	39	79	]	]	PUNCT
ma-86	39	80	.	.	PUNCT
ma-86	40	1	continuoustime	continuoustime	PROPN
ma-86	40	2	long	long	ADJ
ma-86	40	3	memory	memory	NOUN
ma-86	40	4	jump	jump	NOUN
ma-86	40	5	process	process	NOUN
ma-86	40	6	is	be	AUX
ma-86	40	7	fractional	fractional	ADJ
ma-86	40	8	levy	levy	NOUN
ma-86	40	9	process	process	NOUN
ma-86	40	10	.	.	PUNCT
ma-86	41	1	hence	hence	ADV
ma-86	41	2	fractional	fractional	ADJ
ma-86	41	3	levy	levy	NOUN
ma-86	41	4	process	process	NOUN
ma-86	41	5	can	can	AUX
ma-86	41	6	alsobe	alsobe	VERB
ma-86	41	7	called	call	VERB
ma-86	41	8	the	the	DET
ma-86	41	9	kolmogorov	kolmogorov	ADJ
ma-86	41	10	-	-	PUNCT
ma-86	41	11	levy	levy	NOUN
ma-86	41	12	process.we	process.we	PRON
ma-86	41	13	generalize	generalize	VERB
ma-86	41	14	fractional	fractional	ADJ
ma-86	41	15	spde	spde	NOUN
ma-86	41	16	process	process	NOUN
ma-86	41	17	to	to	PART
ma-86	41	18	include	include	VERB
ma-86	41	19	non	non	ADJ
ma-86	41	20	-	-	ADJ
ma-86	41	21	normal	normal	ADJ
ma-86	41	22	innovations	innovation	NOUN
ma-86	41	23	.	.	PUNCT
ma-86	42	1	we	we	PRON
ma-86	42	2	consider	consider	VERB
ma-86	42	3	hurstparameter	hurstparameter	VERB
ma-86	42	4	greater	great	ADJ
ma-86	42	5	than	than	ADP
ma-86	42	6	half	half	NOUN
ma-86	42	7	.	.	PUNCT
ma-86	43	1	this	this	DET
ma-86	43	2	model	model	NOUN
ma-86	43	3	is	be	AUX
ma-86	43	4	interesting	interesting	ADJ
ma-86	43	5	as	as	SCONJ
ma-86	43	6	it	it	PRON
ma-86	43	7	preserves	preserve	VERB
ma-86	43	8	both	both	DET
ma-86	43	9	jumps	jump	VERB
ma-86	43	10	and	and	CCONJ
ma-86	43	11	long	long	ADV
ma-86	43	12	memory.a	memory.a	ADV
ma-86	43	13	normalized	normalize	VERB
ma-86	43	14	fractional	fractional	ADJ
ma-86	43	15	brownian	brownian	ADJ
ma-86	43	16	motion	motion	NOUN
ma-86	43	17	{	{	PUNCT
ma-86	43	18	wh	wh	NOUN
ma-86	43	19	t	t	PROPN
ma-86	43	20	,	,	PUNCT
ma-86	43	21	t	t	PROPN
ma-86	43	22	≥	≥	NUM
ma-86	43	23	0	0	NUM
ma-86	43	24	}	}	PUNCT
ma-86	43	25	with	with	ADP
ma-86	43	26	hurst	hurst	PROPN
ma-86	43	27	parameter	parameter	PROPN
ma-86	43	28	h	h	PROPN
ma-86	43	29	∈	∈	PROPN
ma-86	43	30	(	(	PUNCT
ma-86	43	31	0	0	NUM
ma-86	43	32	,	,	PUNCT
ma-86	43	33	1	1	NUM
ma-86	43	34	)	)	PUNCT
ma-86	43	35	is	be	AUX
ma-86	43	36	acentered	acentere	VERB
ma-86	43	37	gaussian	gaussian	ADJ
ma-86	43	38	process	process	NOUN
ma-86	43	39	with	with	ADP
ma-86	43	40	continuous	continuous	ADJ
ma-86	43	41	sample	sample	NOUN
ma-86	43	42	paths	path	NOUN
ma-86	43	43	whose	whose	DET
ma-86	43	44	covariance	covariance	NOUN
ma-86	43	45	kernel	kernel	NOUN
ma-86	43	46	is	be	AUX
ma-86	43	47	given	give	VERB
ma-86	43	48	by	by	ADP
ma-86	43	49	e(wh	e(wh	PROPN
ma-86	43	50	t	t	PROPN
ma-86	43	51	w	w	PROPN
ma-86	43	52	h	h	PROPN
ma-86	43	53	s	s	PART
ma-86	43	54	)	)	PUNCT
ma-86	43	55	=	=	SYM
ma-86	43	56	1	1	NUM
ma-86	43	57	2	2	NUM
ma-86	43	58	(	(	PUNCT
ma-86	43	59	s2h	s2h	NOUN
ma-86	43	60	+	+	PROPN
ma-86	43	61	t2h	t2h	PROPN
ma-86	43	62	−	−	PROPN
ma-86	43	63	|t	|t	NOUN
ma-86	43	64	−	−	PROPN
ma-86	43	65	s|2h	s|2h	ADJ
ma-86	43	66	)	)	PUNCT
ma-86	43	67	,	,	PUNCT
ma-86	43	68	s	s	PROPN
ma-86	43	69	,	,	PUNCT
ma-86	43	70	t	t	PROPN
ma-86	43	71	≥	≥	NUM
ma-86	43	72	0	0	NUM
ma-86	43	73	.	.	PUNCT
ma-86	44	1	the	the	DET
ma-86	44	2	process	process	NOUN
ma-86	44	3	is	be	AUX
ma-86	44	4	self	self	NOUN
ma-86	44	5	similar	similar	ADJ
ma-86	44	6	(	(	PUNCT
ma-86	44	7	scale	scale	NOUN
ma-86	44	8	invariant	invariant	ADJ
ma-86	44	9	)	)	PUNCT
ma-86	44	10	and	and	CCONJ
ma-86	44	11	it	it	PRON
ma-86	44	12	can	can	AUX
ma-86	44	13	be	be	AUX
ma-86	44	14	represented	represent	VERB
ma-86	44	15	as	as	ADP
ma-86	44	16	a	a	DET
ma-86	44	17	stochastic	stochastic	NOUN
ma-86	44	18	integralwith	integralwith	ADJ
ma-86	44	19	respect	respect	NOUN
ma-86	44	20	to	to	ADP
ma-86	44	21	standard	standard	ADJ
ma-86	44	22	brownian	brownian	ADJ
ma-86	44	23	motion	motion	NOUN
ma-86	44	24	.	.	PUNCT
ma-86	45	1	for	for	ADP
ma-86	45	2	h	h	NOUN
ma-86	45	3	=	=	SYM
ma-86	45	4	1	1	NUM
ma-86	45	5	2	2	NUM
ma-86	45	6	,	,	PUNCT
ma-86	45	7	the	the	DET
ma-86	45	8	process	process	NOUN
ma-86	45	9	is	be	AUX
ma-86	45	10	a	a	DET
ma-86	45	11	standard	standard	ADJ
ma-86	45	12	brownian	brownian	NOUN
ma-86	45	13	motion.for	motion.for	ADP
ma-86	45	14	h	h	NOUN
ma-86	45	15	6=	6=	SYM
ma-86	45	16	1	1	NUM
ma-86	45	17	2	2	NUM
ma-86	45	18	,	,	PUNCT
ma-86	45	19	the	the	DET
ma-86	45	20	fbm	fbm	NOUN
ma-86	45	21	is	be	AUX
ma-86	45	22	not	not	PART
ma-86	45	23	a	a	DET
ma-86	45	24	semimartingale	semimartingale	NOUN
ma-86	45	25	and	and	CCONJ
ma-86	45	26	not	not	PART
ma-86	45	27	a	a	DET
ma-86	45	28	markov	markov	NOUN
ma-86	45	29	process	process	NOUN
ma-86	45	30	,	,	PUNCT
ma-86	45	31	but	but	CCONJ
ma-86	45	32	a	a	DET
ma-86	45	33	dirichlet	dirichlet	NOUN
ma-86	45	34	process.the	process.the	DET
ma-86	45	35	increments	increment	NOUN
ma-86	45	36	of	of	ADP
ma-86	45	37	the	the	DET
ma-86	45	38	fbm	fbm	NOUN
ma-86	45	39	are	be	AUX
ma-86	45	40	negatively	negatively	ADV
ma-86	45	41	correlated	correlate	VERB
ma-86	45	42	for	for	ADP
ma-86	45	43	h	h	NOUN
ma-86	45	44	<	<	X
ma-86	45	45	1	1	NUM
ma-86	45	46	2	2	NUM
ma-86	45	47	and	and	CCONJ
ma-86	45	48	positively	positively	ADV
ma-86	45	49	correlated	correlate	VERB
ma-86	45	50	for	for	ADP
ma-86	45	51	for	for	ADP
ma-86	45	52	h	h	NOUN
ma-86	45	53	<	<	X
ma-86	45	54	1	1	NUM
ma-86	45	55	2	2	NUM
ma-86	45	56	and	and	CCONJ
ma-86	45	57	in	in	ADP
ma-86	45	58	this	this	DET
ma-86	45	59	case	case	NOUN
ma-86	45	60	they	they	PRON
ma-86	45	61	display	display	VERB
ma-86	45	62	long	long	ADJ
ma-86	45	63	-	-	PUNCT
ma-86	45	64	range	range	NOUN
ma-86	45	65	dependence	dependence	NOUN
ma-86	45	66	.	.	PUNCT
ma-86	46	1	the	the	DET
ma-86	46	2	parameter	parameter	PROPN
ma-86	46	3	h	h	NOUN
ma-86	46	4	which	which	PRON
ma-86	46	5	is	be	AUX
ma-86	46	6	alsocalled	alsocalle	VERB
ma-86	46	7	the	the	DET
ma-86	46	8	self	self	NOUN
ma-86	46	9	similarity	similarity	NOUN
ma-86	46	10	parameter	parameter	NOUN
ma-86	46	11	,	,	PUNCT
ma-86	46	12	measures	measure	VERB
ma-86	46	13	the	the	DET
ma-86	46	14	intensity	intensity	NOUN
ma-86	46	15	of	of	ADP
ma-86	46	16	the	the	DET
ma-86	46	17	long	long	ADJ
ma-86	46	18	range	range	NOUN
ma-86	46	19	dependence	dependence	NOUN
ma-86	46	20	.	.	PUNCT
ma-86	47	1	thearima(p	thearima(p	NOUN
ma-86	47	2	,	,	PUNCT
ma-86	47	3	d	d	NOUN
ma-86	47	4	,	,	PUNCT
ma-86	47	5	q	q	NOUN
ma-86	47	6	)	)	PUNCT
ma-86	47	7	with	with	ADP
ma-86	47	8	autoregressive	autoregressive	ADJ
ma-86	47	9	part	part	NOUN
ma-86	47	10	of	of	ADP
ma-86	47	11	order	order	NOUN
ma-86	47	12	p	p	X
ma-86	47	13	,	,	PUNCT
ma-86	47	14	moving	move	VERB
ma-86	47	15	average	average	ADJ
ma-86	47	16	part	part	NOUN
ma-86	47	17	of	of	ADP
ma-86	47	18	order	order	NOUN
ma-86	47	19	q	q	NOUN
ma-86	47	20	and	and	CCONJ
ma-86	47	21	fractionaldifference	fractionaldifference	NOUN
ma-86	47	22	parameter	parameter	NOUN
ma-86	47	23	d	d	PROPN
ma-86	47	24	∈	∈	PROPN
ma-86	47	25	(	(	PUNCT
ma-86	47	26	0	0	NUM
ma-86	47	27	,	,	PUNCT
ma-86	47	28	0.5	0.5	NUM
ma-86	47	29	)	)	PUNCT
ma-86	47	30	process	process	NOUN
ma-86	47	31	converge	converge	NOUN
ma-86	47	32	in	in	ADP
ma-86	47	33	donsker	donsker	ADJ
ma-86	47	34	sense	sense	NOUN
ma-86	47	35	to	to	ADP
ma-86	47	36	fbm	fbm	PROPN
ma-86	47	37	.	.	PUNCT
ma-86	48	1	see	see	VERB
ma-86	48	2	mishura	mishura	PROPN
ma-86	49	1	[	[	X
ma-86	49	2	22].the	22].the	DET
ma-86	49	3	fractional	fractional	ADJ
ma-86	49	4	levy	levy	NOUN
ma-86	49	5	ornstein	ornstein	PROPN
ma-86	49	6	-	-	PUNCT
ma-86	49	7	uhlenbeck	uhlenbeck	PROPN
ma-86	49	8	(	(	PUNCT
ma-86	49	9	fou	fou	PROPN
ma-86	49	10	)	)	PUNCT
ma-86	49	11	process	process	NOUN
ma-86	49	12	,	,	PUNCT
ma-86	49	13	is	be	AUX
ma-86	49	14	an	an	DET
ma-86	49	15	extension	extension	NOUN
ma-86	49	16	of	of	ADP
ma-86	49	17	fractional	fractional	ADJ
ma-86	49	18	ornstein	ornstein	PROPN
ma-86	49	19	-	-	PUNCT
ma-86	49	20	uhlenbeck	uhlenbeck	PROPN
ma-86	49	21	process	process	NOUN
ma-86	49	22	with	with	ADP
ma-86	49	23	fractional	fractional	ADJ
ma-86	49	24	levy	levy	NOUN
ma-86	49	25	motion	motion	NOUN
ma-86	49	26	(	(	PUNCT
ma-86	49	27	flm	flm	NOUN
ma-86	49	28	)	)	PUNCT
ma-86	49	29	driving	drive	VERB
ma-86	49	30	term	term	NOUN
ma-86	49	31	.	.	PUNCT
ma-86	50	1	in	in	ADP
ma-86	50	2	finance	finance	NOUN
ma-86	50	3	,	,	PUNCT
ma-86	50	4	it	it	PRON
ma-86	50	5	could	could	AUX
ma-86	50	6	be	be	AUX
ma-86	50	7	useful	useful	ADJ
ma-86	50	8	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	X
ma-86	50	9	eur	eur	PROPN
ma-86	50	10	.	.	PUNCT
ma-86	51	1	j.	j.	PROPN
ma-86	51	2	math	math	PROPN
ma-86	51	3	.	.	PUNCT
ma-86	52	1	anal	anal	PROPN
ma-86	52	2	.	.	PUNCT
ma-86	53	1	10.28924	10.28924	NUM
ma-86	53	2	/	/	SYM
ma-86	53	3	ada	ada	NOUN
ma-86	53	4	/	/	SYM
ma-86	53	5	ma.2.15	ma.2.15	NOUN
ma-86	53	6	3as	3as	NOUN
ma-86	53	7	a	a	DET
ma-86	53	8	generalization	generalization	NOUN
ma-86	53	9	of	of	ADP
ma-86	53	10	fractional	fractional	ADJ
ma-86	53	11	vasicek	vasicek	PROPN
ma-86	53	12	model	model	NOUN
ma-86	53	13	,	,	PUNCT
ma-86	53	14	as	as	SCONJ
ma-86	53	15	one	one	NUM
ma-86	53	16	-	-	PUNCT
ma-86	53	17	factor	factor	NOUN
ma-86	53	18	short	short	ADJ
ma-86	53	19	-	-	PUNCT
ma-86	53	20	term	term	NOUN
ma-86	53	21	interest	interest	NOUN
ma-86	53	22	rate	rate	NOUN
ma-86	53	23	model	model	NOUN
ma-86	53	24	whichcould	whichcould	AUX
ma-86	53	25	take	take	VERB
ma-86	53	26	into	into	ADP
ma-86	53	27	account	account	NOUN
ma-86	53	28	the	the	DET
ma-86	53	29	long	long	ADJ
ma-86	53	30	memory	memory	NOUN
ma-86	53	31	effect	effect	NOUN
ma-86	53	32	and	and	CCONJ
ma-86	53	33	jump	jump	NOUN
ma-86	53	34	of	of	ADP
ma-86	53	35	the	the	DET
ma-86	53	36	interest	interest	NOUN
ma-86	53	37	rate	rate	NOUN
ma-86	53	38	.	.	PUNCT
ma-86	54	1	the	the	DET
ma-86	54	2	model	model	NOUN
ma-86	54	3	parameteris	parameteris	PROPN
ma-86	54	4	usually	usually	ADV
ma-86	54	5	unknown	unknown	ADJ
ma-86	54	6	and	and	CCONJ
ma-86	54	7	must	must	AUX
ma-86	54	8	be	be	AUX
ma-86	54	9	estimated	estimate	VERB
ma-86	54	10	from	from	ADP
ma-86	54	11	data.fractional	data.fractional	ADJ
ma-86	54	12	levy	levy	NOUN
ma-86	54	13	process	process	NOUN
ma-86	54	14	(	(	PUNCT
ma-86	54	15	flp	flp	NOUN
ma-86	54	16	)	)	PUNCT
ma-86	54	17	is	be	AUX
ma-86	54	18	defined	define	VERB
ma-86	54	19	as	as	ADP
ma-86	54	20	mh	mh	PROPN
ma-86	54	21	,	,	PUNCT
ma-86	54	22	t	t	PROPN
ma-86	54	23	=	=	SYM
ma-86	54	24	1	1	NUM
ma-86	54	25	γ(h	γ(h	NOUN
ma-86	55	1	+	+	CCONJ
ma-86	55	2	1	1	NUM
ma-86	55	3	2	2	NUM
ma-86	55	4	)	)	PUNCT
ma-86	55	5	∫	∫	NOUN
ma-86	56	1	r	r	NOUN
ma-86	56	2	[	[	X
ma-86	56	3	(	(	PUNCT
ma-86	56	4	t	t	PROPN
ma-86	56	5	−	−	PROPN
ma-86	56	6	s	s	PART
ma-86	56	7	)	)	PUNCT
ma-86	56	8	h−1/2	h−1/2	PROPN
ma-86	56	9	+	+	CCONJ
ma-86	56	10	−	−	PROPN
ma-86	56	11	(	(	PUNCT
ma-86	56	12	−s	−s	NOUN
ma-86	56	13	)	)	PUNCT
ma-86	56	14	h−1/2	h−1/2	NOUN
ma-86	57	1	+	+	NUM
ma-86	57	2	]	]	X
ma-86	57	3	dms	dms	NOUN
ma-86	57	4	,	,	PUNCT
ma-86	57	5	t	t	PROPN
ma-86	57	6	∈	∈	PROPN
ma-86	57	7	r	r	NOUN
ma-86	57	8	where	where	SCONJ
ma-86	57	9	{	{	PUNCT
ma-86	57	10	mt	mt	PROPN
ma-86	57	11	,	,	PUNCT
ma-86	57	12	t	t	PROPN
ma-86	57	13	∈	∈	PROPN
ma-86	57	14	r	r	X
ma-86	57	15	}	}	PUNCT
ma-86	57	16	is	be	AUX
ma-86	57	17	a	a	DET
ma-86	57	18	levy	levy	NOUN
ma-86	57	19	process	process	NOUN
ma-86	57	20	on	on	ADP
ma-86	57	21	r	r	NOUN
ma-86	57	22	with	with	ADP
ma-86	57	23	e(m1	e(m1	NOUN
ma-86	57	24	)	)	PUNCT
ma-86	57	25	=	=	SYM
ma-86	57	26	0	0	NUM
ma-86	57	27	,	,	PUNCT
ma-86	57	28	e(m2	e(m2	X
ma-86	57	29	1	1	NUM
ma-86	57	30	)	)	PUNCT
ma-86	57	31	<	<	X
ma-86	57	32	∞	∞	PROPN
ma-86	57	33	and	and	CCONJ
ma-86	57	34	without	without	ADP
ma-86	57	35	browniancomponent.here	browniancomponent.here	ADV
ma-86	57	36	are	be	AUX
ma-86	57	37	some	some	DET
ma-86	57	38	properties	property	NOUN
ma-86	57	39	of	of	ADP
ma-86	57	40	the	the	DET
ma-86	57	41	fractional	fractional	ADJ
ma-86	57	42	levy	levy	NOUN
ma-86	57	43	process:1	process:1	VERB
ma-86	57	44	)	)	PUNCT
ma-86	57	45	the	the	DET
ma-86	57	46	covariance	covariance	NOUN
ma-86	57	47	of	of	ADP
ma-86	57	48	the	the	DET
ma-86	57	49	process	process	NOUN
ma-86	57	50	is	be	AUX
ma-86	57	51	given	give	VERB
ma-86	57	52	by	by	ADP
ma-86	57	53	cov(mh	cov(mh	NOUN
ma-86	57	54	,	,	PUNCT
ma-86	57	55	t	t	PROPN
ma-86	57	56	,	,	PUNCT
ma-86	57	57	mh	mh	PROPN
ma-86	57	58	,	,	PUNCT
ma-86	57	59	s	s	PART
ma-86	57	60	)	)	PUNCT
ma-86	57	61	=	=	SYM
ma-86	57	62	e(m2	e(m2	NOUN
ma-86	57	63	1	1	NUM
ma-86	57	64	)	)	PUNCT
ma-86	57	65	2γ(2h	2γ(2h	NUM
ma-86	57	66	+	+	CCONJ
ma-86	57	67	1	1	NUM
ma-86	57	68	)	)	PUNCT
ma-86	57	69	sin(πh	sin(πh	NOUN
ma-86	57	70	)	)	PUNCT
ma-86	58	1	[	[	X
ma-86	58	2	|t|2h	|t|2h	ADJ
ma-86	58	3	+	+	CCONJ
ma-86	58	4	|s|2h	|s|2h	ADJ
ma-86	58	5	−	−	PROPN
ma-86	58	6	|t	|t	NOUN
ma-86	58	7	−	−	PROPN
ma-86	58	8	s|2h	s|2h	ADJ
ma-86	58	9	]	]	PUNCT
ma-86	58	10	.	.	PUNCT
ma-86	59	1	2	2	X
ma-86	59	2	)	)	PUNCT
ma-86	59	3	mh	mh	PROPN
ma-86	59	4	is	be	AUX
ma-86	59	5	not	not	PART
ma-86	59	6	a	a	DET
ma-86	59	7	martingale	martingale	NOUN
ma-86	59	8	.	.	PUNCT
ma-86	60	1	for	for	ADP
ma-86	60	2	a	a	DET
ma-86	60	3	large	large	ADJ
ma-86	60	4	class	class	NOUN
ma-86	60	5	of	of	ADP
ma-86	60	6	levy	levy	NOUN
ma-86	60	7	processes	process	NOUN
ma-86	60	8	,	,	PUNCT
ma-86	60	9	mh	mh	PROPN
ma-86	60	10	is	be	AUX
ma-86	60	11	neither	neither	CCONJ
ma-86	60	12	a	a	DET
ma-86	60	13	semimartingale.3)mh	semimartingale.3)mh	PRON
ma-86	60	14	is	be	AUX
ma-86	60	15	hölder	hölder	NOUN
ma-86	60	16	continuous	continuous	ADJ
ma-86	60	17	of	of	ADP
ma-86	60	18	any	any	DET
ma-86	60	19	order	order	NOUN
ma-86	60	20	β	β	X
ma-86	60	21	less	less	ADJ
ma-86	60	22	than	than	ADP
ma-86	60	23	h	h	NOUN
ma-86	60	24	−	−	NOUN
ma-86	60	25	1	1	NUM
ma-86	60	26	2	2	NUM
ma-86	60	27	.4	.4	NUM
ma-86	60	28	)	)	PUNCT
ma-86	61	1	mh	mh	PROPN
ma-86	61	2	has	have	VERB
ma-86	61	3	stationary	stationary	ADJ
ma-86	61	4	increments.5	increments.5	PROPN
ma-86	61	5	)	)	PUNCT
ma-86	61	6	mh	mh	PROPN
ma-86	61	7	is	be	AUX
ma-86	61	8	symmetric.6	symmetric.6	PROPN
ma-86	61	9	)	)	PUNCT
ma-86	62	1	m	m	VERB
ma-86	62	2	is	be	AUX
ma-86	62	3	self	self	NOUN
ma-86	62	4	-	-	PUNCT
ma-86	62	5	similar	similar	ADJ
ma-86	62	6	,	,	PUNCT
ma-86	62	7	but	but	CCONJ
ma-86	62	8	mh	mh	PROPN
ma-86	62	9	is	be	AUX
ma-86	62	10	not	not	PART
ma-86	62	11	self	self	NOUN
ma-86	62	12	-	-	PUNCT
ma-86	62	13	similar.7	similar.7	NOUN
ma-86	62	14	)	)	PUNCT
ma-86	62	15	mh	mh	PROPN
ma-86	62	16	has	have	AUX
ma-86	62	17	infinite	infinite	VERB
ma-86	62	18	total	total	ADJ
ma-86	62	19	variation	variation	NOUN
ma-86	62	20	on	on	ADP
ma-86	62	21	compacts.thus	compacts.thus	X
ma-86	62	22	flp	flp	NOUN
ma-86	62	23	is	be	AUX
ma-86	62	24	a	a	DET
ma-86	62	25	generalization	generalization	NOUN
ma-86	62	26	and	and	CCONJ
ma-86	62	27	a	a	DET
ma-86	62	28	natural	natural	ADJ
ma-86	62	29	counterpart	counterpart	NOUN
ma-86	62	30	of	of	ADP
ma-86	62	31	fbm	fbm	PROPN
ma-86	62	32	.	.	PUNCT
ma-86	63	1	fractional	fractional	ADJ
ma-86	63	2	stable	stable	ADJ
ma-86	63	3	motion	motion	NOUN
ma-86	63	4	is	be	AUX
ma-86	63	5	aspecial	aspecial	ADJ
ma-86	63	6	case	case	NOUN
ma-86	63	7	of	of	ADP
ma-86	63	8	flp	flp	PROPN
ma-86	63	9	.	.	PUNCT
ma-86	64	1	first	first	ADV
ma-86	64	2	we	we	PRON
ma-86	64	3	discuss	discuss	VERB
ma-86	64	4	estimation	estimation	NOUN
ma-86	64	5	in	in	ADP
ma-86	64	6	partially	partially	ADV
ma-86	64	7	observed	observe	VERB
ma-86	64	8	models	model	NOUN
ma-86	64	9	and	and	CCONJ
ma-86	64	10	then	then	ADV
ma-86	64	11	we	we	PRON
ma-86	64	12	discussestimation	discussestimation	VERB
ma-86	64	13	in	in	ADP
ma-86	64	14	directly	directly	ADV
ma-86	64	15	observed	observe	VERB
ma-86	64	16	model	model	NOUN
ma-86	64	17	in	in	ADP
ma-86	64	18	finite	finite	ADJ
ma-86	64	19	dimensional	dimensional	ADJ
ma-86	64	20	set	set	NOUN
ma-86	64	21	up	up	ADP
ma-86	64	22	.	.	PUNCT
ma-86	65	1	in	in	ADP
ma-86	65	2	finance	finance	NOUN
ma-86	65	3	,	,	PUNCT
ma-86	65	4	the	the	DET
ma-86	65	5	log	log	NOUN
ma-86	65	6	-	-	PUNCT
ma-86	65	7	volatilityprocess	volatilityprocess	NOUN
ma-86	65	8	can	can	AUX
ma-86	65	9	be	be	AUX
ma-86	65	10	modeled	model	VERB
ma-86	65	11	as	as	ADP
ma-86	65	12	a	a	DET
ma-86	65	13	fractionally	fractionally	ADV
ma-86	65	14	integrated	integrate	VERB
ma-86	65	15	moving	move	VERB
ma-86	65	16	average	average	ADJ
ma-86	65	17	(	(	PUNCT
ma-86	65	18	fima	fima	NOUN
ma-86	65	19	)	)	PUNCT
ma-86	65	20	process	process	NOUN
ma-86	65	21	which	which	PRON
ma-86	65	22	isdefined	isdefine	VERB
ma-86	65	23	as	as	ADP
ma-86	65	24	yh(t	yh(t	NOUN
ma-86	65	25	)	)	PUNCT
ma-86	65	26	=	=	SYM
ma-86	65	27	∫	∫	PROPN
ma-86	65	28	t	t	PROPN
ma-86	66	1	−∞	−∞	ADP
ma-86	66	2	gh(t	gh(t	NOUN
ma-86	66	3	−	−	PROPN
ma-86	66	4	u)dmu	u)dmu	PROPN
ma-86	66	5	,	,	PUNCT
ma-86	66	6	t	t	PROPN
ma-86	66	7	∈	∈	PROPN
ma-86	66	8	r	r	NOUN
ma-86	66	9	where	where	SCONJ
ma-86	66	10	gh(t	gh(t	PUNCT
ma-86	66	11	)	)	PUNCT
ma-86	66	12	=	=	SYM
ma-86	66	13	1	1	NUM
ma-86	66	14	γ(h	γ(h	NOUN
ma-86	66	15	−	−	NOUN
ma-86	66	16	1	1	NUM
ma-86	66	17	2	2	NUM
ma-86	66	18	)	)	PUNCT
ma-86	66	19	∫	∫	PROPN
ma-86	66	20	t	t	PROPN
ma-86	66	21	0	0	NUM
ma-86	66	22	g(t	g(t	PROPN
ma-86	66	23	−	−	PROPN
ma-86	67	1	s)sh−	s)sh−	PROPN
ma-86	67	2	3	3	NUM
ma-86	67	3	2	2	NUM
ma-86	67	4	ds	ds	NOUN
ma-86	67	5	,	,	PUNCT
ma-86	67	6	t	t	PROPN
ma-86	67	7	∈	∈	PROPN
ma-86	67	8	r	r	NOUN
ma-86	67	9	which	which	PRON
ma-86	67	10	is	be	AUX
ma-86	67	11	the	the	DET
ma-86	67	12	riemann	riemann	PROPN
ma-86	67	13	-	-	PUNCT
ma-86	67	14	liouville	liouville	VERB
ma-86	67	15	fractional	fractional	ADJ
ma-86	67	16	integral	integral	ADJ
ma-86	67	17	of	of	ADP
ma-86	67	18	order	order	NOUN
ma-86	67	19	h	h	NOUN
ma-86	67	20	and	and	CCONJ
ma-86	67	21	the	the	DET
ma-86	67	22	kernel	kernel	PROPN
ma-86	67	23	g	g	PROPN
ma-86	67	24	is	be	AUX
ma-86	67	25	the	the	DET
ma-86	67	26	kernel	kernel	NOUN
ma-86	67	27	of	of	ADP
ma-86	67	28	ashort	ashort	NOUN
ma-86	67	29	memory	memory	NOUN
ma-86	67	30	moving	move	VERB
ma-86	67	31	average	average	ADJ
ma-86	67	32	process	process	NOUN
ma-86	67	33	.	.	PUNCT
ma-86	68	1	the	the	DET
ma-86	68	2	log	log	NOUN
ma-86	68	3	-	-	PUNCT
ma-86	68	4	volatility	volatility	NOUN
ma-86	68	5	process	process	NOUN
ma-86	68	6	will	will	AUX
ma-86	68	7	have	have	VERB
ma-86	68	8	slow	slow	ADJ
ma-86	68	9	(	(	PUNCT
ma-86	68	10	hyperbolic	hyperbolic	ADJ
ma-86	68	11	rate)decay	rate)decay	NOUN
ma-86	68	12	of	of	ADP
ma-86	68	13	the	the	DET
ma-86	68	14	auto	auto	NOUN
ma-86	68	15	-	-	PUNCT
ma-86	68	16	correlation	correlation	NOUN
ma-86	68	17	function	function	NOUN
ma-86	68	18	(	(	PUNCT
ma-86	68	19	acf).the	acf).the	DET
ma-86	68	20	process	process	NOUN
ma-86	68	21	yh(t	yh(t	PUNCT
ma-86	68	22	)	)	PUNCT
ma-86	68	23	can	can	AUX
ma-86	68	24	be	be	AUX
ma-86	68	25	written	write	VERB
ma-86	68	26	as	as	ADP
ma-86	68	27	yh(t	yh(t	NOUN
ma-86	68	28	)	)	PUNCT
ma-86	69	1	=	=	SYM
ma-86	69	2	∫	∫	PROPN
ma-86	69	3	t	t	PROPN
ma-86	69	4	−∞	−∞	ADP
ma-86	69	5	g(t	g(t	PROPN
ma-86	69	6	−	−	PROPN
ma-86	69	7	u)dmh	u)dmh	PROPN
ma-86	69	8	,	,	PUNCT
ma-86	69	9	u	u	NOUN
ma-86	69	10	,	,	PUNCT
ma-86	69	11	t	t	PROPN
ma-86	69	12	∈	∈	PROPN
ma-86	69	13	r.	r.	NOUN
ma-86	69	14	we	we	PRON
ma-86	69	15	assume	assume	VERB
ma-86	69	16	the	the	DET
ma-86	69	17	following	follow	VERB
ma-86	69	18	conditions	condition	NOUN
ma-86	69	19	on	on	ADP
ma-86	69	20	the	the	DET
ma-86	69	21	kernel	kernel	NOUN
ma-86	69	22	g	g	NOUN
ma-86	69	23	:	:	PUNCT
ma-86	69	24	r	r	NOUN
ma-86	69	25	→	→	SYM
ma-86	69	26	r	r	NOUN
ma-86	69	27	,	,	PUNCT
ma-86	69	28	namely	namely	ADV
ma-86	69	29	1	1	NUM
ma-86	69	30	)	)	PUNCT
ma-86	69	31	g(t	g(t	PROPN
ma-86	69	32	)	)	PUNCT
ma-86	70	1	=	=	SYM
ma-86	70	2	0	0	NUM
ma-86	70	3	for	for	ADP
ma-86	70	4	all	all	DET
ma-86	70	5	t	t	NOUN
ma-86	70	6	<	<	X
ma-86	70	7	0(causality	0(causality	NOUN
ma-86	70	8	)	)	PUNCT
ma-86	70	9	,	,	PUNCT
ma-86	70	10	2	2	X
ma-86	70	11	)	)	PUNCT
ma-86	70	12	|g(t)|	|g(t)|	ADJ
ma-86	70	13	≤	≤	ADJ
ma-86	70	14	ce−ct	ce−ct	NOUN
ma-86	70	15	for	for	ADP
ma-86	70	16	some	some	DET
ma-86	70	17	constants	constant	NOUN
ma-86	70	18	c	c	NOUN
ma-86	70	19	>	>	X
ma-86	70	20	0	0	PUNCT
ma-86	71	1	and	and	CCONJ
ma-86	71	2	c	c	X
ma-86	71	3	>	>	X
ma-86	71	4	0	0	PUNCT
ma-86	72	1	(	(	PUNCT
ma-86	72	2	short	short	ADJ
ma-86	72	3	memory	memory	NOUN
ma-86	72	4	)	)	PUNCT
ma-86	72	5	.	.	PUNCT
ma-86	73	1	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	PROPN
ma-86	73	2	eur	eur	PROPN
ma-86	73	3	.	.	PUNCT
ma-86	74	1	j.	j.	PROPN
ma-86	74	2	math	math	PROPN
ma-86	74	3	.	.	PUNCT
ma-86	75	1	anal	anal	PROPN
ma-86	75	2	.	.	PUNCT
ma-86	76	1	10.28924	10.28924	NUM
ma-86	76	2	/	/	SYM
ma-86	76	3	ada	ada	NOUN
ma-86	76	4	/	/	SYM
ma-86	76	5	ma.2.15	ma.2.15	PROPN
ma-86	76	6	4the	4the	PROPN
ma-86	76	7	fima	fima	NOUN
ma-86	76	8	process	process	NOUN
ma-86	76	9	is	be	AUX
ma-86	76	10	stationary	stationary	ADJ
ma-86	76	11	and	and	CCONJ
ma-86	76	12	is	be	AUX
ma-86	76	13	infinite	infinite	ADJ
ma-86	76	14	divisible	divisible	ADJ
ma-86	76	15	.	.	PUNCT
ma-86	77	1	it	it	PRON
ma-86	77	2	has	have	VERB
ma-86	77	3	long	long	ADJ
ma-86	77	4	memory	memory	NOUN
ma-86	77	5	and	and	CCONJ
ma-86	77	6	jumps	jump	VERB
ma-86	77	7	whichagree	whichagree	NOUN
ma-86	77	8	empirically	empirically	ADV
ma-86	77	9	with	with	ADP
ma-86	77	10	stochastic	stochastic	ADJ
ma-86	77	11	volatility	volatility	NOUN
ma-86	77	12	models	model	NOUN
ma-86	77	13	.	.	PUNCT
ma-86	78	1	the	the	DET
ma-86	78	2	asset	asset	NOUN
ma-86	78	3	return	return	NOUN
ma-86	78	4	can	can	AUX
ma-86	78	5	be	be	AUX
ma-86	78	6	modeled	model	VERB
ma-86	78	7	as	as	ADP
ma-86	78	8	a	a	DET
ma-86	78	9	coga	coga	NOUN
ma-86	78	10	-	-	PUNCT
ma-86	78	11	rch	rch	NOUN
ma-86	78	12	process	process	NOUN
ma-86	78	13	dx(t	dx(t	NOUN
ma-86	78	14	)	)	PUNCT
ma-86	78	15	=	=	SYM
ma-86	79	1	√	√	PROPN
ma-86	79	2	eyh(t)dltwhere	eyh(t)dltwhere	VERB
ma-86	79	3	(	(	PUNCT
ma-86	79	4	lt	lt	INTJ
ma-86	79	5	,	,	PUNCT
ma-86	79	6	t	t	PROPN
ma-86	79	7	∈	∈	PROPN
ma-86	79	8	r	r	NOUN
ma-86	79	9	is	be	AUX
ma-86	79	10	another	another	DET
ma-86	79	11	levy	levy	NOUN
ma-86	79	12	process	process	NOUN
ma-86	79	13	and	and	CCONJ
ma-86	79	14	the	the	DET
ma-86	79	15	initial	initial	ADJ
ma-86	79	16	value	value	NOUN
ma-86	79	17	yh(0	yh(0	NOUN
ma-86	79	18	)	)	PUNCT
ma-86	79	19	is	be	AUX
ma-86	79	20	independent	independent	ADJ
ma-86	79	21	of	of	ADP
ma-86	79	22	l.consider	l.consider	NOUN
ma-86	80	1	the	the	DET
ma-86	80	2	kernel	kernel	PROPN
ma-86	80	3	g(t	g(t	PROPN
ma-86	80	4	−	−	PROPN
ma-86	80	5	s	s	PART
ma-86	80	6	)	)	PUNCT
ma-86	80	7	=	=	SYM
ma-86	80	8	σe−θ(t−s)i(0,∞)(t	σe−θ(t−s)i(0,∞)(t	ADJ
ma-86	80	9	−	−	PROPN
ma-86	80	10	s	s	NOUN
ma-86	80	11	)	)	PUNCT
ma-86	80	12	,	,	PUNCT
ma-86	80	13	θ	θ	PROPN
ma-86	80	14	>	>	PUNCT
ma-86	80	15	0	0	PUNCT
ma-86	80	16	then	then	ADV
ma-86	80	17	gh(t	gh(t	PUNCT
ma-86	80	18	)	)	PUNCT
ma-86	81	1	=	=	SYM
ma-86	81	2	σ	σ	PROPN
ma-86	81	3	γ(h	γ(h	PROPN
ma-86	81	4	−	−	PROPN
ma-86	81	5	1	1	NUM
ma-86	81	6	2	2	NUM
ma-86	81	7	)	)	PUNCT
ma-86	81	8	∫	∫	PROPN
ma-86	82	1	∞	∞	PROPN
ma-86	82	2	0	0	X
ma-86	82	3	eθ(t−s)i(0,∞)(t	eθ(t−s)i(0,∞)(t	PROPN
ma-86	83	1	−	−	PROPN
ma-86	84	1	s)sh−	s)sh−	NOUN
ma-86	84	2	3	3	NUM
ma-86	84	3	2	2	NUM
ma-86	84	4	ds	ds	NOUN
ma-86	84	5	,	,	PUNCT
ma-86	84	6	t	t	PROPN
ma-86	84	7	∈	∈	PROPN
ma-86	84	8	r.	r.	PROPN
ma-86	84	9	note	note	VERB
ma-86	84	10	that	that	SCONJ
ma-86	84	11	uh	uh	INTJ
ma-86	84	12	,	,	PUNCT
ma-86	84	13	θ	θ	PROPN
ma-86	84	14	,	,	PUNCT
ma-86	84	15	σt	σt	ADP
ma-86	84	16	=	=	SYM
ma-86	84	17	∫	∫	PROPN
ma-86	85	1	r	r	NOUN
ma-86	85	2	gh(t	gh(t	PUNCT
ma-86	85	3	−	−	PROPN
ma-86	85	4	u)dmu	u)dmu	PROPN
ma-86	85	5	,	,	PUNCT
ma-86	85	6	t	t	PROPN
ma-86	85	7	∈	∈	PROPN
ma-86	85	8	r	r	NOUN
ma-86	85	9	is	be	AUX
ma-86	85	10	the	the	DET
ma-86	85	11	fractional	fractional	ADJ
ma-86	85	12	levy	levy	NOUN
ma-86	85	13	ornstein	ornstein	PROPN
ma-86	85	14	-	-	PUNCT
ma-86	85	15	uhlenbeck	uhlenbeck	PROPN
ma-86	85	16	(	(	PUNCT
ma-86	85	17	flou	flou	NOUN
ma-86	85	18	)	)	PUNCT
ma-86	85	19	process	process	NOUN
ma-86	85	20	satisfying	satisfy	VERB
ma-86	85	21	the	the	DET
ma-86	85	22	fractional	fractional	ADJ
ma-86	85	23	langevin	langevin	PROPN
ma-86	85	24	equa	equa	NOUN
ma-86	85	25	-	-	PUNCT
ma-86	85	26	tion	tion	NOUN
ma-86	85	27	dut	dut	NOUN
ma-86	85	28	=	=	PUNCT
ma-86	85	29	−θutdt	−θutdt	PROPN
ma-86	85	30	+	+	CCONJ
ma-86	85	31	σdmh	σdmh	ADJ
ma-86	85	32	,	,	PUNCT
ma-86	85	33	t	t	PROPN
ma-86	85	34	,	,	PUNCT
ma-86	85	35	t	t	PROPN
ma-86	85	36	∈	∈	PROPN
ma-86	85	37	r.the	r.the	DET
ma-86	85	38	process	process	NOUN
ma-86	85	39	has	have	VERB
ma-86	85	40	long	long	ADJ
ma-86	85	41	memory	memory	NOUN
ma-86	85	42	.	.	PUNCT
ma-86	86	1	levy	levy	NOUN
ma-86	86	2	driven	drive	VERB
ma-86	86	3	processes	process	NOUN
ma-86	86	4	of	of	ADP
ma-86	86	5	ornstein	ornstein	PROPN
ma-86	86	6	-	-	PUNCT
ma-86	86	7	uhlenbeck	uhlenbeck	PROPN
ma-86	86	8	type	type	NOUN
ma-86	86	9	have	have	AUX
ma-86	86	10	beenextensively	beenextensively	ADV
ma-86	86	11	studied	study	VERB
ma-86	86	12	over	over	ADP
ma-86	86	13	the	the	DET
ma-86	86	14	last	last	ADJ
ma-86	86	15	few	few	ADJ
ma-86	86	16	years	year	NOUN
ma-86	86	17	and	and	CCONJ
ma-86	86	18	widely	widely	ADV
ma-86	86	19	used	use	VERB
ma-86	86	20	in	in	ADP
ma-86	86	21	finance	finance	NOUN
ma-86	86	22	,	,	PUNCT
ma-86	86	23	see	see	VERB
ma-86	86	24	barndorff	barndorff	NOUN
ma-86	86	25	-	-	PUNCT
ma-86	86	26	neilsenand	neilsenand	NOUN
ma-86	86	27	shephard	shephard	NOUN
ma-86	86	28	[	[	X
ma-86	86	29	1	1	NUM
ma-86	86	30	]	]	PUNCT
ma-86	86	31	.	.	PUNCT
ma-86	87	1	flou	flou	PROPN
ma-86	87	2	process	process	NOUN
ma-86	87	3	generalizes	generalize	VERB
ma-86	87	4	fou	fou	PROPN
ma-86	87	5	process	process	NOUN
ma-86	87	6	to	to	PART
ma-86	87	7	include	include	VERB
ma-86	87	8	jumps	jump	NOUN
ma-86	87	9	.	.	PUNCT
ma-86	88	1	maximum	maximum	ADJ
ma-86	88	2	quasi	quasi	ADJ
ma-86	88	3	-	-	ADJ
ma-86	88	4	likelihood	likelihood	ADJ
ma-86	88	5	estimation	estimation	NOUN
ma-86	88	6	in	in	ADP
ma-86	88	7	fractional	fractional	ADJ
ma-86	88	8	levy	levy	NOUN
ma-86	88	9	stochastic	stochastic	ADJ
ma-86	88	10	volatility	volatility	NOUN
ma-86	88	11	model	model	NOUN
ma-86	88	12	was	be	AUX
ma-86	88	13	studied	study	VERB
ma-86	88	14	in	in	ADP
ma-86	88	15	bishwal	bishwal	NOUN
ma-86	88	16	[	[	X
ma-86	88	17	6].berry	6].berry	NUM
ma-86	88	18	-	-	PUNCT
ma-86	88	19	esseen	esseen	VERB
ma-86	88	20	inequalities	inequality	NOUN
ma-86	88	21	for	for	ADP
ma-86	88	22	the	the	DET
ma-86	88	23	discretely	discretely	ADV
ma-86	88	24	observed	observe	VERB
ma-86	88	25	ornstein	ornstein	NOUN
ma-86	88	26	-	-	PUNCT
ma-86	88	27	uhlenbeck	uhlenbeck	ADJ
ma-86	88	28	-	-	PUNCT
ma-86	88	29	gamma	gamma	NOUN
ma-86	88	30	process	process	NOUN
ma-86	88	31	wasstudied	wasstudie	VERB
ma-86	88	32	in	in	ADP
ma-86	88	33	bishwal	bishwal	NOUN
ma-86	88	34	[	[	X
ma-86	88	35	7	7	NUM
ma-86	88	36	]	]	PUNCT
ma-86	88	37	.	.	PUNCT
ma-86	89	1	minimum	minimum	ADJ
ma-86	89	2	contrast	contrast	NOUN
ma-86	89	3	estimation	estimation	NOUN
ma-86	89	4	in	in	ADP
ma-86	89	5	fractional	fractional	PROPN
ma-86	89	6	ornstein	ornstein	PROPN
ma-86	89	7	-	-	PUNCT
ma-86	89	8	uhlenbeck	uhlenbeck	PROPN
ma-86	89	9	processbased	processbase	VERB
ma-86	89	10	on	on	ADP
ma-86	89	11	both	both	CCONJ
ma-86	89	12	continuous	continuous	ADJ
ma-86	89	13	and	and	CCONJ
ma-86	89	14	discrete	discrete	ADJ
ma-86	89	15	observations	observation	NOUN
ma-86	89	16	was	be	AUX
ma-86	89	17	studied	study	VERB
ma-86	89	18	in	in	ADP
ma-86	89	19	bishwal	bishwal	NOUN
ma-86	90	1	[	[	X
ma-86	90	2	8].consider	8].consider	NUM
ma-86	90	3	the	the	DET
ma-86	90	4	asset	asset	NOUN
ma-86	90	5	return	return	NOUN
ma-86	90	6	driven	drive	VERB
ma-86	90	7	by	by	ADP
ma-86	90	8	fractional	fractional	ADJ
ma-86	90	9	levy	levy	NOUN
ma-86	90	10	process	process	NOUN
ma-86	90	11	dsh	dsh	NOUN
ma-86	90	12	,	,	PUNCT
ma-86	90	13	t	t	NOUN
ma-86	90	14	=	=	SYM
ma-86	90	15	σt−dlh	σt−dlh	PROPN
ma-86	90	16	,	,	PUNCT
ma-86	90	17	t	t	PROPN
ma-86	90	18	,	,	PUNCT
ma-86	90	19	t	t	PROPN
ma-86	90	20	>	>	X
ma-86	90	21	0	0	PROPN
ma-86	90	22	,	,	PUNCT
ma-86	90	23	s0	s0	PROPN
ma-86	90	24	=	=	SYM
ma-86	90	25	0	0	NUM
ma-86	90	26	,	,	PUNCT
ma-86	90	27	with	with	ADP
ma-86	90	28	log	log	NOUN
ma-86	90	29	-	-	PUNCT
ma-86	90	30	volatility	volatility	NOUN
ma-86	90	31	logσ2	logσ2	NOUN
ma-86	90	32	t	t	PROPN
ma-86	90	33	=	=	SYM
ma-86	90	34	µ+xt	µ+xt	PROPN
ma-86	90	35	,	,	PUNCT
ma-86	90	36	t	t	PROPN
ma-86	90	37	≥	≥	NOUN
ma-86	90	38	0	0	NUM
ma-86	90	39	where	where	SCONJ
ma-86	90	40	the	the	DET
ma-86	90	41	levy	levy	NOUN
ma-86	90	42	driven	drive	VERB
ma-86	90	43	ou	ou	NOUN
ma-86	90	44	process	process	NOUN
ma-86	90	45	x	x	PRON
ma-86	90	46	satisfies	satisfy	VERB
ma-86	90	47	dxt	dxt	PROPN
ma-86	90	48	=	=	PUNCT
ma-86	91	1	−θxtdt	−θxtdt	PROPN
ma-86	92	1	+	+	CCONJ
ma-86	92	2	dmt	dmt	INTJ
ma-86	92	3	,	,	PUNCT
ma-86	92	4	t	t	PROPN
ma-86	92	5	>	>	X
ma-86	92	6	0	0	PUNCT
ma-86	92	7	with	with	ADP
ma-86	92	8	θ	θ	PROPN
ma-86	92	9	∈	∈	PROPN
ma-86	92	10	r+	r+	NOUN
ma-86	92	11	and	and	CCONJ
ma-86	92	12	the	the	DET
ma-86	92	13	driving	drive	VERB
ma-86	92	14	compound	compound	NOUN
ma-86	92	15	poisson	poisson	NOUN
ma-86	92	16	process	process	NOUN
ma-86	92	17	m	m	PROPN
ma-86	92	18	is	be	AUX
ma-86	92	19	a	a	DET
ma-86	92	20	levy	levy	NOUN
ma-86	92	21	process	process	NOUN
ma-86	92	22	with	with	ADP
ma-86	92	23	levy	levy	NOUN
ma-86	92	24	symbol	symbol	NOUN
ma-86	92	25	ψm(u	ψm(u	NUM
ma-86	92	26	)	)	PUNCT
ma-86	93	1	=	=	SYM
ma-86	93	2	−	−	PROPN
ma-86	93	3	u2	u2	NOUN
ma-86	93	4	2	2	NUM
ma-86	93	5	+	+	CCONJ
ma-86	93	6	∫	∫	PROPN
ma-86	93	7	r	r	NOUN
ma-86	93	8	(	(	PUNCT
ma-86	93	9	e	e	NOUN
ma-86	93	10	iux	iux	PROPN
ma-86	93	11	−	−	PROPN
ma-86	93	12	1)φ0,1	1)φ0,1	NUM
ma-86	93	13	/	/	SYM
ma-86	93	14	λ(dx	λ(dx	PROPN
ma-86	93	15	)	)	PUNCT
ma-86	93	16	,	,	PUNCT
ma-86	93	17	where	where	SCONJ
ma-86	93	18	φ0,1	φ0,1	ADV
ma-86	93	19	/	/	SYM
ma-86	93	20	λ	λ	NOUN
ma-86	93	21	being	be	AUX
ma-86	93	22	a	a	DET
ma-86	93	23	normal	normal	ADJ
ma-86	93	24	distribution	distribution	NOUN
ma-86	93	25	with	with	ADP
ma-86	93	26	mean	mean	NOUN
ma-86	93	27	0	0	NUM
ma-86	93	28	and	and	CCONJ
ma-86	93	29	variance	variance	NOUN
ma-86	93	30	1	1	NUM
ma-86	93	31	/	/	SYM
ma-86	93	32	λ	λ	NOUN
ma-86	93	33	.	.	PUNCT
ma-86	94	1	this	this	PRON
ma-86	94	2	means	mean	VERB
ma-86	94	3	that	that	SCONJ
ma-86	94	4	m	m	NOUN
ma-86	94	5	is	be	AUX
ma-86	94	6	thesum	thesum	NOUN
ma-86	94	7	of	of	ADP
ma-86	94	8	a	a	DET
ma-86	94	9	standard	standard	ADJ
ma-86	94	10	brownian	brownian	ADJ
ma-86	94	11	motion	motion	NOUN
ma-86	94	12	w	w	PROPN
ma-86	94	13	and	and	CCONJ
ma-86	94	14	a	a	DET
ma-86	94	15	compound	compound	NOUN
ma-86	94	16	poisson	poisson	NOUN
ma-86	94	17	process	process	NOUN
ma-86	94	18	jt	jt	PROPN
ma-86	94	19	=	=	PRON
ma-86	94	20	∑nt	∑nt	PUNCT
ma-86	95	1	k=1	k=1	PROPN
ma-86	95	2	zk	zk	PROPN
ma-86	95	3	,	,	PUNCT
ma-86	95	4	j−t	j−t	PROPN
ma-86	95	5	=	=	SYM
ma-86	95	6	∑−n−t	∑−n−t	NOUN
ma-86	95	7	k=1	k=1	PROPN
ma-86	95	8	z−k	z−k	NOUN
ma-86	95	9	,	,	PUNCT
ma-86	95	10	t	t	PROPN
ma-86	95	11	≥	≥	NOUN
ma-86	95	12	0	0	PUNCT
ma-86	95	13	where	where	SCONJ
ma-86	95	14	(	(	PUNCT
ma-86	95	15	nt	not	PART
ma-86	95	16	,	,	PUNCT
ma-86	95	17	t	t	PROPN
ma-86	95	18	∈	∈	PROPN
ma-86	95	19	r	r	X
ma-86	95	20	)	)	PUNCT
ma-86	95	21	is	be	AUX
ma-86	95	22	an	an	DET
ma-86	95	23	independent	independent	ADJ
ma-86	95	24	poisson	poisson	NOUN
ma-86	95	25	process	process	NOUN
ma-86	95	26	with	with	ADP
ma-86	95	27	intensity	intensity	NOUN
ma-86	95	28	λ	λ	X
ma-86	95	29	>	>	X
ma-86	95	30	0	0	PUNCT
ma-86	96	1	and	and	CCONJ
ma-86	96	2	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	PROPN
ma-86	96	3	eur	eur	PROPN
ma-86	96	4	.	.	PUNCT
ma-86	97	1	j.	j.	PROPN
ma-86	97	2	math	math	PROPN
ma-86	97	3	.	.	PUNCT
ma-86	98	1	anal	anal	PROPN
ma-86	98	2	.	.	PUNCT
ma-86	99	1	10.28924	10.28924	NUM
ma-86	99	2	/	/	SYM
ma-86	99	3	ada	ada	NOUN
ma-86	99	4	/	/	SYM
ma-86	99	5	ma.2.15	ma.2.15	PROPN
ma-86	99	6	5jump	5jump	NUM
ma-86	99	7	times	time	NOUN
ma-86	99	8	(	(	PUNCT
ma-86	99	9	tk)k∈z	tk)k∈z	NUM
ma-86	99	10	,	,	PUNCT
ma-86	99	11	i.e.	i.e.	X
ma-86	99	12	,	,	PUNCT
ma-86	99	13	mt	mt	PROPN
ma-86	99	14	=	=	PROPN
ma-86	99	15	wt	wt	PROPN
ma-86	100	1	+	+	X
ma-86	100	2	jt	jt	PROPN
ma-86	100	3	.	.	PUNCT
ma-86	101	1	the	the	DET
ma-86	101	2	poisson	poisson	NOUN
ma-86	101	3	process	process	NOUN
ma-86	101	4	n	n	ADV
ma-86	101	5	is	be	AUX
ma-86	101	6	also	also	ADV
ma-86	101	7	independent	independent	ADJ
ma-86	101	8	from	from	ADP
ma-86	101	9	the	the	DET
ma-86	101	10	i.i.d.sequence	i.i.d.sequence	PROPN
ma-86	101	11	of	of	ADP
ma-86	101	12	jump	jump	NOUN
ma-86	101	13	sizes	size	NOUN
ma-86	101	14	(	(	PUNCT
ma-86	101	15	zk)k∈z	zk)k∈z	X
ma-86	101	16	with	with	ADP
ma-86	101	17	z1	z1	ADJ
ma-86	101	18	∼	∼	NOUN
ma-86	101	19	n(0	n(0	NOUN
ma-86	101	20	,	,	PUNCT
ma-86	101	21	1	1	NUM
ma-86	101	22	/	/	SYM
ma-86	101	23	λ	λ	NOUN
ma-86	101	24	)	)	PUNCT
ma-86	101	25	.	.	PUNCT
ma-86	102	1	the	the	DET
ma-86	102	2	levy	levy	NOUN
ma-86	102	3	process	process	NOUN
ma-86	102	4	m	m	VERB
ma-86	102	5	in	in	ADP
ma-86	102	6	this	this	DET
ma-86	102	7	case	case	NOUN
ma-86	102	8	is	be	AUX
ma-86	102	9	given	give	VERB
ma-86	102	10	by	by	ADP
ma-86	102	11	mt	mt	PROPN
ma-86	102	12	=	=	PROPN
ma-86	102	13	nt∑	nt∑	PROPN
ma-86	102	14	k=1	k=1	X
ma-86	102	15	(	(	PUNCT
ma-86	102	16	αzk	αzk	NOUN
ma-86	102	17	+	+	PUNCT
ma-86	102	18	γ|zk	γ|zk	NOUN
ma-86	102	19	|)−	|)−	PROPN
ma-86	102	20	ct	ct	PROPN
ma-86	102	21	,	,	PUNCT
ma-86	102	22	t	t	X
ma-86	102	23	>	>	X
ma-86	102	24	0	0	PUNCT
ma-86	102	25	and	and	CCONJ
ma-86	102	26	c	c	NOUN
ma-86	102	27	:	:	PUNCT
ma-86	102	28	=	=	SYM
ma-86	102	29	γ	γ	X
ma-86	102	30	∫	∫	PROPN
ma-86	102	31	r	r	NOUN
ma-86	102	32	|x	|x	NOUN
ma-86	102	33	|λφ0,1	|λφ0,1	NOUN
ma-86	102	34	/	/	SYM
ma-86	102	35	λ(dx	λ(dx	PROPN
ma-86	102	36	)	)	PUNCT
ma-86	102	37	=	=	SYM
ma-86	103	1	√	√	NUM
ma-86	103	2	2λ	2λ	NUM
ma-86	103	3	π	π	PROPN
ma-86	103	4	γ	γ	X
ma-86	103	5	.	.	PROPN
ma-86	103	6	{	{	PUNCT
ma-86	103	7	m−t	m−t	PROPN
ma-86	103	8	,	,	PUNCT
ma-86	103	9	t	t	PROPN
ma-86	103	10	≥	≥	NOUN
ma-86	103	11	0	0	NUM
ma-86	103	12	}	}	PUNCT
ma-86	103	13	is	be	AUX
ma-86	103	14	defined	define	VERB
ma-86	103	15	analogously	analogously	ADV
ma-86	103	16	.	.	PUNCT
ma-86	104	1	the	the	DET
ma-86	104	2	stationary	stationary	ADJ
ma-86	104	3	log	log	NOUN
ma-86	104	4	-	-	PUNCT
ma-86	104	5	volatility	volatility	NOUN
ma-86	104	6	is	be	AUX
ma-86	104	7	given	give	VERB
ma-86	104	8	by	by	ADP
ma-86	104	9	logσ2	logσ2	PROPN
ma-86	104	10	t	t	PROPN
ma-86	104	11	=	=	SYM
ma-86	104	12	µ+	µ+	PUNCT
ma-86	104	13	∫	∫	PROPN
ma-86	104	14	t	t	PROPN
ma-86	104	15	−∞	−∞	ADP
ma-86	104	16	e−θ(t−s)dms	e−θ(t−s)dms	PROPN
ma-86	104	17	.	.	PUNCT
ma-86	105	1	we	we	PRON
ma-86	105	2	observe	observe	VERB
ma-86	105	3	s	s	PRON
ma-86	105	4	at	at	ADP
ma-86	105	5	n	n	CCONJ
ma-86	105	6	consecutive	consecutive	ADJ
ma-86	105	7	jump	jump	NOUN
ma-86	105	8	times	time	NOUN
ma-86	105	9	0	0	PUNCT
ma-86	106	1	=	=	SYM
ma-86	106	2	t0	t0	PROPN
ma-86	106	3	<	<	X
ma-86	106	4	t1	t1	NOUN
ma-86	106	5	<	<	X
ma-86	106	6	.	.	PUNCT
ma-86	106	7	.	.	PUNCT
ma-86	106	8	.	.	PUNCT
ma-86	107	1	<	<	X
ma-86	107	2	tn	tn	X
ma-86	107	3	<	<	X
ma-86	107	4	t	t	X
ma-86	107	5	<	<	X
ma-86	107	6	tn+1	tn+1	PROPN
ma-86	107	7	,	,	PUNCT
ma-86	107	8	n	n	PROPN
ma-86	107	9	∈	∈	PROPN
ma-86	107	10	z	z	NOUN
ma-86	107	11	over	over	ADP
ma-86	107	12	the	the	DET
ma-86	107	13	timeinterval	timeinterval	NOUN
ma-86	108	1	[	[	X
ma-86	108	2	0	0	NUM
ma-86	108	3	,	,	PUNCT
ma-86	108	4	t	t	X
ma-86	108	5	]	]	PUNCT
ma-86	108	6	.	.	PUNCT
ma-86	109	1	the	the	DET
ma-86	109	2	state	state	NOUN
ma-86	109	3	process	process	NOUN
ma-86	109	4	x	x	PUNCT
ma-86	109	5	has	have	VERB
ma-86	109	6	then	then	ADV
ma-86	109	7	the	the	DET
ma-86	109	8	following	following	ADJ
ma-86	109	9	autoregressive	autoregressive	ADJ
ma-86	109	10	representation	representation	NOUN
ma-86	109	11	xti	xti	PROPN
ma-86	109	12	=	=	SYM
ma-86	109	13	e−θ∆tixti−1	e−θ∆tixti−1	PROPN
ma-86	109	14	+	+	CCONJ
ma-86	109	15	nti∑	nti∑	X
ma-86	110	1	k	k	X
ma-86	110	2	=	=	PROPN
ma-86	110	3	nti−1	nti−1	PROPN
ma-86	110	4	+1	+1	PROPN
ma-86	110	5	e−θ(ti−tk)[αzk	e−θ(ti−tk)[αzk	PROPN
ma-86	110	6	+	+	X
ma-86	110	7	γ|zk	γ|zk	NOUN
ma-86	110	8	|]−	|]−	VERB
ma-86	110	9	∫	∫	PROPN
ma-86	110	10	ti	ti	PROPN
ma-86	110	11	ti−1	ti−1	NOUN
ma-86	110	12	e−θ(ti−s)cds	e−θ(ti−s)cd	NOUN
ma-86	110	13	=	=	PUNCT
ma-86	110	14	e−θ∆tixti−1	e−θ∆tixti−1	PROPN
ma-86	110	15	+	+	CCONJ
ma-86	110	16	αzi	αzi	NOUN
ma-86	110	17	+	+	CCONJ
ma-86	110	18	(	(	PUNCT
ma-86	110	19	|zi	|zi	X
ma-86	110	20	|	|	ADV
ma-86	110	21	−	−	ADP
ma-86	110	22	c	c	NOUN
ma-86	110	23	θ	θ	PROPN
ma-86	110	24	(	(	PUNCT
ma-86	110	25	1−	1−	NUM
ma-86	110	26	e−θ∆ti	e−θ∆ti	NOUN
ma-86	110	27	)	)	PUNCT
ma-86	110	28	)	)	PUNCT
ma-86	110	29	where	where	SCONJ
ma-86	110	30	∆ti	∆ti	NOUN
ma-86	110	31	:	:	PUNCT
ma-86	110	32	=	=	SYM
ma-86	110	33	ti	ti	NOUN
ma-86	110	34	−	−	PROPN
ma-86	110	35	ti−1	ti−1	NOUN
ma-86	110	36	,	,	PUNCT
ma-86	110	37	i	i	NOUN
ma-86	110	38	=	=	NOUN
ma-86	110	39	1	1	NUM
ma-86	110	40	,	,	PUNCT
ma-86	110	41	2	2	NUM
ma-86	110	42	,	,	PUNCT
ma-86	110	43	.	.	PUNCT
ma-86	110	44	.	.	PUNCT
ma-86	111	1	.	.	PUNCT
ma-86	112	1	,	,	PUNCT
ma-86	112	2	n	n	PROPN
ma-86	112	3	and	and	CCONJ
ma-86	112	4	nti−1	nti−1	PROPN
ma-86	113	1	+	+	CCONJ
ma-86	113	2	1	1	NUM
ma-86	113	3	=	=	SYM
ma-86	113	4	nti	nti	X
ma-86	113	5	=	=	PUNCT
ma-86	114	1	i	i	PRON
ma-86	114	2	.we	.we	PUNCT
ma-86	115	1	do	do	VERB
ma-86	115	2	the	the	DET
ma-86	115	3	parameter	parameter	NOUN
ma-86	115	4	estimation	estimation	NOUN
ma-86	115	5	in	in	ADP
ma-86	115	6	two	two	NUM
ma-86	115	7	steps	step	NOUN
ma-86	115	8	.	.	PUNCT
ma-86	116	1	the	the	DET
ma-86	116	2	rate	rate	NOUN
ma-86	116	3	λ	λ	PROPN
ma-86	116	4	of	of	ADP
ma-86	116	5	the	the	DET
ma-86	116	6	poisson	poisson	NOUN
ma-86	116	7	process	process	NOUN
ma-86	116	8	n	n	PRON
ma-86	116	9	can	can	AUX
ma-86	116	10	beestimated	beestimate	VERB
ma-86	116	11	given	give	VERB
ma-86	116	12	the	the	DET
ma-86	116	13	jump	jump	NOUN
ma-86	116	14	times	time	NOUN
ma-86	116	15	ti	ti	PROPN
ma-86	116	16	,	,	PUNCT
ma-86	116	17	therefore	therefore	ADV
ma-86	116	18	it	it	PRON
ma-86	116	19	is	be	AUX
ma-86	116	20	done	do	VERB
ma-86	116	21	at	at	ADP
ma-86	116	22	a	a	DET
ma-86	116	23	first	first	ADJ
ma-86	116	24	step	step	NOUN
ma-86	116	25	.	.	PUNCT
ma-86	117	1	since	since	SCONJ
ma-86	117	2	we	we	PRON
ma-86	117	3	observe	observe	VERB
ma-86	117	4	totalnumber	totalnumber	NOUN
ma-86	117	5	of	of	ADP
ma-86	117	6	jumps	jump	NOUN
ma-86	117	7	n	n	PROPN
ma-86	117	8	of	of	ADP
ma-86	117	9	the	the	DET
ma-86	117	10	poisson	poisson	NOUN
ma-86	117	11	process	process	NOUN
ma-86	117	12	n	n	NOUN
ma-86	117	13	over	over	ADP
ma-86	117	14	the	the	DET
ma-86	117	15	t	t	NOUN
ma-86	117	16	intervals	interval	NOUN
ma-86	117	17	of	of	ADP
ma-86	117	18	length	length	NOUN
ma-86	117	19	one	one	NUM
ma-86	117	20	,	,	PUNCT
ma-86	117	21	the	the	DET
ma-86	117	22	mle	mle	NOUN
ma-86	117	23	of	of	ADP
ma-86	117	24	λ	λ	NOUN
ma-86	117	25	isgiven	isgiven	VERB
ma-86	117	26	by	by	ADP
ma-86	117	27	λ̂n	λ̂n	PUNCT
ma-86	117	28	:	:	PUNCT
ma-86	117	29	=	=	SYM
ma-86	117	30	n	n	PRON
ma-86	117	31	t	t	NOUN
ma-86	117	32	.to	.to	PUNCT
ma-86	117	33	estimate	estimate	VERB
ma-86	117	34	the	the	DET
ma-86	117	35	remaining	remain	VERB
ma-86	117	36	parameters	parameter	NOUN
ma-86	117	37	(	(	PUNCT
ma-86	117	38	α	α	NOUN
ma-86	117	39	,	,	PUNCT
ma-86	117	40	θ	θ	PROPN
ma-86	117	41	,	,	PUNCT
ma-86	117	42	µ	µ	NOUN
ma-86	117	43	)	)	PUNCT
ma-86	117	44	,	,	PUNCT
ma-86	117	45	we	we	PRON
ma-86	117	46	use	use	VERB
ma-86	117	47	the	the	DET
ma-86	117	48	quasi	quasi	ADJ
ma-86	117	49	maximum	maximum	ADJ
ma-86	117	50	likelihood	likelihood	NOUN
ma-86	117	51	estimationprocedure	estimationprocedure	NOUN
ma-86	117	52	in	in	ADP
ma-86	117	53	conditionally	conditionally	ADV
ma-86	117	54	heteroscedastic	heteroscedastic	ADJ
ma-86	117	55	time	time	NOUN
ma-86	117	56	series	series	NOUN
ma-86	117	57	models	model	NOUN
ma-86	117	58	developed	develop	VERB
ma-86	117	59	by	by	ADP
ma-86	117	60	straumann	straumann	NOUN
ma-86	118	1	[	[	X
ma-86	118	2	25].assuming	25].assuming	NOUN
ma-86	118	3	that	that	DET
ma-86	118	4	s∆ti	s∆ti	NOUN
ma-86	118	5	h	h	NOUN
ma-86	118	6	,	,	PUNCT
ma-86	118	7	ti	ti	PROPN
ma-86	118	8	given	give	VERB
ma-86	118	9	s∆ti−1	s∆ti−1	PROPN
ma-86	118	10	h	h	NOUN
ma-86	118	11	,	,	PUNCT
ma-86	118	12	ti−1	ti−1	NOUN
ma-86	118	13	,	,	PUNCT
ma-86	118	14	.	.	PUNCT
ma-86	118	15	.	.	PUNCT
ma-86	118	16	.	.	PUNCT
ma-86	119	1	,	,	PUNCT
ma-86	119	2	s∆t1	s∆t1	PUNCT
ma-86	119	3	h	h	NOUN
ma-86	119	4	,	,	PUNCT
ma-86	119	5	t1	t1	PROPN
ma-86	119	6	,	,	PUNCT
ma-86	119	7	x0	x0	PROPN
ma-86	119	8	is	be	AUX
ma-86	119	9	conditionally	conditionally	ADV
ma-86	119	10	normally	normally	ADV
ma-86	119	11	distributed	distribute	VERB
ma-86	119	12	with	with	ADP
ma-86	119	13	meanzero	meanzero	NOUN
ma-86	119	14	and	and	CCONJ
ma-86	119	15	variance	variance	NOUN
ma-86	119	16	σ2	σ2	PROPN
ma-86	119	17	ti−/λ	ti−/λ	NOUN
ma-86	119	18	,	,	PUNCT
ma-86	119	19	the	the	DET
ma-86	119	20	conditional	conditional	ADJ
ma-86	119	21	log	log	NOUN
ma-86	119	22	-	-	PUNCT
ma-86	119	23	likelihood	likelihood	NOUN
ma-86	119	24	given	give	VERB
ma-86	119	25	the	the	DET
ma-86	119	26	initial	initial	ADJ
ma-86	119	27	value	value	NOUN
ma-86	119	28	x0	x0	PROPN
ma-86	119	29	has	have	VERB
ma-86	119	30	the	the	DET
ma-86	119	31	repre	repre	ADJ
ma-86	119	32	-	-	PUNCT
ma-86	119	33	sentation	sentation	NOUN
ma-86	119	34	l(ϑ|s∆	l(ϑ|s∆	NOUN
ma-86	119	35	h	h	NOUN
ma-86	119	36	,	,	PUNCT
ma-86	119	37	λ	λ	NOUN
ma-86	119	38	)	)	PUNCT
ma-86	119	39	:	:	PUNCT
ma-86	120	1	=	=	SYM
ma-86	120	2	−	−	PROPN
ma-86	120	3	n	n	NUM
ma-86	120	4	2	2	NUM
ma-86	120	5	log(2π)−	log(2π)−	SYM
ma-86	120	6	1	1	NUM
ma-86	120	7	2	2	NUM
ma-86	120	8	(	(	PUNCT
ma-86	120	9	n∑	n∑	NOUN
ma-86	120	10	i=1	i=1	PROPN
ma-86	120	11	log(σ2	log(σ2	PROPN
ma-86	121	1	ti−/λ)−	ti−/λ)−	X
ma-86	121	2	n∑	n∑	X
ma-86	121	3	i=1	i=1	PROPN
ma-86	122	1	(	(	PUNCT
ma-86	122	2	s∆ti	s∆ti	NOUN
ma-86	122	3	h	h	NOUN
ma-86	122	4	,	,	PUNCT
ma-86	122	5	ti	ti	NOUN
ma-86	122	6	)	)	PUNCT
ma-86	122	7	2	2	NUM
ma-86	122	8	σ2	σ2	NOUN
ma-86	122	9	ti−/λ	ti−/λ	NOUN
ma-86	122	10	)	)	PUNCT
ma-86	122	11	.	.	PUNCT
ma-86	123	1	where	where	SCONJ
ma-86	123	2	s∆ti	s∆ti	NOUN
ma-86	123	3	h	h	NOUN
ma-86	123	4	,	,	PUNCT
ma-86	123	5	ti	ti	X
ma-86	123	6	=	=	SYM
ma-86	123	7	sh	sh	PROPN
ma-86	123	8	,	,	PUNCT
ma-86	123	9	ti	ti	PROPN
ma-86	123	10	−	−	PROPN
ma-86	123	11	sh	sh	PROPN
ma-86	123	12	,	,	PUNCT
ma-86	123	13	ti−1	ti−1	NOUN
ma-86	123	14	is	be	AUX
ma-86	123	15	the	the	DET
ma-86	123	16	return	return	NOUN
ma-86	123	17	at	at	ADP
ma-86	123	18	time	time	NOUN
ma-86	123	19	ti	ti	X
ma-86	123	20	.	.	PUNCT
ma-86	124	1	since	since	SCONJ
ma-86	124	2	the	the	DET
ma-86	124	3	volatility	volatility	NOUN
ma-86	124	4	is	be	AUX
ma-86	124	5	unobservable	unobservable	ADJ
ma-86	124	6	,	,	PUNCT
ma-86	124	7	this	this	DET
ma-86	124	8	log	log	NOUN
ma-86	124	9	-	-	PUNCT
ma-86	124	10	likelihood	likelihood	NOUN
ma-86	124	11	can	can	AUX
ma-86	124	12	not	not	PART
ma-86	124	13	be	be	AUX
ma-86	124	14	evaluated	evaluate	VERB
ma-86	124	15	numerically	numerically	ADV
ma-86	124	16	.	.	PUNCT
ma-86	125	1	the	the	DET
ma-86	125	2	quasi	quasi	ADJ
ma-86	125	3	log	log	NOUN
ma-86	125	4	-	-	PUNCT
ma-86	125	5	likelihood	likelihood	NOUN
ma-86	125	6	function	function	NOUN
ma-86	125	7	for	for	ADP
ma-86	125	8	ϑ	ϑ	X
ma-86	125	9	=	=	SYM
ma-86	125	10	(	(	PUNCT
ma-86	125	11	θ	θ	PROPN
ma-86	125	12	,	,	PUNCT
ma-86	125	13	α	α	PROPN
ma-86	125	14	,	,	PUNCT
ma-86	125	15	γ	γ	PROPN
ma-86	125	16	,	,	PUNCT
ma-86	125	17	µ)given	µ)given	DET
ma-86	125	18	the	the	DET
ma-86	125	19	data	datum	NOUN
ma-86	125	20	s∆	s∆	PROPN
ma-86	125	21	h	h	NOUN
ma-86	125	22	:	:	PUNCT
ma-86	125	23	=	=	SYM
ma-86	125	24	(	(	PUNCT
ma-86	125	25	s∆t1	s∆t1	PROPN
ma-86	125	26	h	h	NOUN
ma-86	125	27	,	,	PUNCT
ma-86	125	28	t1	t1	NOUN
ma-86	125	29	,	,	PUNCT
ma-86	125	30	s∆t2	s∆t2	PROPN
ma-86	125	31	h	h	NOUN
ma-86	125	32	,	,	PUNCT
ma-86	125	33	t2	t2	NOUN
ma-86	125	34	,	,	PUNCT
ma-86	125	35	.	.	PUNCT
ma-86	125	36	.	.	PUNCT
ma-86	125	37	.	.	PUNCT
ma-86	126	1	,	,	PUNCT
ma-86	126	2	s∆tn	s∆tn	VERB
ma-86	126	3	h	h	NOUN
ma-86	126	4	,	,	PUNCT
ma-86	126	5	tn	tn	PROPN
ma-86	126	6	)	)	PUNCT
ma-86	126	7	and	and	CCONJ
ma-86	126	8	the	the	DET
ma-86	126	9	mle	mle	PROPN
ma-86	126	10	λ̂n	λ̂n	X
ma-86	126	11	is	be	AUX
ma-86	126	12	defined	define	VERB
ma-86	126	13	as	as	ADP
ma-86	126	14	l(ϑ|s∆	l(ϑ|s∆	NOUN
ma-86	126	15	h	h	NOUN
ma-86	126	16	,	,	PUNCT
ma-86	126	17	λ̂n	λ̂n	NOUN
ma-86	126	18	)	)	PUNCT
ma-86	126	19	:	:	PUNCT
ma-86	127	1	=	=	SYM
ma-86	127	2	−	−	PROPN
ma-86	127	3	1	1	NUM
ma-86	127	4	2	2	NUM
ma-86	127	5	n∑	n∑	NOUN
ma-86	127	6	i=1	i=1	PROPN
ma-86	128	1	log(σ̂2	log(σ̂2	PROPN
ma-86	128	2	h	h	NOUN
ma-86	128	3	,	,	PUNCT
ma-86	128	4	ti	ti	PROPN
ma-86	128	5	(	(	PUNCT
ma-86	128	6	ϑ	ϑ	X
ma-86	128	7	,	,	PUNCT
ma-86	128	8	λ̂n))−	λ̂n))−	PROPN
ma-86	128	9	1	1	NUM
ma-86	128	10	2	2	NUM
ma-86	128	11	n∑	n∑	NOUN
ma-86	128	12	i=1	i=1	PROPN
ma-86	128	13	(	(	PUNCT
ma-86	128	14	s∆ti	s∆ti	NOUN
ma-86	128	15	h	h	NOUN
ma-86	128	16	,	,	PUNCT
ma-86	128	17	ti	ti	NOUN
ma-86	128	18	)	)	PUNCT
ma-86	128	19	2	2	NUM
ma-86	128	20	σ̂2	σ̂2	NOUN
ma-86	128	21	h	h	NOUN
ma-86	128	22	,	,	PUNCT
ma-86	128	23	ti	ti	PROPN
ma-86	128	24	(	(	PUNCT
ma-86	128	25	ϑ	ϑ	X
ma-86	128	26	,	,	PUNCT
ma-86	128	27	λ̂n)/λ̂nwhere	λ̂n)/λ̂nwhere	VERB
ma-86	128	28	the	the	DET
ma-86	128	29	estimates	estimate	NOUN
ma-86	128	30	of	of	ADP
ma-86	128	31	the	the	DET
ma-86	128	32	volatility	volatility	NOUN
ma-86	128	33	σ2	σ2	PROPN
ma-86	128	34	h	h	PROPN
ma-86	128	35	,	,	PUNCT
ma-86	128	36	ti	ti	X
ma-86	128	37	,	,	PUNCT
ma-86	128	38	i	i	PRON
ma-86	128	39	=	=	NOUN
ma-86	128	40	1	1	NUM
ma-86	128	41	,	,	PUNCT
ma-86	128	42	2	2	NUM
ma-86	128	43	,	,	PUNCT
ma-86	128	44	.	.	PUNCT
ma-86	128	45	.	.	PUNCT
ma-86	128	46	.	.	PUNCT
ma-86	129	1	,	,	PUNCT
ma-86	129	2	n	n	PRON
ma-86	129	3	are	be	AUX
ma-86	129	4	given	give	VERB
ma-86	129	5	by	by	ADP
ma-86	129	6	σ̂2	σ̂2	PROPN
ma-86	129	7	h	h	PROPN
ma-86	129	8	,	,	PUNCT
ma-86	129	9	ti	ti	PROPN
ma-86	129	10	(	(	PUNCT
ma-86	129	11	ϑ	ϑ	X
ma-86	129	12	,	,	PUNCT
ma-86	129	13	λn	λn	NOUN
ma-86	129	14	)	)	PUNCT
ma-86	129	15	:	:	PUNCT
ma-86	129	16	=	=	SYM
ma-86	129	17	exp(µ+	exp(µ+	PROPN
ma-86	129	18	e−α∆tixh	e−α∆tixh	NOUN
ma-86	129	19	,	,	PUNCT
ma-86	129	20	ti−1	ti−1	NOUN
ma-86	129	21	(	(	PUNCT
ma-86	129	22	ϑ	ϑ	X
ma-86	129	23	,	,	PUNCT
ma-86	129	24	λ)−	λ)−	PROPN
ma-86	129	25	ĉ∆ti	ĉ∆ti	PROPN
ma-86	129	26	)	)	PUNCT
ma-86	129	27	,	,	PUNCT
ma-86	129	28	ß	ß	NOUN
ma-86	129	29	=	=	SYM
ma-86	129	30	1	1	NUM
ma-86	129	31	,	,	PUNCT
ma-86	129	32	2	2	NUM
ma-86	129	33	,	,	PUNCT
ma-86	129	34	.	.	PUNCT
ma-86	129	35	.	.	PUNCT
ma-86	130	1	.	.	PUNCT
ma-86	131	1	,	,	PUNCT
ma-86	131	2	n	n	PROPN
ma-86	131	3	and	and	CCONJ
ma-86	131	4	given	give	VERB
ma-86	131	5	the	the	DET
ma-86	131	6	parameters	parameter	NOUN
ma-86	131	7	ϑ	ϑ	X
ma-86	131	8	and	and	CCONJ
ma-86	131	9	λ	λ	X
ma-86	131	10	the	the	DET
ma-86	131	11	estimates	estimate	NOUN
ma-86	131	12	of	of	ADP
ma-86	131	13	the	the	DET
ma-86	131	14	state	state	NOUN
ma-86	131	15	process	process	NOUN
ma-86	131	16	x	x	PRON
ma-86	131	17	are	be	AUX
ma-86	131	18	given	give	VERB
ma-86	131	19	by	by	ADP
ma-86	131	20	the	the	DET
ma-86	131	21	recursion	recursion	NOUN
ma-86	131	22	x̂h	x̂h	NUM
ma-86	131	23	,	,	PUNCT
ma-86	131	24	ti	ti	X
ma-86	131	25	=	=	PUNCT
ma-86	131	26	e−θ∆ti	e−θ∆ti	NOUN
ma-86	131	27	x̂h	x̂h	NOUN
ma-86	131	28	,	,	PUNCT
ma-86	131	29	ti−1	ti−1	NOUN
ma-86	131	30	+	+	CCONJ
ma-86	131	31	α	α	PROPN
ma-86	131	32	sh	sh	PROPN
ma-86	131	33	,	,	PUNCT
ma-86	131	34	ti	ti	X
ma-86	131	35	σ̂ti	σ̂ti	NOUN
ma-86	131	36	(	(	PUNCT
ma-86	131	37	ϑ	ϑ	X
ma-86	131	38	,	,	PUNCT
ma-86	131	39	λ	λ	NOUN
ma-86	131	40	)	)	PUNCT
ma-86	132	1	+	+	CCONJ
ma-86	132	2	(	(	PUNCT
ma-86	132	3	sh	sh	INTJ
ma-86	132	4	,	,	PUNCT
ma-86	132	5	ti	ti	X
ma-86	132	6	σ̂ti	σ̂ti	NOUN
ma-86	132	7	(	(	PUNCT
ma-86	132	8	ϑ	ϑ	X
ma-86	132	9	,	,	PUNCT
ma-86	132	10	λ	λ	NOUN
ma-86	132	11	)	)	PUNCT
ma-86	132	12	−	−	PROPN
ma-86	132	13	ĉ∆ti	ĉ∆ti	PROPN
ma-86	132	14	)	)	PUNCT
ma-86	132	15	,	,	PUNCT
ma-86	132	16	i	i	PRON
ma-86	132	17	=	=	NOUN
ma-86	132	18	1	1	NUM
ma-86	132	19	,	,	PUNCT
ma-86	132	20	2	2	NUM
ma-86	132	21	,	,	PUNCT
ma-86	132	22	.	.	PUNCT
ma-86	132	23	.	.	PUNCT
ma-86	133	1	.	.	PUNCT
ma-86	134	1	,	,	PUNCT
ma-86	134	2	n	n	PROPN
ma-86	134	3	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	VERB
ma-86	134	4	eur	eur	PROPN
ma-86	134	5	.	.	PUNCT
ma-86	135	1	j.	j.	PROPN
ma-86	135	2	math	math	PROPN
ma-86	135	3	.	.	PUNCT
ma-86	136	1	anal	anal	PROPN
ma-86	136	2	.	.	PUNCT
ma-86	137	1	10.28924	10.28924	NUM
ma-86	137	2	/	/	SYM
ma-86	137	3	ada	ada	NOUN
ma-86	137	4	/	/	SYM
ma-86	137	5	ma.2.15	ma.2.15	PROPN
ma-86	137	6	6	6	NUM
ma-86	137	7	note	note	NOUN
ma-86	137	8	that	that	SCONJ
ma-86	137	9	e(|w	e(|w	PROPN
ma-86	137	10	|	|	NOUN
ma-86	137	11	)	)	PUNCT
ma-86	137	12	=	=	SYM
ma-86	137	13	√	√	ADP
ma-86	137	14	2	2	NUM
ma-86	137	15	πλ	πλ	NOUN
ma-86	137	16	,	,	PUNCT
ma-86	137	17	w	w	NOUN
ma-86	137	18	∼	∼	NOUN
ma-86	137	19	n(0	n(0	NOUN
ma-86	137	20	,	,	PUNCT
ma-86	137	21	1	1	NUM
ma-86	137	22	/	/	SYM
ma-86	137	23	λ).here	λ).here	PROPN
ma-86	137	24	the	the	DET
ma-86	137	25	approximation	approximation	NOUN
ma-86	137	26	(	(	PUNCT
ma-86	137	27	1−e−z	1−e−z	NUM
ma-86	137	28	)	)	PUNCT
ma-86	138	1	≈	≈	PROPN
ma-86	138	2	z	z	NOUN
ma-86	138	3	for	for	ADP
ma-86	138	4	small	small	ADJ
ma-86	138	5	z	z	NOUN
ma-86	138	6	is	be	AUX
ma-86	138	7	used	use	VERB
ma-86	138	8	and	and	CCONJ
ma-86	138	9	sh	sh	INTJ
ma-86	138	10	,	,	PUNCT
ma-86	138	11	ti	ti	X
ma-86	138	12	σ̂ti	σ̂ti	NOUN
ma-86	138	13	(	(	PUNCT
ma-86	138	14	ϑ,λ	ϑ,λ	NOUN
ma-86	138	15	)	)	PUNCT
ma-86	138	16	approximates	approximate	VERB
ma-86	138	17	the	the	DET
ma-86	138	18	innovation	innovation	NOUN
ma-86	138	19	zi	zi	NOUN
ma-86	138	20	.	.	PUNCT
ma-86	139	1	the	the	DET
ma-86	139	2	recursion	recursion	NOUN
ma-86	139	3	needs	need	VERB
ma-86	139	4	a	a	DET
ma-86	139	5	starting	starting	NOUN
ma-86	139	6	value	value	NOUN
ma-86	139	7	x̂h,0	x̂h,0	PUNCT
ma-86	140	1	which	which	PRON
ma-86	140	2	will	will	AUX
ma-86	140	3	be	be	AUX
ma-86	140	4	set	set	VERB
ma-86	140	5	equal	equal	ADJ
ma-86	140	6	to	to	ADP
ma-86	140	7	the	the	DET
ma-86	140	8	mean	mean	ADJ
ma-86	140	9	value	value	NOUN
ma-86	140	10	of	of	ADP
ma-86	140	11	thestationary	thestationary	ADJ
ma-86	140	12	distribution	distribution	NOUN
ma-86	140	13	of	of	ADP
ma-86	140	14	x	x	PUNCT
ma-86	140	15	which	which	PRON
ma-86	140	16	is	be	AUX
ma-86	140	17	zero	zero	NUM
ma-86	140	18	.	.	PUNCT
ma-86	141	1	the	the	DET
ma-86	141	2	mean	mean	ADJ
ma-86	141	3	value	value	NOUN
ma-86	141	4	zero	zero	NUM
ma-86	141	5	of	of	ADP
ma-86	141	6	the	the	DET
ma-86	141	7	stationary	stationary	ADJ
ma-86	141	8	distribution	distribution	NOUN
ma-86	141	9	of	of	ADP
ma-86	141	10	x	x	X
ma-86	141	11	.qmle	.qmle	ADP
ma-86	141	12	of	of	ADP
ma-86	141	13	ϑ	ϑ	PROPN
ma-86	141	14	is	be	AUX
ma-86	141	15	defined	define	VERB
ma-86	141	16	as	as	ADP
ma-86	141	17	ϑ̂n	ϑ̂n	NOUN
ma-86	141	18	:	:	PUNCT
ma-86	141	19	=	=	SYM
ma-86	141	20	arg	arg	NOUN
ma-86	141	21	max	max	PROPN
ma-86	141	22	ϑ∈θ	ϑ∈θ	NOUN
ma-86	141	23	l(ϑ|s∆	l(ϑ|s∆	NOUN
ma-86	141	24	h	h	NOUN
ma-86	141	25	,	,	PUNCT
ma-86	141	26	λ̂n	λ̂n	NOUN
ma-86	141	27	)	)	PUNCT
ma-86	141	28	.	.	PUNCT
ma-86	142	1	let	let	VERB
ma-86	142	2	(	(	PUNCT
ma-86	142	3	ω	ω	PROPN
ma-86	142	4	,	,	PUNCT
ma-86	142	5	f	f	PROPN
ma-86	142	6	,	,	PUNCT
ma-86	142	7	{	{	PUNCT
ma-86	142	8	ft}t≥0	ft}t≥0	NOUN
ma-86	142	9	,	,	PUNCT
ma-86	142	10	p	p	NOUN
ma-86	142	11	)	)	PUNCT
ma-86	142	12	be	be	AUX
ma-86	142	13	the	the	DET
ma-86	142	14	stochastic	stochastic	ADJ
ma-86	142	15	basis	basis	NOUN
ma-86	142	16	on	on	ADP
ma-86	142	17	which	which	PRON
ma-86	142	18	is	be	AUX
ma-86	142	19	defined	define	VERB
ma-86	142	20	the	the	DET
ma-86	142	21	ornstein	ornstein	PROPN
ma-86	142	22	-	-	PUNCT
ma-86	142	23	uhlenbeck	uhlenbeck	PROPN
ma-86	142	24	process	process	NOUN
ma-86	142	25	xt	xt	PUNCT
ma-86	143	1	satisfying	satisfy	VERB
ma-86	143	2	the	the	DET
ma-86	143	3	itô	itô	PROPN
ma-86	143	4	stochastic	stochastic	ADJ
ma-86	143	5	differential	differential	NOUN
ma-86	143	6	equation	equation	NOUN
ma-86	143	7	dxt	dxt	PROPN
ma-86	143	8	=	=	PUNCT
ma-86	144	1	−θxtdt	−θxtdt	PROPN
ma-86	145	1	+	+	CCONJ
ma-86	145	2	dmh	dmh	PROPN
ma-86	145	3	t	t	PROPN
ma-86	145	4	,	,	PUNCT
ma-86	145	5	t	t	PROPN
ma-86	145	6	≥	≥	PROPN
ma-86	145	7	0	0	NUM
ma-86	145	8	,	,	PUNCT
ma-86	145	9	where	where	SCONJ
ma-86	145	10	{	{	PUNCT
ma-86	145	11	mh	mh	PROPN
ma-86	145	12	t	t	PROPN
ma-86	145	13	}	}	PUNCT
ma-86	145	14	is	be	AUX
ma-86	145	15	a	a	DET
ma-86	145	16	fractional	fractional	ADJ
ma-86	145	17	levy	levy	NOUN
ma-86	145	18	motion	motion	NOUN
ma-86	145	19	with	with	ADP
ma-86	145	20	h	h	PROPN
ma-86	145	21	>	>	X
ma-86	145	22	1/2	1/2	NUM
ma-86	145	23	with	with	ADP
ma-86	145	24	the	the	DET
ma-86	145	25	filtration	filtration	NOUN
ma-86	145	26	{	{	PUNCT
ma-86	145	27	ft}t≥0	ft}t≥0	NOUN
ma-86	145	28	and	and	CCONJ
ma-86	145	29	θ	θ	PROPN
ma-86	145	30	∈	∈	PROPN
ma-86	145	31	r+	r+	VERB
ma-86	145	32	isthe	isthe	ADJ
ma-86	145	33	unknown	unknown	ADJ
ma-86	145	34	parameter	parameter	NOUN
ma-86	145	35	to	to	PART
ma-86	145	36	be	be	AUX
ma-86	145	37	estimated	estimate	VERB
ma-86	145	38	on	on	ADP
ma-86	145	39	the	the	DET
ma-86	145	40	basis	basis	NOUN
ma-86	145	41	of	of	ADP
ma-86	145	42	completely	completely	ADV
ma-86	145	43	directly	directly	ADV
ma-86	145	44	observed	observe	VERB
ma-86	145	45	continuousobservation	continuousobservation	NOUN
ma-86	145	46	of	of	ADP
ma-86	145	47	the	the	DET
ma-86	145	48	process	process	NOUN
ma-86	145	49	{	{	PUNCT
ma-86	145	50	xt	xt	ADP
ma-86	145	51	}	}	PUNCT
ma-86	145	52	on	on	ADP
ma-86	145	53	the	the	DET
ma-86	145	54	time	time	NOUN
ma-86	145	55	interval	interval	NOUN
ma-86	145	56	[	[	X
ma-86	145	57	0	0	NUM
ma-86	145	58	,	,	PUNCT
ma-86	145	59	t	t	X
ma-86	145	60	]	]	PUNCT
ma-86	145	61	.	.	PUNCT
ma-86	146	1	observe	observe	VERB
ma-86	146	2	that	that	PRON
ma-86	146	3	xt	xt	PUNCT
ma-86	147	1	=	=	SYM
ma-86	147	2	∫	∫	PROPN
ma-86	147	3	t	t	PROPN
ma-86	147	4	−∞	−∞	ADP
ma-86	147	5	e−θ(t−s)dmh	e−θ(t−s)dmh	PROPN
ma-86	147	6	s	s	PART
ma-86	147	7	.	.	PUNCT
ma-86	148	1	this	this	DET
ma-86	148	2	process	process	NOUN
ma-86	148	3	is	be	AUX
ma-86	148	4	stationary	stationary	ADJ
ma-86	148	5	and	and	CCONJ
ma-86	148	6	is	be	AUX
ma-86	148	7	a	a	DET
ma-86	148	8	process	process	NOUN
ma-86	148	9	with	with	ADP
ma-86	148	10	long	long	ADJ
ma-86	148	11	memory	memory	NOUN
ma-86	148	12	.	.	PUNCT
ma-86	149	1	it	it	PRON
ma-86	149	2	can	can	AUX
ma-86	149	3	be	be	AUX
ma-86	149	4	shown	show	VERB
ma-86	149	5	that	that	SCONJ
ma-86	149	6	xti	xti	PROPN
ma-86	149	7	is	be	AUX
ma-86	149	8	astationary	astationary	ADJ
ma-86	149	9	discrete	discrete	ADJ
ma-86	149	10	time	time	NOUN
ma-86	149	11	ar(1	ar(1	NOUN
ma-86	149	12	)	)	PUNCT
ma-86	149	13	process	process	NOUN
ma-86	149	14	with	with	ADP
ma-86	149	15	autoregression	autoregression	NOUN
ma-86	149	16	coefficient	coefficient	NOUN
ma-86	149	17	φ	φ	PROPN
ma-86	149	18	∈	∈	PROPN
ma-86	149	19	(	(	PUNCT
ma-86	149	20	0	0	NUM
ma-86	149	21	,	,	PUNCT
ma-86	149	22	1	1	NUM
ma-86	149	23	)	)	PUNCT
ma-86	149	24	with	with	ADP
ma-86	149	25	the	the	DET
ma-86	149	26	followingrepresentation	followingrepresentation	NOUN
ma-86	149	27	xti	xti	X
ma-86	150	1	=	=	SYM
ma-86	150	2	φxti−1	φxti−1	PROPN
ma-86	150	3	+	+	CCONJ
ma-86	150	4	εti−1where	εti−1where	X
ma-86	150	5	φ	φ	NOUN
ma-86	150	6	=	=	SYM
ma-86	150	7	e−θ∆	e−θ∆	PROPN
ma-86	150	8	and	and	CCONJ
ma-86	150	9	εti−1	εti−1	PROPN
ma-86	150	10	=	=	SYM
ma-86	150	11	∫	∫	PROPN
ma-86	150	12	ti	ti	PROPN
ma-86	150	13	ti−1	ti−1	NOUN
ma-86	150	14	e−θ(ti−u)dmh	e−θ(ti−u)dmh	PROPN
ma-86	150	15	u	u	NOUN
ma-86	150	16	.then	.then	NOUN
ma-86	150	17	the	the	DET
ma-86	150	18	problem	problem	NOUN
ma-86	150	19	is	be	AUX
ma-86	150	20	a	a	DET
ma-86	150	21	ar(1	ar(1	NOUN
ma-86	150	22	)	)	PUNCT
ma-86	150	23	estimation	estimation	NOUN
ma-86	150	24	with	with	ADP
ma-86	150	25	non	non	ADJ
ma-86	150	26	-	-	ADJ
ma-86	150	27	gaussian	gaussian	ADJ
ma-86	150	28	non	non	ADJ
ma-86	150	29	-	-	ADJ
ma-86	150	30	martingale	martingale	ADJ
ma-86	150	31	error	error	NOUN
ma-86	150	32	.	.	PUNCT
ma-86	151	1	for	for	ADP
ma-86	151	2	equidistantsampling	equidistantsample	VERB
ma-86	151	3	,	,	PUNCT
ma-86	151	4	one	one	PRON
ma-86	151	5	can	can	AUX
ma-86	151	6	study	study	VERB
ma-86	151	7	the	the	DET
ma-86	151	8	least	least	ADJ
ma-86	151	9	squares	square	NOUN
ma-86	151	10	estimator	estimator	NOUN
ma-86	151	11	which	which	PRON
ma-86	151	12	boils	boil	VERB
ma-86	151	13	down	down	ADP
ma-86	151	14	to	to	ADP
ma-86	151	15	the	the	DET
ma-86	151	16	study	study	NOUN
ma-86	151	17	of	of	ADP
ma-86	151	18	error	error	NOUN
ma-86	151	19	distribu	distribu	NOUN
ma-86	151	20	-	-	PUNCT
ma-86	151	21	tion	tion	NOUN
ma-86	151	22	for	for	ADP
ma-86	151	23	non	non	NOUN
ma-86	151	24	-	-	NOUN
ma-86	151	25	semimartingales	semimartingale	NOUN
ma-86	151	26	.	.	PUNCT
ma-86	152	1	one	one	PRON
ma-86	152	2	can	can	AUX
ma-86	152	3	specialize	specialize	VERB
ma-86	152	4	to	to	ADP
ma-86	152	5	the	the	DET
ma-86	152	6	case	case	NOUN
ma-86	152	7	when	when	SCONJ
ma-86	152	8	m	m	PROPN
ma-86	152	9	is	be	AUX
ma-86	152	10	a	a	DET
ma-86	152	11	either	either	CCONJ
ma-86	152	12	a	a	DET
ma-86	152	13	gamma	gamma	NOUN
ma-86	152	14	processor	processor	NOUN
ma-86	152	15	an	an	DET
ma-86	152	16	inverse	inverse	ADJ
ma-86	152	17	gaussian	gaussian	NOUN
ma-86	152	18	process	process	NOUN
ma-86	152	19	in	in	ADP
ma-86	152	20	order	order	NOUN
ma-86	152	21	to	to	PART
ma-86	152	22	have	have	AUX
ma-86	152	23	infinite	infinite	ADJ
ma-86	152	24	number	number	NOUN
ma-86	152	25	of	of	ADP
ma-86	152	26	jumps	jump	NOUN
ma-86	152	27	in	in	ADP
ma-86	152	28	a	a	DET
ma-86	152	29	finite	finite	ADJ
ma-86	152	30	time	time	NOUN
ma-86	152	31	inter	inter	NOUN
ma-86	152	32	-	-	NOUN
ma-86	152	33	val	val	ADJ
ma-86	152	34	unlike	unlike	ADP
ma-86	152	35	the	the	DET
ma-86	152	36	compound	compound	NOUN
ma-86	152	37	poissoan	poissoan	NOUN
ma-86	152	38	case	case	NOUN
ma-86	152	39	which	which	PRON
ma-86	152	40	have	have	VERB
ma-86	152	41	finite	finite	ADJ
ma-86	152	42	number	number	NOUN
ma-86	152	43	of	of	ADP
ma-86	152	44	jumps	jump	NOUN
ma-86	152	45	in	in	ADP
ma-86	152	46	a	a	DET
ma-86	152	47	finite	finite	ADJ
ma-86	152	48	time	time	NOUN
ma-86	152	49	interval.these	interval.these	ADJ
ma-86	152	50	fractional	fractional	ADJ
ma-86	152	51	gamma	gamma	NOUN
ma-86	152	52	and	and	CCONJ
ma-86	152	53	fractional	fractional	ADJ
ma-86	152	54	inverse	inverse	NOUN
ma-86	152	55	gaussian	gaussian	NOUN
ma-86	152	56	ornstein	ornstein	PROPN
ma-86	152	57	-	-	PUNCT
ma-86	152	58	uhlenbeck	uhlenbeck	PROPN
ma-86	152	59	(	(	PUNCT
ma-86	152	60	flou	flou	NOUN
ma-86	152	61	)	)	PUNCT
ma-86	152	62	processes	process	NOUN
ma-86	152	63	arelou	arelou	NOUN
ma-86	152	64	processes	process	NOUN
ma-86	152	65	which	which	PRON
ma-86	152	66	include	include	VERB
ma-86	152	67	long	long	ADJ
ma-86	152	68	memory	memory	NOUN
ma-86	152	69	.	.	PUNCT
ma-86	153	1	in	in	ADP
ma-86	153	2	the	the	DET
ma-86	153	3	next	next	ADJ
ma-86	153	4	section	section	NOUN
ma-86	153	5	we	we	PRON
ma-86	153	6	deal	deal	VERB
ma-86	153	7	with	with	ADP
ma-86	153	8	completely	completely	ADV
ma-86	153	9	observedprocess.the	observedprocess.the	DET
ma-86	153	10	rest	rest	NOUN
ma-86	153	11	of	of	ADP
ma-86	153	12	the	the	DET
ma-86	153	13	paper	paper	NOUN
ma-86	153	14	is	be	AUX
ma-86	153	15	organized	organize	VERB
ma-86	153	16	as	as	SCONJ
ma-86	153	17	follows	follow	VERB
ma-86	153	18	:	:	PUNCT
ma-86	153	19	section	section	NOUN
ma-86	153	20	2	2	NUM
ma-86	153	21	contains	contain	VERB
ma-86	153	22	model	model	NOUN
ma-86	153	23	,	,	PUNCT
ma-86	153	24	assumptions	assumption	VERB
ma-86	153	25	andpreliminaries	andpreliminarie	NOUN
ma-86	153	26	.	.	PUNCT
ma-86	154	1	section	section	NOUN
ma-86	154	2	3	3	NUM
ma-86	154	3	contains	contain	VERB
ma-86	154	4	the	the	DET
ma-86	154	5	asymptotic	asymptotic	ADJ
ma-86	154	6	properties	property	NOUN
ma-86	154	7	of	of	ADP
ma-86	154	8	quasi	quasi	ADJ
ma-86	154	9	likelihood	likelihood	NOUN
ma-86	154	10	estimator	estimator	NOUN
ma-86	154	11	.	.	PUNCT
ma-86	155	1	2	2	X
ma-86	155	2	.	.	X
ma-86	155	3	flspde	flspde	NOUN
ma-86	155	4	model	model	NOUN
ma-86	155	5	and	and	CCONJ
ma-86	155	6	preliminaries	preliminary	NOUN
ma-86	155	7	in	in	ADP
ma-86	155	8	order	order	NOUN
ma-86	155	9	to	to	PART
ma-86	155	10	introduce	introduce	VERB
ma-86	155	11	fractional	fractional	ADJ
ma-86	155	12	levy	levy	NOUN
ma-86	155	13	stochastic	stochastic	ADJ
ma-86	155	14	partial	partial	ADJ
ma-86	155	15	differential	differential	NOUN
ma-86	155	16	equation	equation	NOUN
ma-86	155	17	(	(	PUNCT
ma-86	155	18	flsode	flsode	NOUN
ma-86	155	19	)	)	PUNCT
ma-86	155	20	we	we	PRON
ma-86	155	21	proceedas	proceedas	PROPN
ma-86	155	22	follows	follow	VERB
ma-86	155	23	.	.	PUNCT
ma-86	156	1	let	let	VERB
ma-86	156	2	us	we	PRON
ma-86	156	3	fix	fix	VERB
ma-86	156	4	θ0	θ0	NOUN
ma-86	156	5	,	,	PUNCT
ma-86	156	6	the	the	DET
ma-86	156	7	unknown	unknown	ADJ
ma-86	156	8	true	true	ADJ
ma-86	156	9	value	value	NOUN
ma-86	156	10	of	of	ADP
ma-86	156	11	the	the	DET
ma-86	156	12	parameter	parameter	NOUN
ma-86	156	13	θ	θ	PROPN
ma-86	156	14	.	.	PUNCT
ma-86	157	1	let	let	AUX
ma-86	157	2	(	(	PUNCT
ma-86	157	3	ω	ω	PROPN
ma-86	157	4	,	,	PUNCT
ma-86	157	5	f	f	PROPN
ma-86	157	6	,	,	PUNCT
ma-86	157	7	p	p	NOUN
ma-86	157	8	)	)	PUNCT
ma-86	157	9	be	be	AUX
ma-86	157	10	a	a	DET
ma-86	157	11	complete	complete	ADJ
ma-86	157	12	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	X
ma-86	157	13	eur	eur	PROPN
ma-86	157	14	.	.	PUNCT
ma-86	158	1	j.	j.	PROPN
ma-86	158	2	math	math	PROPN
ma-86	158	3	.	.	PUNCT
ma-86	159	1	anal	anal	PROPN
ma-86	159	2	.	.	PUNCT
ma-86	160	1	10.28924	10.28924	NUM
ma-86	160	2	/	/	SYM
ma-86	160	3	ada	ada	NOUN
ma-86	160	4	/	/	SYM
ma-86	160	5	ma.2.15	ma.2.15	PROPN
ma-86	160	6	7probability	7probability	NUM
ma-86	160	7	space	space	NOUN
ma-86	160	8	and	and	CCONJ
ma-86	160	9	w	w	PROPN
ma-86	160	10	(	(	PUNCT
ma-86	160	11	t	t	PROPN
ma-86	160	12	,	,	PUNCT
ma-86	160	13	x	x	PRON
ma-86	160	14	)	)	PUNCT
ma-86	160	15	be	be	VERB
ma-86	160	16	a	a	DET
ma-86	160	17	process	process	NOUN
ma-86	160	18	on	on	ADP
ma-86	160	19	this	this	DET
ma-86	160	20	space	space	NOUN
ma-86	160	21	with	with	ADP
ma-86	160	22	values	value	NOUN
ma-86	160	23	in	in	ADP
ma-86	160	24	the	the	DET
ma-86	160	25	schwarz	schwarz	PROPN
ma-86	160	26	space	space	NOUN
ma-86	160	27	ofdistributions	ofdistribution	NOUN
ma-86	160	28	d′(g	d′(g	PUNCT
ma-86	160	29	)	)	PUNCT
ma-86	160	30	such	such	ADJ
ma-86	160	31	that	that	PRON
ma-86	160	32	for	for	ADP
ma-86	160	33	φ	φ	PROPN
ma-86	160	34	,	,	PUNCT
ma-86	161	1	ψ	ψ	X
ma-86	161	2	∈	∈	ADP
ma-86	161	3	c∞0	c∞0	X
ma-86	161	4	(	(	PUNCT
ma-86	161	5	g	g	NOUN
ma-86	161	6	)	)	PUNCT
ma-86	161	7	,	,	PUNCT
ma-86	161	8	‖φ‖−1	‖φ‖−1	PROPN
ma-86	161	9	l2(g	l2(g	NOUN
ma-86	161	10	)	)	PUNCT
ma-86	161	11	〈	〈	PROPN
ma-86	161	12	w	w	PROPN
ma-86	161	13	(	(	PUNCT
ma-86	161	14	t	t	PROPN
ma-86	161	15	,	,	PUNCT
ma-86	161	16	·	·	PUNCT
ma-86	161	17	)	)	PUNCT
ma-86	161	18	,	,	PUNCT
ma-86	161	19	φ	φ	X
ma-86	161	20	(	(	PUNCT
ma-86	161	21	·	·	PUNCT
ma-86	161	22	)	)	PUNCT
ma-86	161	23	〉	〉	PROPN
ma-86	161	24	is	be	AUX
ma-86	161	25	a	a	DET
ma-86	161	26	one	one	NUM
ma-86	161	27	dimensionalwiener	dimensionalwiener	NOUN
ma-86	161	28	process	process	NOUN
ma-86	161	29	and	and	CCONJ
ma-86	161	30	e(〈w	e(〈w	NOUN
ma-86	161	31	(	(	PUNCT
ma-86	161	32	s	s	PROPN
ma-86	161	33	,	,	PUNCT
ma-86	161	34	·	·	PUNCT
ma-86	161	35	)	)	PUNCT
ma-86	161	36	,	,	PUNCT
ma-86	161	37	φ(·)〉〈w	φ(·)〉〈w	PROPN
ma-86	161	38	(	(	PUNCT
ma-86	161	39	t	t	PROPN
ma-86	161	40	,	,	PUNCT
ma-86	161	41	·	·	PUNCT
ma-86	161	42	)	)	PUNCT
ma-86	161	43	,	,	PUNCT
ma-86	161	44	ψ	ψ	X
ma-86	161	45	(	(	PUNCT
ma-86	161	46	·	·	PUNCT
ma-86	161	47	)	)	PUNCT
ma-86	161	48	〉	〉	NOUN
ma-86	161	49	)	)	PUNCT
ma-86	161	50	=	=	PRON
ma-86	162	1	(	(	PUNCT
ma-86	162	2	s	s	VERB
ma-86	162	3	∧	∧	PROPN
ma-86	162	4	t)(φ	t)(φ	NOUN
ma-86	162	5	,	,	PUNCT
ma-86	162	6	ψ)l2(g).this	ψ)l2(g).this	PRON
ma-86	162	7	process	process	NOUN
ma-86	162	8	is	be	AUX
ma-86	162	9	usually	usually	ADV
ma-86	162	10	referred	refer	VERB
ma-86	162	11	to	to	ADP
ma-86	162	12	as	as	ADP
ma-86	162	13	the	the	DET
ma-86	162	14	cylindrical	cylindrical	ADJ
ma-86	162	15	brownian	brownian	ADJ
ma-86	162	16	motion	motion	NOUN
ma-86	162	17	(	(	PUNCT
ma-86	162	18	c.b.m.).we	c.b.m.).we	NOUN
ma-86	162	19	assume	assume	VERB
ma-86	162	20	that	that	SCONJ
ma-86	162	21	there	there	PRON
ma-86	162	22	exists	exist	VERB
ma-86	162	23	a	a	DET
ma-86	162	24	complete	complete	ADJ
ma-86	162	25	orthonormal	orthonormal	ADJ
ma-86	162	26	system	system	NOUN
ma-86	162	27	{	{	PUNCT
ma-86	162	28	hi}∞i=1	hi}∞i=1	X
ma-86	162	29	in	in	ADP
ma-86	162	30	l2(g	l2(g	NOUN
ma-86	162	31	)	)	PUNCT
ma-86	162	32	)	)	PUNCT
ma-86	163	1	such	such	ADJ
ma-86	163	2	that	that	DET
ma-86	163	3	forevery	forevery	NOUN
ma-86	163	4	i	i	NOUN
ma-86	163	5	=	=	NOUN
ma-86	163	6	1	1	NUM
ma-86	163	7	,	,	PUNCT
ma-86	163	8	2	2	NUM
ma-86	163	9	,	,	PUNCT
ma-86	163	10	.	.	PUNCT
ma-86	163	11	.	.	PUNCT
ma-86	163	12	.	.	PUNCT
ma-86	164	1	,	,	PUNCT
ma-86	165	1	hi	hi	INTJ
ma-86	165	2	∈	∈	PROPN
ma-86	165	3	wm,2	wm,2	PROPN
ma-86	165	4	0	0	PUNCT
ma-86	166	1	(	(	PUNCT
ma-86	166	2	g	g	NOUN
ma-86	166	3	)	)	PUNCT
ma-86	166	4	∩	∩	NOUN
ma-86	166	5	c∞(g	c∞(g	PROPN
ma-86	166	6	)	)	PUNCT
ma-86	166	7	and	and	CCONJ
ma-86	166	8	λθhi	λθhi	NOUN
ma-86	166	9	=	=	SYM
ma-86	166	10	βi(θ)hi	βi(θ)hi	NOUN
ma-86	166	11	,	,	PUNCT
ma-86	166	12	and	and	CCONJ
ma-86	166	13	lθhi	lθhi	PROPN
ma-86	166	14	=	=	PUNCT
ma-86	166	15	µi(θ)hi	µi(θ)hi	PROPN
ma-86	166	16	for	for	ADP
ma-86	166	17	all	all	DET
ma-86	166	18	θ	θ	PRON
ma-86	166	19	∈	∈	NOUN
ma-86	166	20	θ	θ	NOUN
ma-86	166	21	where	where	SCONJ
ma-86	166	22	lθ	lθ	NOUN
ma-86	166	23	is	be	AUX
ma-86	166	24	a	a	DET
ma-86	166	25	closed	closed	ADJ
ma-86	166	26	self	self	NOUN
ma-86	166	27	adjoint	adjoint	NOUN
ma-86	166	28	extension	extension	NOUN
ma-86	166	29	of	of	ADP
ma-86	166	30	aθ	aθ	NOUN
ma-86	166	31	,	,	PUNCT
ma-86	166	32	λθ	λθ	X
ma-86	166	33	:	:	PUNCT
ma-86	166	34	=	=	SYM
ma-86	166	35	(	(	PUNCT
ma-86	166	36	k(θ)i	k(θ)i	PROPN
ma-86	166	37	−	−	PROPN
ma-86	166	38	lθ)1/2	lθ)1/2	PROPN
ma-86	166	39	m	m	PROPN
ma-86	166	40	,	,	PUNCT
ma-86	166	41	k(θ	k(θ	PROPN
ma-86	166	42	)	)	PUNCT
ma-86	166	43	is	be	AUX
ma-86	166	44	a	a	DET
ma-86	166	45	constant	constant	ADJ
ma-86	166	46	andand	andand	NOUN
ma-86	166	47	the	the	DET
ma-86	166	48	spectrum	spectrum	NOUN
ma-86	166	49	of	of	ADP
ma-86	166	50	the	the	DET
ma-86	166	51	operator	operator	NOUN
ma-86	166	52	λθ	λθ	ADP
ma-86	166	53	consists	consist	NOUN
ma-86	166	54	of	of	ADP
ma-86	166	55	eigen	eigen	PROPN
ma-86	166	56	values	value	NOUN
ma-86	166	57	{	{	PUNCT
ma-86	166	58	βi(θ)}∞i=1	βi(θ)}∞i=1	NUM
ma-86	166	59	of	of	ADP
ma-86	166	60	finite	finite	PROPN
ma-86	166	61	multiplicities	multiplicity	NOUN
ma-86	166	62	and	and	CCONJ
ma-86	166	63	µi	µi	PROPN
ma-86	166	64	=	=	PROPN
ma-86	166	65	−β2	−β2	PROPN
ma-86	166	66	m	m	VERB
ma-86	166	67	i	i	PROPN
ma-86	166	68	+	+	CCONJ
ma-86	166	69	k(θ).cflp	k(θ).cflp	PROPN
ma-86	166	70	mh(t	mh(t	PUNCT
ma-86	166	71	)	)	PUNCT
ma-86	166	72	can	can	AUX
ma-86	166	73	be	be	AUX
ma-86	166	74	expanded	expand	VERB
ma-86	166	75	in	in	ADP
ma-86	166	76	the	the	DET
ma-86	166	77	series	series	NOUN
ma-86	166	78	mh(t	mh(t	NOUN
ma-86	166	79	,	,	PUNCT
ma-86	166	80	x	x	X
ma-86	166	81	)	)	PUNCT
ma-86	166	82	=	=	PUNCT
ma-86	167	1	∞∑	∞∑	NUM
ma-86	167	2	i=1	i=1	PROPN
ma-86	167	3	mh	mh	PROPN
ma-86	167	4	,	,	PUNCT
ma-86	167	5	i(t)hi(x	i(t)hi(x	NOUN
ma-86	167	6	)	)	PUNCT
ma-86	167	7	where	where	SCONJ
ma-86	167	8	{	{	PUNCT
ma-86	167	9	mh	mh	PROPN
ma-86	167	10	,	,	PUNCT
ma-86	167	11	i(t)}∞i=1	i(t)}∞i=1	PROPN
ma-86	167	12	are	be	AUX
ma-86	167	13	independent	independent	ADJ
ma-86	167	14	one	one	NUM
ma-86	167	15	dimensional	dimensional	ADJ
ma-86	167	16	flps	flp	NOUN
ma-86	167	17	,	,	PUNCT
ma-86	167	18	see	see	VERB
ma-86	167	19	peszat	peszat	NOUN
ma-86	167	20	and	and	CCONJ
ma-86	167	21	zabczyk	zabczyk	NOUN
ma-86	167	22	[	[	X
ma-86	167	23	24	24	NUM
ma-86	167	24	]	]	PUNCT
ma-86	167	25	.	.	PUNCT
ma-86	168	1	thelatter	thelatter	PROPN
ma-86	168	2	series	series	PROPN
ma-86	168	3	converges	converge	VERB
ma-86	168	4	p	p	NOUN
ma-86	168	5	-a.s	-a.s	PUNCT
ma-86	168	6	.	.	PUNCT
ma-86	169	1	in	in	ADP
ma-86	169	2	h−ν	h−ν	PROPN
ma-86	169	3	for	for	ADP
ma-86	169	4	ν	ν	X
ma-86	169	5	>	>	X
ma-86	169	6	d/2	d/2	PROPN
ma-86	169	7	.	.	PUNCT
ma-86	170	1	indeed	indeed	ADV
ma-86	170	2	‖mh(t)‖2	‖mh(t)‖2	PUNCT
ma-86	170	3	−ν	−ν	NOUN
ma-86	170	4	=	=	PUNCT
ma-86	171	1	∞∑	∞∑	NUM
ma-86	171	2	i=1	i=1	PROPN
ma-86	171	3	m2	m2	PROPN
ma-86	171	4	h	h	PROPN
ma-86	171	5	,	,	PUNCT
ma-86	171	6	i(t)‖hi‖2	i(t)‖hi‖2	PROPN
ma-86	171	7	−ν	−ν	NOUN
ma-86	171	8	=	=	PUNCT
ma-86	172	1	∞∑	∞∑	NUM
ma-86	172	2	i=1	i=1	PROPN
ma-86	172	3	m2	m2	PROPN
ma-86	172	4	h	h	PROPN
ma-86	172	5	,	,	PUNCT
ma-86	172	6	i(t)β	i(t)β	PROPN
ma-86	172	7	−2ν	−2ν	PROPN
ma-86	172	8	i	i	PRON
ma-86	172	9	and	and	CCONJ
ma-86	172	10	the	the	DET
ma-86	172	11	later	later	ADJ
ma-86	172	12	series	series	NOUN
ma-86	172	13	converges	converge	VERB
ma-86	172	14	p	p	PRON
ma-86	172	15	-a.s.consider	-a.s.consider	DET
ma-86	172	16	the	the	DET
ma-86	172	17	parabolic	parabolic	ADJ
ma-86	172	18	spde	spde	NOUN
ma-86	172	19	duθ(t	duθ(t	PROPN
ma-86	172	20	,	,	PUNCT
ma-86	172	21	x	x	NOUN
ma-86	172	22	)	)	PUNCT
ma-86	172	23	=	=	SYM
ma-86	172	24	θuθ(t	θuθ(t	PROPN
ma-86	172	25	,	,	PUNCT
ma-86	172	26	x	x	NOUN
ma-86	172	27	)	)	PUNCT
ma-86	173	1	+	+	CCONJ
ma-86	173	2	∂2	∂2	NUM
ma-86	173	3	∂x2	∂x2	NOUN
ma-86	173	4	uθ(t	uθ(t	NOUN
ma-86	173	5	,	,	PUNCT
ma-86	173	6	x)dt	x)dt	PROPN
ma-86	173	7	+	+	NUM
ma-86	173	8	dmh(t	dmh(t	PROPN
ma-86	173	9	,	,	PUNCT
ma-86	173	10	x	x	NOUN
ma-86	173	11	)	)	PUNCT
ma-86	173	12	,	,	PUNCT
ma-86	173	13	t	t	PROPN
ma-86	173	14	≥	≥	NUM
ma-86	173	15	0	0	NUM
ma-86	173	16	,	,	PUNCT
ma-86	173	17	x	x	SYM
ma-86	173	18	∈	∈	PROPN
ma-86	174	1	[	[	X
ma-86	174	2	0	0	NUM
ma-86	174	3	,	,	PUNCT
ma-86	174	4	1	1	NUM
ma-86	174	5	]	]	PUNCT
ma-86	174	6	(	(	PUNCT
ma-86	174	7	2.1	2.1	NUM
ma-86	174	8	)	)	PUNCT
ma-86	174	9	u(0	u(0	NOUN
ma-86	174	10	,	,	PUNCT
ma-86	174	11	x	x	NOUN
ma-86	174	12	)	)	PUNCT
ma-86	174	13	=	=	SYM
ma-86	174	14	u0(x	u0(x	NUM
ma-86	174	15	)	)	PUNCT
ma-86	174	16	∈	∈	NOUN
ma-86	174	17	l2([0	l2([0	VERB
ma-86	174	18	,	,	PUNCT
ma-86	174	19	1	1	NUM
ma-86	174	20	]	]	NUM
ma-86	174	21	)	)	PUNCT
ma-86	174	22	(	(	PUNCT
ma-86	174	23	2.2	2.2	NUM
ma-86	174	24	)	)	PUNCT
ma-86	174	25	uθ(t	uθ(t	NOUN
ma-86	174	26	,	,	PUNCT
ma-86	174	27	0	0	NUM
ma-86	174	28	)	)	PUNCT
ma-86	174	29	=	=	SYM
ma-86	175	1	uθ(t	uθ(t	NOUN
ma-86	175	2	,	,	PUNCT
ma-86	175	3	1	1	NUM
ma-86	175	4	)	)	PUNCT
ma-86	175	5	,	,	PUNCT
ma-86	175	6	t	t	PROPN
ma-86	175	7	∈	∈	PROPN
ma-86	176	1	[	[	X
ma-86	176	2	0	0	NUM
ma-86	176	3	,	,	PUNCT
ma-86	176	4	t	t	X
ma-86	176	5	]	]	PUNCT
ma-86	176	6	,	,	PUNCT
ma-86	176	7	(	(	PUNCT
ma-86	176	8	2.3)here	2.3)here	NUM
ma-86	176	9	θ	θ	PROPN
ma-86	176	10	∈	∈	NOUN
ma-86	176	11	θ	θ	NOUN
ma-86	176	12	⊆	⊆	NUM
ma-86	176	13	r	r	NOUN
ma-86	176	14	is	be	AUX
ma-86	176	15	the	the	DET
ma-86	176	16	unknown	unknown	ADJ
ma-86	176	17	parameter	parameter	NOUN
ma-86	176	18	to	to	PART
ma-86	176	19	be	be	AUX
ma-86	176	20	estimated	estimate	VERB
ma-86	176	21	on	on	ADP
ma-86	176	22	the	the	DET
ma-86	176	23	basis	basis	NOUN
ma-86	176	24	of	of	ADP
ma-86	176	25	the	the	DET
ma-86	176	26	observationsof	observationsof	NOUN
ma-86	176	27	the	the	DET
ma-86	176	28	field	field	NOUN
ma-86	176	29	uθ(t	uθ(t	VERB
ma-86	176	30	,	,	PUNCT
ma-86	176	31	x	x	NOUN
ma-86	176	32	)	)	PUNCT
ma-86	176	33	,	,	PUNCT
ma-86	176	34	t	t	PROPN
ma-86	176	35	≥	≥	NUM
ma-86	176	36	0	0	NUM
ma-86	176	37	,	,	PUNCT
ma-86	176	38	x	x	SYM
ma-86	176	39	∈	∈	PROPN
ma-86	177	1	[	[	X
ma-86	177	2	0	0	NUM
ma-86	177	3	,	,	PUNCT
ma-86	177	4	1	1	NUM
ma-86	177	5	]	]	PUNCT
ma-86	177	6	.	.	PUNCT
ma-86	178	1	for	for	ADP
ma-86	178	2	x	x	PROPN
ma-86	178	3	∈	∈	PROPN
ma-86	178	4	[	[	X
ma-86	178	5	0	0	NUM
ma-86	178	6	,	,	PUNCT
ma-86	178	7	1	1	NUM
ma-86	178	8	]	]	PUNCT
ma-86	178	9	,	,	PUNCT
ma-86	178	10	we	we	PRON
ma-86	178	11	observe	observe	VERB
ma-86	178	12	the	the	DET
ma-86	178	13	process	process	NOUN
ma-86	178	14	{	{	PUNCT
ma-86	178	15	ut	ut	PROPN
ma-86	178	16	,	,	PUNCT
ma-86	178	17	t	t	PROPN
ma-86	178	18	≥	≥	NUM
ma-86	178	19	0	0	NUM
ma-86	178	20	}	}	PUNCT
ma-86	178	21	attimes	attime	NOUN
ma-86	178	22	{	{	PUNCT
ma-86	178	23	t0	t0	PROPN
ma-86	178	24	,	,	PUNCT
ma-86	178	25	t1	t1	NOUN
ma-86	178	26	,	,	PUNCT
ma-86	178	27	t2	t2	NOUN
ma-86	178	28	,	,	PUNCT
ma-86	178	29	....	....	PUNCT
ma-86	178	30	}	}	PUNCT
ma-86	178	31	.	.	PUNCT
ma-86	179	1	we	we	PRON
ma-86	179	2	assume	assume	VERB
ma-86	179	3	that	that	SCONJ
ma-86	179	4	the	the	DET
ma-86	179	5	sampling	sample	VERB
ma-86	179	6	instants	instant	NOUN
ma-86	179	7	{	{	PUNCT
ma-86	179	8	ti	ti	NOUN
ma-86	179	9	,	,	PUNCT
ma-86	179	10	i	i	PRON
ma-86	179	11	=	=	NOUN
ma-86	179	12	0	0	NUM
ma-86	179	13	,	,	PUNCT
ma-86	179	14	1	1	NUM
ma-86	179	15	,	,	PUNCT
ma-86	179	16	2	2	NUM
ma-86	179	17	...	...	PUNCT
ma-86	179	18	}	}	PUNCT
ma-86	179	19	are	be	AUX
ma-86	179	20	generated	generate	VERB
ma-86	179	21	bya	bya	PROPN
ma-86	179	22	poisson	poisson	NOUN
ma-86	179	23	process	process	NOUN
ma-86	179	24	on	on	ADP
ma-86	179	25	[	[	X
ma-86	179	26	0,∞	0,∞	NOUN
ma-86	179	27	)	)	PUNCT
ma-86	179	28	,	,	PUNCT
ma-86	179	29	i.e.	i.e.	X
ma-86	179	30	,	,	PUNCT
ma-86	179	31	t0	t0	X
ma-86	179	32	=	=	SYM
ma-86	179	33	0	0	NUM
ma-86	179	34	,	,	PUNCT
ma-86	179	35	ti	ti	X
ma-86	179	36	=	=	X
ma-86	179	37	ti−1	ti−1	NOUN
ma-86	179	38	+	+	CCONJ
ma-86	179	39	ξi	ξi	NOUN
ma-86	179	40	,	,	PUNCT
ma-86	179	41	i	i	PRON
ma-86	179	42	=	=	NOUN
ma-86	179	43	1	1	NUM
ma-86	179	44	,	,	PUNCT
ma-86	179	45	2	2	NUM
ma-86	179	46	,	,	PUNCT
ma-86	179	47	...	...	PUNCT
ma-86	179	48	where	where	SCONJ
ma-86	179	49	ξi	ξi	NOUN
ma-86	179	50	are	be	AUX
ma-86	179	51	i.i.d	i.i.d	ADJ
ma-86	179	52	.	.	PUNCT
ma-86	180	1	positiverandom	positiverandom	PROPN
ma-86	180	2	variables	variable	VERB
ma-86	180	3	with	with	ADP
ma-86	180	4	a	a	DET
ma-86	180	5	common	common	ADJ
ma-86	180	6	exponential	exponential	ADJ
ma-86	180	7	distribution	distribution	NOUN
ma-86	180	8	f	f	X
ma-86	180	9	(	(	PUNCT
ma-86	180	10	x	x	X
ma-86	180	11	)	)	PUNCT
ma-86	180	12	=	=	SYM
ma-86	180	13	1−exp(−λx	1−exp(−λx	NUM
ma-86	180	14	)	)	PUNCT
ma-86	180	15	.	.	PUNCT
ma-86	181	1	note	note	VERB
ma-86	181	2	that	that	SCONJ
ma-86	181	3	intensityparameter	intensityparameter	NOUN
ma-86	181	4	λ	λ	X
ma-86	181	5	>	>	X
ma-86	181	6	0	0	NUM
ma-86	181	7	is	be	AUX
ma-86	181	8	the	the	DET
ma-86	181	9	average	average	ADJ
ma-86	181	10	sampling	sampling	NOUN
ma-86	181	11	rate	rate	NOUN
ma-86	181	12	which	which	PRON
ma-86	181	13	is	be	AUX
ma-86	181	14	assumed	assume	VERB
ma-86	181	15	to	to	PART
ma-86	181	16	be	be	AUX
ma-86	181	17	known	know	VERB
ma-86	181	18	.	.	PUNCT
ma-86	182	1	it	it	PRON
ma-86	182	2	is	be	AUX
ma-86	182	3	also	also	ADV
ma-86	182	4	assumedthat	assumedthat	NOUN
ma-86	182	5	the	the	DET
ma-86	182	6	sampling	sampling	NOUN
ma-86	182	7	process	process	NOUN
ma-86	182	8	ti	ti	NOUN
ma-86	182	9	,	,	PUNCT
ma-86	182	10	i	i	PRON
ma-86	182	11	=	=	NOUN
ma-86	182	12	0	0	NUM
ma-86	182	13	,	,	PUNCT
ma-86	182	14	1	1	NUM
ma-86	182	15	,	,	PUNCT
ma-86	182	16	2	2	NUM
ma-86	182	17	,	,	PUNCT
ma-86	182	18	...	...	PUNCT
ma-86	182	19	is	be	AUX
ma-86	182	20	independent	independent	ADJ
ma-86	182	21	of	of	ADP
ma-86	182	22	the	the	DET
ma-86	182	23	observation	observation	NOUN
ma-86	182	24	process	process	NOUN
ma-86	182	25	{	{	PUNCT
ma-86	182	26	xt	xt	PROPN
ma-86	182	27	,	,	PUNCT
ma-86	182	28	t	t	PROPN
ma-86	182	29	≥	≥	NUM
ma-86	182	30	0}.we	0}.we	NUM
ma-86	182	31	note	note	VERB
ma-86	182	32	that	that	SCONJ
ma-86	182	33	the	the	DET
ma-86	182	34	probability	probability	NOUN
ma-86	182	35	density	density	NOUN
ma-86	182	36	function	function	NOUN
ma-86	182	37	of	of	ADP
ma-86	182	38	tk+i	tk+i	NOUN
ma-86	182	39	−	−	PROPN
ma-86	182	40	tk	tk	PROPN
ma-86	182	41	is	be	AUX
ma-86	182	42	independent	independent	ADJ
ma-86	182	43	of	of	ADP
ma-86	182	44	k	k	PROPN
ma-86	182	45	and	and	CCONJ
ma-86	182	46	is	be	AUX
ma-86	182	47	given	give	VERB
ma-86	182	48	by	by	ADP
ma-86	182	49	thegamma	thegamma	PROPN
ma-86	182	50	density	density	NOUN
ma-86	182	51	fi(t	fi(t	NOUN
ma-86	182	52	)	)	PUNCT
ma-86	182	53	=	=	PUNCT
ma-86	183	1	λ(λt)i−1	λ(λt)i−1	NOUN
ma-86	183	2	exp(−λt)it/(i	exp(−λt)it/(i	NOUN
ma-86	183	3	−	−	PROPN
ma-86	183	4	1	1	NUM
ma-86	183	5	)	)	PUNCT
ma-86	183	6	!	!	PUNCT
ma-86	183	7	,	,	PUNCT
ma-86	183	8	i	i	PRON
ma-86	183	9	=	=	NOUN
ma-86	183	10	0	0	NUM
ma-86	183	11	,	,	PUNCT
ma-86	183	12	1	1	NUM
ma-86	183	13	,	,	PUNCT
ma-86	183	14	2	2	NUM
ma-86	183	15	,	,	PUNCT
ma-86	183	16	....	....	PUNCT
ma-86	184	1	(	(	PUNCT
ma-86	184	2	2.4)where	2.4)where	NUM
ma-86	184	3	it	it	PRON
ma-86	184	4	=	=	PUNCT
ma-86	184	5	1	1	NUM
ma-86	184	6	if	if	SCONJ
ma-86	184	7	t	t	PROPN
ma-86	184	8	≥	≥	NOUN
ma-86	184	9	0	0	PUNCT
ma-86	184	10	and	and	CCONJ
ma-86	184	11	it	it	PRON
ma-86	185	1	=	=	SYM
ma-86	185	2	0	0	PUNCT
ma-86	186	1	if	if	SCONJ
ma-86	186	2	t	t	PROPN
ma-86	186	3	<	<	X
ma-86	186	4	0	0	NUM
ma-86	186	5	.	.	PUNCT
ma-86	186	6	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	PROPN
ma-86	186	7	eur	eur	PROPN
ma-86	186	8	.	.	PUNCT
ma-86	187	1	j.	j.	PROPN
ma-86	187	2	math	math	PROPN
ma-86	187	3	.	.	PUNCT
ma-86	188	1	anal	anal	PROPN
ma-86	188	2	.	.	PUNCT
ma-86	189	1	10.28924	10.28924	NUM
ma-86	189	2	/	/	SYM
ma-86	189	3	ada	ada	NOUN
ma-86	189	4	/	/	SYM
ma-86	189	5	ma.2.15	ma.2.15	PROPN
ma-86	189	6	8consider	8consider	NUM
ma-86	189	7	the	the	DET
ma-86	189	8	fourier	fourier	ADJ
ma-86	189	9	expansion	expansion	NOUN
ma-86	189	10	of	of	ADP
ma-86	189	11	the	the	DET
ma-86	189	12	process	process	NOUN
ma-86	189	13	u(t	u(t	NOUN
ma-86	189	14	,	,	PUNCT
ma-86	189	15	x	x	NOUN
ma-86	189	16	)	)	PUNCT
ma-86	190	1	=	=	PUNCT
ma-86	190	2	∞∑	∞∑	NUM
ma-86	190	3	t=1	t=1	ADV
ma-86	190	4	ui(t)φi(x	ui(t)φi(x	NOUN
ma-86	190	5	)	)	PUNCT
ma-86	190	6	(	(	PUNCT
ma-86	190	7	2.5	2.5	NUM
ma-86	190	8	)	)	PUNCT
ma-86	190	9	corresponding	correspond	VERB
ma-86	190	10	to	to	ADP
ma-86	190	11	some	some	DET
ma-86	190	12	orthogonal	orthogonal	ADJ
ma-86	190	13	basis	basis	NOUN
ma-86	190	14	{	{	PUNCT
ma-86	190	15	φi(x)}∞i=1	φi(x)}∞i=1	NOUN
ma-86	190	16	.	.	PUNCT
ma-86	191	1	note	note	VERB
ma-86	191	2	that	that	SCONJ
ma-86	191	3	the	the	DET
ma-86	191	4	fourier	fourier	NOUN
ma-86	191	5	coefficients	coefficient	NOUN
ma-86	191	6	{	{	PUNCT
ma-86	191	7	uθi	uθi	NOUN
ma-86	191	8	(	(	PUNCT
ma-86	191	9	t	t	PROPN
ma-86	191	10	)	)	PUNCT
ma-86	191	11	,	,	PUNCT
ma-86	191	12	i	i	PRON
ma-86	191	13	≥	≥	VERB
ma-86	191	14	1	1	NUM
ma-86	191	15	}	}	PUNCT
ma-86	191	16	are	be	AUX
ma-86	191	17	independent	independent	ADJ
ma-86	191	18	one	one	NUM
ma-86	191	19	dimensional	dimensional	ADJ
ma-86	191	20	ornstein	ornstein	NOUN
ma-86	191	21	-	-	PUNCT
ma-86	191	22	uhlenbeck	uhlenbeck	PROPN
ma-86	191	23	processes	process	NOUN
ma-86	191	24	duθi	duθi	NOUN
ma-86	191	25	(	(	PUNCT
ma-86	191	26	t	t	NOUN
ma-86	191	27	)	)	PUNCT
ma-86	191	28	=	=	PUNCT
ma-86	191	29	µθi	µθi	VERB
ma-86	191	30	u	u	NOUN
ma-86	191	31	θ	θ	NOUN
ma-86	191	32	i	i	PRON
ma-86	191	33	(	(	PUNCT
ma-86	191	34	t)dt	t)dt	PROPN
ma-86	191	35	+	+	NUM
ma-86	191	36	β−νi	β−νi	PROPN
ma-86	191	37	dmh	dmh	NOUN
ma-86	191	38	,	,	PUNCT
ma-86	191	39	i(t	i(t	PROPN
ma-86	191	40	)	)	PUNCT
ma-86	191	41	(	(	PUNCT
ma-86	191	42	2.6	2.6	NUM
ma-86	191	43	)	)	PUNCT
ma-86	191	44	uθi	uθi	NOUN
ma-86	191	45	(	(	PUNCT
ma-86	191	46	0	0	NUM
ma-86	191	47	)	)	PUNCT
ma-86	191	48	=	=	VERB
ma-86	192	1	uθ0i	uθ0i	ADJ
ma-86	192	2	,	,	PUNCT
ma-86	192	3	recall	recall	VERB
ma-86	192	4	that	that	PRON
ma-86	192	5	µi(θ	µi(θ	NOUN
ma-86	192	6	)	)	PUNCT
ma-86	192	7	=	=	SYM
ma-86	193	1	k(θ)−	k(θ)−	PROPN
ma-86	193	2	β2	β2	VERB
ma-86	193	3	m	m	NOUN
ma-86	193	4	i	i	PRON
ma-86	193	5	.	.	PUNCT
ma-86	194	1	thus	thus	ADV
ma-86	194	2	duθi	duθi	NOUN
ma-86	194	3	(	(	PUNCT
ma-86	194	4	t	t	NOUN
ma-86	194	5	)	)	PUNCT
ma-86	194	6	=	=	PUNCT
ma-86	194	7	(	(	PUNCT
ma-86	194	8	k(θ)−	k(θ)−	PROPN
ma-86	194	9	β2	β2	PROPN
ma-86	194	10	m	m	PROPN
ma-86	194	11	i	i	NOUN
ma-86	194	12	)	)	PUNCT
ma-86	194	13	uθi	uθi	NOUN
ma-86	194	14	(	(	PUNCT
ma-86	194	15	t)dt	t)dt	PROPN
ma-86	194	16	+	+	NUM
ma-86	194	17	β−νi	β−νi	PROPN
ma-86	194	18	dmh	dmh	NOUN
ma-86	194	19	,	,	PUNCT
ma-86	194	20	i(t	i(t	PROPN
ma-86	194	21	)	)	PUNCT
ma-86	194	22	(	(	PUNCT
ma-86	194	23	2.7	2.7	NUM
ma-86	194	24	)	)	PUNCT
ma-86	194	25	the	the	DET
ma-86	194	26	random	random	ADJ
ma-86	194	27	field	field	NOUN
ma-86	194	28	u(t	u(t	NOUN
ma-86	194	29	,	,	PUNCT
ma-86	194	30	x	x	X
ma-86	194	31	)	)	PUNCT
ma-86	194	32	is	be	AUX
ma-86	194	33	observed	observe	VERB
ma-86	194	34	at	at	ADP
ma-86	194	35	discrete	discrete	ADJ
ma-86	194	36	times	time	NOUN
ma-86	194	37	t	t	NOUN
ma-86	194	38	and	and	CCONJ
ma-86	194	39	discrete	discrete	ADJ
ma-86	194	40	positions	position	NOUN
ma-86	194	41	x	x	X
ma-86	194	42	.	.	PUNCT
ma-86	195	1	equivalently	equivalently	ADV
ma-86	195	2	,	,	PUNCT
ma-86	195	3	thefourier	thefouri	ADJ
ma-86	195	4	coefficients	coefficient	NOUN
ma-86	195	5	uθi	uθi	PROPN
ma-86	195	6	(	(	PUNCT
ma-86	195	7	t	t	NOUN
ma-86	195	8	)	)	PUNCT
ma-86	195	9	are	be	AUX
ma-86	195	10	observed	observe	VERB
ma-86	195	11	at	at	ADP
ma-86	195	12	discrete	discrete	ADJ
ma-86	195	13	time	time	NOUN
ma-86	195	14	points.now	points.now	NOUN
ma-86	195	15	we	we	PRON
ma-86	195	16	focus	focus	VERB
ma-86	195	17	on	on	ADP
ma-86	195	18	the	the	DET
ma-86	195	19	fundamental	fundamental	ADJ
ma-86	195	20	semimartingale	semimartingale	NOUN
ma-86	195	21	behind	behind	ADP
ma-86	195	22	the	the	DET
ma-86	195	23	o	o	PROPN
ma-86	195	24	-	-	PROPN
ma-86	195	25	u	u	ADJ
ma-86	195	26	model	model	NOUN
ma-86	195	27	.	.	PUNCT
ma-86	196	1	define	define	VERB
ma-86	196	2	κh	κh	INTJ
ma-86	196	3	:	:	PUNCT
ma-86	196	4	=	=	SYM
ma-86	196	5	2hγ(3/2−h)γ(h	2hγ(3/2−h)γ(h	NUM
ma-86	196	6	+	+	NUM
ma-86	196	7	1/2	1/2	NUM
ma-86	196	8	)	)	PUNCT
ma-86	196	9	,	,	PUNCT
ma-86	196	10	kh(t	kh(t	X
ma-86	196	11	,	,	PUNCT
ma-86	196	12	s	s	X
ma-86	196	13	)	)	PUNCT
ma-86	196	14	:	:	PUNCT
ma-86	196	15	=	=	PUNCT
ma-86	196	16	κ−1	κ−1	PROPN
ma-86	196	17	h	h	NOUN
ma-86	196	18	(	(	PUNCT
ma-86	196	19	s(t	s(t	PROPN
ma-86	196	20	−	−	PROPN
ma-86	196	21	s	s	PART
ma-86	196	22	)	)	PUNCT
ma-86	196	23	)	)	PUNCT
ma-86	196	24	1	1	NUM
ma-86	196	25	2	2	NUM
ma-86	196	26	−h	−h	VERB
ma-86	196	27	,	,	PUNCT
ma-86	196	28	ηh	ηh	ADP
ma-86	196	29	:	:	PUNCT
ma-86	196	30	=	=	SYM
ma-86	196	31	2hγ(3−	2hγ(3−	NUM
ma-86	196	32	2h)γ(h	2h)γ(h	NUM
ma-86	196	33	+	+	CCONJ
ma-86	196	34	1	1	NUM
ma-86	196	35	2	2	NUM
ma-86	196	36	)	)	PUNCT
ma-86	196	37	γ(3/2−h	γ(3/2−h	NOUN
ma-86	196	38	)	)	PUNCT
ma-86	196	39	,	,	PUNCT
ma-86	196	40	vt	vt	PROPN
ma-86	196	41	≡	≡	PROPN
ma-86	196	42	vht	vht	NOUN
ma-86	196	43	:	:	PUNCT
ma-86	196	44	=	=	SYM
ma-86	196	45	η−1	η−1	PROPN
ma-86	196	46	h	h	NOUN
ma-86	196	47	t2−2h	t2−2h	PROPN
ma-86	196	48	,	,	PUNCT
ma-86	196	49	mh	mh	PROPN
ma-86	196	50	t	t	PROPN
ma-86	196	51	:	:	PUNCT
ma-86	197	1	=	=	SYM
ma-86	197	2	∫	∫	PROPN
ma-86	197	3	t	t	PROPN
ma-86	197	4	0	0	NUM
ma-86	197	5	kh(t	kh(t	NUM
ma-86	197	6	,	,	PUNCT
ma-86	197	7	s)dmh	s)dmh	PROPN
ma-86	197	8	s	s	PART
ma-86	197	9	.	.	PUNCT
ma-86	198	1	for	for	ADP
ma-86	198	2	using	use	VERB
ma-86	198	3	girsanov	girsanov	PROPN
ma-86	198	4	theorem	theorem	NOUN
ma-86	198	5	for	for	ADP
ma-86	198	6	brownian	brownian	ADJ
ma-86	198	7	motion	motion	NOUN
ma-86	198	8	,	,	PUNCT
ma-86	198	9	since	since	SCONJ
ma-86	198	10	a	a	DET
ma-86	198	11	radon	radon	PROPN
ma-86	198	12	-	-	PUNCT
ma-86	198	13	nikodym	nikodym	ADJ
ma-86	198	14	derivative	derivative	ADJ
ma-86	198	15	process	process	NOUN
ma-86	198	16	is	be	AUX
ma-86	198	17	al	al	PROPN
ma-86	198	18	-	-	PUNCT
ma-86	198	19	ways	way	NOUN
ma-86	198	20	a	a	DET
ma-86	198	21	martingale	martingale	NOUN
ma-86	198	22	,	,	PUNCT
ma-86	198	23	a	a	DET
ma-86	198	24	central	central	ADJ
ma-86	198	25	problem	problem	NOUN
ma-86	198	26	is	be	AUX
ma-86	198	27	how	how	SCONJ
ma-86	198	28	to	to	PART
ma-86	198	29	construct	construct	VERB
ma-86	198	30	an	an	DET
ma-86	198	31	appropriate	appropriate	ADJ
ma-86	198	32	martingale	martingale	NOUN
ma-86	198	33	which	which	DET
ma-86	198	34	generatesthe	generatesthe	PRON
ma-86	198	35	same	same	ADJ
ma-86	198	36	filtration	filtration	NOUN
ma-86	198	37	,	,	PUNCT
ma-86	198	38	up	up	ADP
ma-86	198	39	to	to	ADP
ma-86	198	40	sets	set	NOUN
ma-86	198	41	of	of	ADP
ma-86	198	42	measure	measure	NOUN
ma-86	198	43	zero	zero	NUM
ma-86	198	44	,	,	PUNCT
ma-86	198	45	as	as	SCONJ
ma-86	198	46	the	the	DET
ma-86	198	47	non	non	ADJ
ma-86	198	48	-	-	NOUN
ma-86	198	49	semimartingale	semimartingale	NOUN
ma-86	198	50	called	call	VERB
ma-86	198	51	the	the	DET
ma-86	198	52	fundamental	fundamental	ADJ
ma-86	198	53	martingale.extending	martingale.extende	VERB
ma-86	198	54	norros	norro	NOUN
ma-86	198	55	et	et	PROPN
ma-86	198	56	al	al	PROPN
ma-86	198	57	.	.	PUNCT
ma-86	199	1	[	[	X
ma-86	199	2	23	23	NUM
ma-86	199	3	]	]	PUNCT
ma-86	199	4	it	it	PRON
ma-86	199	5	can	can	AUX
ma-86	199	6	be	be	AUX
ma-86	199	7	shown	show	VERB
ma-86	199	8	that	that	SCONJ
ma-86	199	9	mh	mh	PROPN
ma-86	199	10	t	t	PROPN
ma-86	199	11	is	be	AUX
ma-86	199	12	a	a	DET
ma-86	199	13	martingale	martingale	NOUN
ma-86	199	14	,	,	PUNCT
ma-86	199	15	called	call	VERB
ma-86	199	16	the	the	DET
ma-86	199	17	fundamen	fundaman	NOUN
ma-86	199	18	-	-	PUNCT
ma-86	199	19	tal	tal	ADJ
ma-86	199	20	martingale	martingale	NOUN
ma-86	199	21	whose	whose	DET
ma-86	199	22	quadratic	quadratic	ADJ
ma-86	199	23	variation	variation	NOUN
ma-86	199	24	〈	〈	PROPN
ma-86	199	25	mh〉t	mh〉t	PROPN
ma-86	199	26	is	be	AUX
ma-86	199	27	vht	vht	ADJ
ma-86	199	28	.	.	PUNCT
ma-86	200	1	moreover	moreover	ADV
ma-86	200	2	,	,	PUNCT
ma-86	200	3	the	the	DET
ma-86	200	4	natural	natural	ADJ
ma-86	200	5	filtration	filtration	NOUN
ma-86	200	6	of	of	ADP
ma-86	200	7	themartingale	themartingale	PROPN
ma-86	200	8	mh	mh	PROPN
ma-86	200	9	coincides	coincide	VERB
ma-86	200	10	with	with	ADP
ma-86	200	11	the	the	DET
ma-86	200	12	natural	natural	ADJ
ma-86	200	13	filtration	filtration	NOUN
ma-86	200	14	of	of	ADP
ma-86	200	15	the	the	DET
ma-86	200	16	flp	flp	PROPN
ma-86	200	17	mh	mh	PROPN
ma-86	200	18	since	since	SCONJ
ma-86	200	19	mh	mh	PROPN
ma-86	200	20	t	t	PROPN
ma-86	200	21	:	:	PUNCT
ma-86	201	1	=	=	SYM
ma-86	201	2	∫	∫	PROPN
ma-86	201	3	t	t	PROPN
ma-86	201	4	0	0	NUM
ma-86	201	5	k(t	k(t	NOUN
ma-86	201	6	,	,	PUNCT
ma-86	201	7	s)dmh	s)dmh	PROPN
ma-86	201	8	s	s	PART
ma-86	201	9	holds	hold	NOUN
ma-86	201	10	for	for	ADP
ma-86	201	11	h	h	NOUN
ma-86	201	12	∈	∈	PROPN
ma-86	201	13	(	(	PUNCT
ma-86	201	14	1/2	1/2	NUM
ma-86	201	15	,	,	PUNCT
ma-86	201	16	1	1	NUM
ma-86	201	17	)	)	PUNCT
ma-86	201	18	where	where	SCONJ
ma-86	201	19	kh(t	kh(t	X
ma-86	201	20	,	,	PUNCT
ma-86	201	21	s	s	NOUN
ma-86	201	22	)	)	PUNCT
ma-86	201	23	:	:	PUNCT
ma-86	202	1	=	=	SYM
ma-86	202	2	h(2h	h(2h	PUNCT
ma-86	202	3	−	−	NOUN
ma-86	202	4	1	1	NUM
ma-86	202	5	)	)	PUNCT
ma-86	202	6	∫	∫	PROPN
ma-86	203	1	t	t	PROPN
ma-86	203	2	s	s	PROPN
ma-86	203	3	rh−	rh−	PROPN
ma-86	203	4	1	1	NUM
ma-86	203	5	2	2	NUM
ma-86	203	6	(	(	PUNCT
ma-86	203	7	r	r	NOUN
ma-86	203	8	−	−	PROPN
ma-86	203	9	s)h−	s)h−	NOUN
ma-86	203	10	3	3	NUM
ma-86	203	11	2	2	NUM
ma-86	203	12	dr	dr	PROPN
ma-86	203	13	,	,	PUNCT
ma-86	203	14	0	0	NUM
ma-86	203	15	≤	≤	NUM
ma-86	203	16	s	s	PART
ma-86	203	17	≤	≤	NOUN
ma-86	203	18	t	t	NOUN
ma-86	203	19	and	and	CCONJ
ma-86	203	20	for	for	ADP
ma-86	203	21	h	h	NOUN
ma-86	203	22	=	=	SYM
ma-86	203	23	1/2	1/2	NUM
ma-86	203	24	,	,	PUNCT
ma-86	203	25	the	the	DET
ma-86	203	26	convention	convention	NOUN
ma-86	203	27	k1/2	k1/2	NOUN
ma-86	203	28	≡	≡	PROPN
ma-86	203	29	1	1	NUM
ma-86	203	30	is	be	AUX
ma-86	203	31	used.define	used.define	NUM
ma-86	203	32	qi(t	qi(t	NOUN
ma-86	203	33	)	)	PUNCT
ma-86	203	34	:	:	PUNCT
ma-86	204	1	=	=	SYM
ma-86	204	2	d	d	X
ma-86	204	3	dvt	dvt	PROPN
ma-86	204	4	∫	∫	PROPN
ma-86	204	5	t	t	PROPN
ma-86	204	6	0	0	NUM
ma-86	204	7	kh(t	kh(t	NUM
ma-86	204	8	,	,	PUNCT
ma-86	204	9	s)ui(s)ds	s)ui(s)ds	PROPN
ma-86	204	10	,	,	PUNCT
ma-86	204	11	i	i	PRON
ma-86	204	12	≥	≥	VERB
ma-86	204	13	1	1	NUM
ma-86	204	14	.	.	PUNCT
ma-86	204	15	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	PROPN
ma-86	204	16	eur	eur	PROPN
ma-86	204	17	.	.	PUNCT
ma-86	205	1	j.	j.	PROPN
ma-86	205	2	math	math	PROPN
ma-86	205	3	.	.	PUNCT
ma-86	206	1	anal	anal	PROPN
ma-86	206	2	.	.	PUNCT
ma-86	207	1	10.28924	10.28924	NUM
ma-86	207	2	/	/	SYM
ma-86	207	3	ada	ada	NOUN
ma-86	207	4	/	/	SYM
ma-86	207	5	ma.2.15	ma.2.15	PROPN
ma-86	207	6	9it	9it	NOUN
ma-86	207	7	is	be	AUX
ma-86	207	8	easy	easy	ADJ
ma-86	207	9	to	to	PART
ma-86	207	10	see	see	VERB
ma-86	207	11	that	that	DET
ma-86	207	12	qi(t	qi(t	NOUN
ma-86	207	13	)	)	PUNCT
ma-86	208	1	=	=	VERB
ma-86	208	2	ηh	ηh	VERB
ma-86	208	3	2(2−	2(2−	NUM
ma-86	208	4	2h	2h	NUM
ma-86	208	5	)	)	PUNCT
ma-86	208	6	{	{	PUNCT
ma-86	208	7	t2h−1zi(t	t2h−1zi(t	NOUN
ma-86	208	8	)	)	PUNCT
ma-86	208	9	+	+	CCONJ
ma-86	209	1	∫	∫	PROPN
ma-86	209	2	t	t	PROPN
ma-86	209	3	0	0	NUM
ma-86	209	4	r2h−1dzi(s	r2h−1dzi(s	NOUN
ma-86	209	5	)	)	PUNCT
ma-86	209	6	}	}	PUNCT
ma-86	209	7	.	.	PUNCT
ma-86	210	1	define	define	VERB
ma-86	210	2	the	the	DET
ma-86	210	3	process	process	NOUN
ma-86	210	4	zi	zi	NOUN
ma-86	210	5	=	=	PUNCT
ma-86	210	6	(	(	PUNCT
ma-86	210	7	zi(t	zi(t	NOUN
ma-86	210	8	)	)	PUNCT
ma-86	210	9	,	,	PUNCT
ma-86	210	10	t	t	PROPN
ma-86	210	11	∈	∈	PROPN
ma-86	211	1	[	[	X
ma-86	211	2	0	0	NUM
ma-86	211	3	,	,	PUNCT
ma-86	211	4	t	t	X
ma-86	211	5	]	]	PUNCT
ma-86	211	6	)	)	PUNCT
ma-86	211	7	by	by	ADP
ma-86	211	8	zi(t	zi(t	NOUN
ma-86	211	9	)	)	PUNCT
ma-86	211	10	:	:	PUNCT
ma-86	212	1	=	=	SYM
ma-86	212	2	∫	∫	PROPN
ma-86	212	3	t	t	PROPN
ma-86	212	4	0	0	NUM
ma-86	212	5	kh(t	kh(t	NUM
ma-86	212	6	,	,	PUNCT
ma-86	212	7	s)dui(s	s)dui(s	NUM
ma-86	212	8	)	)	PUNCT
ma-86	212	9	.	.	PUNCT
ma-86	213	1	extending	extend	VERB
ma-86	213	2	kleptsyna	kleptsyna	NOUN
ma-86	213	3	and	and	CCONJ
ma-86	213	4	le	le	X
ma-86	213	5	breton	breton	NOUN
ma-86	214	1	[	[	X
ma-86	214	2	16	16	NUM
ma-86	214	3	]	]	PUNCT
ma-86	214	4	,	,	PUNCT
ma-86	214	5	we	we	PRON
ma-86	214	6	have:(i	have:(i	NOUN
ma-86	214	7	)	)	PUNCT
ma-86	214	8	zi	zi	PROPN
ma-86	214	9	is	be	AUX
ma-86	214	10	the	the	DET
ma-86	214	11	fundamental	fundamental	ADJ
ma-86	214	12	semimartingale	semimartingale	NOUN
ma-86	214	13	associated	associate	VERB
ma-86	214	14	with	with	ADP
ma-86	214	15	the	the	DET
ma-86	214	16	process	process	NOUN
ma-86	214	17	ui	ui	PROPN
ma-86	214	18	.(ii	.(ii	PROPN
ma-86	214	19	)	)	PUNCT
ma-86	214	20	zi	zi	PROPN
ma-86	214	21	is	be	AUX
ma-86	214	22	a	a	DET
ma-86	214	23	(	(	PUNCT
ma-86	214	24	ft	ft	NOUN
ma-86	214	25	)	)	PUNCT
ma-86	214	26	-semimartingale	-semimartingale	NOUN
ma-86	214	27	with	with	ADP
ma-86	214	28	the	the	DET
ma-86	214	29	decomposition	decomposition	NOUN
ma-86	214	30	zi(t	zi(t	NOUN
ma-86	214	31	)	)	PUNCT
ma-86	214	32	=	=	SYM
ma-86	214	33	µi(θ	µi(θ	NOUN
ma-86	214	34	)	)	PUNCT
ma-86	214	35	∫	∫	PROPN
ma-86	214	36	t	t	PROPN
ma-86	214	37	0	0	NUM
ma-86	214	38	qi(s)dvs	qi(s)dvs	PROPN
ma-86	214	39	+	+	CCONJ
ma-86	214	40	β−νi	β−νi	NOUN
ma-86	214	41	m	m	PROPN
ma-86	214	42	h	h	PROPN
ma-86	214	43	t	t	PROPN
ma-86	214	44	.	.	PUNCT
ma-86	215	1	(	(	PUNCT
ma-86	215	2	iii	iii	X
ma-86	215	3	)	)	PUNCT
ma-86	215	4	ui	ui	PROPN
ma-86	215	5	admits	admit	VERB
ma-86	215	6	the	the	DET
ma-86	215	7	representation	representation	NOUN
ma-86	215	8	ui(t	ui(t	NOUN
ma-86	215	9	)	)	PUNCT
ma-86	216	1	=	=	SYM
ma-86	216	2	∫	∫	PROPN
ma-86	216	3	t	t	PROPN
ma-86	216	4	0	0	NUM
ma-86	216	5	kh(t	kh(t	PROPN
ma-86	216	6	,	,	PUNCT
ma-86	216	7	s)dzi(s	s)dzi(s	NOUN
ma-86	216	8	)	)	PUNCT
ma-86	216	9	.	.	PUNCT
ma-86	217	1	(	(	PUNCT
ma-86	217	2	iv	iv	X
ma-86	217	3	)	)	PUNCT
ma-86	217	4	the	the	DET
ma-86	217	5	natural	natural	ADJ
ma-86	217	6	filtration	filtration	NOUN
ma-86	217	7	(	(	PUNCT
ma-86	217	8	zi(t	zi(t	NOUN
ma-86	217	9	)	)	PUNCT
ma-86	217	10	)	)	PUNCT
ma-86	217	11	of	of	ADP
ma-86	217	12	zi	zi	PROPN
ma-86	217	13	and	and	CCONJ
ma-86	217	14	(	(	PUNCT
ma-86	217	15	ui(t	ui(t	NOUN
ma-86	217	16	)	)	PUNCT
ma-86	217	17	)	)	PUNCT
ma-86	217	18	of	of	ADP
ma-86	217	19	ui	ui	PROPN
ma-86	217	20	coincide	coincide	NOUN
ma-86	217	21	.	.	PUNCT
ma-86	218	1	we	we	PRON
ma-86	218	2	focus	focus	VERB
ma-86	218	3	on	on	ADP
ma-86	218	4	our	our	PRON
ma-86	218	5	obserbations	obserbation	NOUN
ma-86	218	6	now	now	ADV
ma-86	218	7	.	.	PUNCT
ma-86	219	1	note	note	VERB
ma-86	219	2	that	that	SCONJ
ma-86	219	3	for	for	ADP
ma-86	219	4	equally	equally	ADV
ma-86	219	5	spaced	space	VERB
ma-86	219	6	data	datum	NOUN
ma-86	219	7	(	(	PUNCT
ma-86	219	8	homoscedastic	homoscedastic	ADJ
ma-86	219	9	case	case	NOUN
ma-86	219	10	)	)	PUNCT
ma-86	219	11	vtk	vtk	NOUN
ma-86	219	12	−	−	PROPN
ma-86	219	13	vtk−1	vtk−1	PROPN
ma-86	219	14	=	=	SYM
ma-86	219	15	η−1	η−1	PROPN
ma-86	219	16	h	h	NOUN
ma-86	219	17	(	(	PUNCT
ma-86	219	18	t	t	PROPN
ma-86	219	19	n	n	CCONJ
ma-86	219	20	)	)	PUNCT
ma-86	219	21	2−2h	2−2h	NUM
ma-86	220	1	[	[	X
ma-86	220	2	k2−2h	k2−2h	INTJ
ma-86	220	3	−	−	PROPN
ma-86	220	4	(	(	PUNCT
ma-86	220	5	k	k	PROPN
ma-86	220	6	−	−	PROPN
ma-86	220	7	1)2−2h	1)2−2h	NUM
ma-86	220	8	]	]	PUNCT
ma-86	220	9	,	,	PUNCT
ma-86	220	10	k	k	X
ma-86	220	11	=	=	SYM
ma-86	220	12	1	1	NUM
ma-86	220	13	,	,	PUNCT
ma-86	220	14	2	2	NUM
ma-86	220	15	,	,	PUNCT
ma-86	220	16	·	·	PUNCT
ma-86	220	17	·	·	PUNCT
ma-86	220	18	·	·	PUNCT
ma-86	220	19	,	,	PUNCT
ma-86	220	20	n.	n.	NOUN
ma-86	220	21	(	(	PUNCT
ma-86	220	22	2.8	2.8	NUM
ma-86	220	23	)	)	PUNCT
ma-86	220	24	for	for	ADP
ma-86	220	25	h	h	NOUN
ma-86	220	26	=	=	SYM
ma-86	220	27	0.5	0.5	NUM
ma-86	220	28	,	,	PUNCT
ma-86	220	29	vtk	vtk	NOUN
ma-86	220	30	−	−	PROPN
ma-86	220	31	vtk−1	vtk−1	PROPN
ma-86	220	32	=	=	SYM
ma-86	220	33	η−1	η−1	PROPN
ma-86	220	34	h	h	NOUN
ma-86	220	35	(	(	PUNCT
ma-86	220	36	t	t	PROPN
ma-86	220	37	n	n	CCONJ
ma-86	220	38	)	)	PUNCT
ma-86	220	39	2−2h	2−2h	NUM
ma-86	221	1	[	[	X
ma-86	221	2	k2−2h	k2−2h	INTJ
ma-86	221	3	−	−	PROPN
ma-86	221	4	(	(	PUNCT
ma-86	221	5	k	k	PROPN
ma-86	221	6	−	−	PROPN
ma-86	221	7	1)2−2h	1)2−2h	NUM
ma-86	221	8	]	]	X
ma-86	221	9	=	=	SYM
ma-86	222	1	t	t	PROPN
ma-86	222	2	n	n	NOUN
ma-86	222	3	,	,	PUNCT
ma-86	222	4	k	k	PROPN
ma-86	222	5	=	=	SYM
ma-86	222	6	1	1	NUM
ma-86	222	7	,	,	PUNCT
ma-86	222	8	2	2	NUM
ma-86	222	9	,	,	PUNCT
ma-86	222	10	.	.	PUNCT
ma-86	222	11	.	.	PUNCT
ma-86	222	12	.	.	PUNCT
ma-86	223	1	,	,	PUNCT
ma-86	223	2	n.	n.	NOUN
ma-86	223	3	we	we	PRON
ma-86	223	4	have	have	VERB
ma-86	223	5	qi(t	qi(t	NOUN
ma-86	223	6	)	)	PUNCT
ma-86	224	1	=	=	SYM
ma-86	225	1	d	d	X
ma-86	225	2	dvt	dvt	PROPN
ma-86	225	3	∫	∫	PROPN
ma-86	225	4	t	t	PROPN
ma-86	225	5	0	0	NUM
ma-86	225	6	kh(t	kh(t	NUM
ma-86	225	7	,	,	PUNCT
ma-86	225	8	s)ui(s)ds	s)ui(s)ds	PROPN
ma-86	226	1	=	=	SYM
ma-86	226	2	κ−1	κ−1	PROPN
ma-86	226	3	h	h	NOUN
ma-86	227	1	d	d	NOUN
ma-86	227	2	dvt	dvt	PROPN
ma-86	227	3	∫	∫	PROPN
ma-86	227	4	t	t	PROPN
ma-86	227	5	0	0	NUM
ma-86	227	6	s1/2−h(t	s1/2−h(t	PROPN
ma-86	227	7	−	−	PROPN
ma-86	227	8	s)1/2−hui(s)ds	s)1/2−hui(s)ds	NOUN
ma-86	227	9	=	=	PUNCT
ma-86	227	10	κ−1	κ−1	PROPN
ma-86	227	11	h	h	NOUN
ma-86	227	12	ηht	ηht	VERB
ma-86	227	13	2h−1	2h−1	NUM
ma-86	228	1	d	d	NOUN
ma-86	228	2	dt	dt	X
ma-86	228	3	∫	∫	PROPN
ma-86	228	4	t	t	PROPN
ma-86	228	5	0	0	NUM
ma-86	228	6	s1/2−h(t	s1/2−h(t	PROPN
ma-86	228	7	−	−	PROPN
ma-86	228	8	s)1/2−hui(s)ds	s)1/2−hui(s)ds	NOUN
ma-86	228	9	=	=	PUNCT
ma-86	228	10	κ−1	κ−1	PROPN
ma-86	228	11	h	h	NOUN
ma-86	228	12	ηht	ηht	VERB
ma-86	228	13	2h−1	2h−1	NUM
ma-86	228	14	∫	∫	NOUN
ma-86	228	15	t	t	NOUN
ma-86	228	16	0	0	NUM
ma-86	229	1	d	d	NOUN
ma-86	229	2	dt	dt	X
ma-86	229	3	s1/2−h(t	s1/2−h(t	PROPN
ma-86	229	4	−	−	PROPN
ma-86	229	5	s)1/2−hui(s)ds	s)1/2−hui(s)ds	NOUN
ma-86	229	6	=	=	PUNCT
ma-86	229	7	κ−1	κ−1	PROPN
ma-86	229	8	h	h	NOUN
ma-86	229	9	ηht	ηht	VERB
ma-86	229	10	2h−1	2h−1	NUM
ma-86	229	11	∫	∫	NOUN
ma-86	229	12	t	t	PROPN
ma-86	229	13	0	0	PUNCT
ma-86	229	14	s1/2−h(t	s1/2−h(t	PROPN
ma-86	229	15	−	−	PROPN
ma-86	229	16	s)−1/2−hui(s)ds	s)−1/2−hui(s)ds	PROPN
ma-86	229	17	.	.	PUNCT
ma-86	230	1	(	(	PUNCT
ma-86	230	2	2.9	2.9	NUM
ma-86	230	3	)	)	PUNCT
ma-86	230	4	the	the	DET
ma-86	230	5	process	process	NOUN
ma-86	230	6	qi	qi	NOUN
ma-86	230	7	depends	depend	VERB
ma-86	230	8	continuously	continuously	ADV
ma-86	230	9	on	on	ADP
ma-86	230	10	ui	ui	PROPN
ma-86	230	11	and	and	CCONJ
ma-86	230	12	therefore	therefore	ADV
ma-86	230	13	,	,	PUNCT
ma-86	230	14	the	the	DET
ma-86	230	15	discrete	discrete	ADJ
ma-86	230	16	observations	observation	NOUN
ma-86	230	17	of	of	ADP
ma-86	230	18	ui	ui	PROPN
ma-86	230	19	doesnot	doesnot	AUX
ma-86	230	20	allow	allow	VERB
ma-86	230	21	one	one	PRON
ma-86	230	22	to	to	PART
ma-86	230	23	obtain	obtain	VERB
ma-86	230	24	the	the	DET
ma-86	230	25	discrete	discrete	ADJ
ma-86	230	26	observations	observation	NOUN
ma-86	230	27	of	of	ADP
ma-86	230	28	qi	qi	PROPN
ma-86	230	29	.	.	PUNCT
ma-86	231	1	the	the	DET
ma-86	231	2	process	process	NOUN
ma-86	231	3	qi	qi	PROPN
ma-86	231	4	can	can	AUX
ma-86	231	5	be	be	AUX
ma-86	231	6	approximated	approximate	VERB
ma-86	231	7	by	by	ADP
ma-86	231	8	q̃i(n	q̃i(n	NUM
ma-86	231	9	)	)	PUNCT
ma-86	232	1	=	=	SYM
ma-86	232	2	κ−1	κ−1	PROPN
ma-86	232	3	h	h	NOUN
ma-86	232	4	ηhn	ηhn	NOUN
ma-86	232	5	2h−1	2h−1	NUM
ma-86	232	6	n−1∑	n−1∑	NUM
ma-86	232	7	j=0	j=0	PROPN
ma-86	232	8	j1/2−h(n	j1/2−h(n	PROPN
ma-86	232	9	−	−	PROPN
ma-86	232	10	j)−1/2−hui(j	j)−1/2−hui(j	ADJ
ma-86	232	11	)	)	PUNCT
ma-86	232	12	.	.	PUNCT
ma-86	233	1	(	(	PUNCT
ma-86	233	2	2.10	2.10	NUM
ma-86	233	3	)	)	PUNCT
ma-86	233	4	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	PROPN
ma-86	233	5	eur	eur	PROPN
ma-86	233	6	.	.	PUNCT
ma-86	234	1	j.	j.	PROPN
ma-86	234	2	math	math	PROPN
ma-86	234	3	.	.	PUNCT
ma-86	235	1	anal	anal	PROPN
ma-86	235	2	.	.	PUNCT
ma-86	236	1	10.28924	10.28924	NUM
ma-86	236	2	/	/	SYM
ma-86	236	3	ada	ada	NOUN
ma-86	236	4	/	/	SYM
ma-86	236	5	ma.2.15	ma.2.15	NOUN
ma-86	236	6	10	10	NUM
ma-86	236	7	it	it	PRON
ma-86	236	8	is	be	AUX
ma-86	236	9	easy	easy	ADJ
ma-86	236	10	to	to	PART
ma-86	236	11	show	show	VERB
ma-86	236	12	that	that	SCONJ
ma-86	236	13	q̃i(n)→	q̃i(n)→	PROPN
ma-86	236	14	qi(t	qi(t	NOUN
ma-86	236	15	)	)	PUNCT
ma-86	236	16	almost	almost	ADV
ma-86	236	17	surely	surely	ADV
ma-86	236	18	as	as	ADP
ma-86	236	19	n	n	X
ma-86	236	20	→∞	→∞	NOUN
ma-86	236	21	,	,	PUNCT
ma-86	236	22	see	see	VERB
ma-86	236	23	tudor	tudor	PROPN
ma-86	236	24	and	and	CCONJ
ma-86	236	25	viens	vien	NOUN
ma-86	236	26	[	[	X
ma-86	236	27	26].define	26].define	PROPN
ma-86	236	28	a	a	DET
ma-86	236	29	new	new	ADJ
ma-86	236	30	partition	partition	NOUN
ma-86	236	31	0	0	NUM
ma-86	236	32	≤	≤	PROPN
ma-86	236	33	r1	r1	PROPN
ma-86	236	34	<	<	X
ma-86	236	35	r2	r2	PROPN
ma-86	236	36	<	<	X
ma-86	236	37	r3	r3	PROPN
ma-86	236	38	<	<	X
ma-86	236	39	·	·	PUNCT
ma-86	236	40	·	·	PUNCT
ma-86	236	41	·	·	PUNCT
ma-86	237	1	<	<	X
ma-86	237	2	rmk	rmk	PROPN
ma-86	237	3	=	=	SYM
ma-86	237	4	tk	tk	PROPN
ma-86	237	5	,	,	PUNCT
ma-86	237	6	k	k	PROPN
ma-86	237	7	=	=	SYM
ma-86	237	8	1	1	NUM
ma-86	237	9	,	,	PUNCT
ma-86	237	10	2	2	NUM
ma-86	237	11	,	,	PUNCT
ma-86	237	12	·	·	PUNCT
ma-86	237	13	·	·	PUNCT
ma-86	237	14	·	·	PUNCT
ma-86	237	15	,	,	PUNCT
ma-86	237	16	n.	n.	NOUN
ma-86	237	17	define	define	VERB
ma-86	237	18	q̃i(tk	q̃i(tk	NOUN
ma-86	237	19	)	)	PUNCT
ma-86	238	1	=	=	SYM
ma-86	238	2	κ−1	κ−1	PROPN
ma-86	238	3	h	h	NOUN
ma-86	238	4	ηht	ηht	VERB
ma-86	238	5	2h−1	2h−1	NUM
ma-86	238	6	k	k	PROPN
ma-86	238	7	mk∑	mk∑	NOUN
ma-86	238	8	j=1	j=1	NOUN
ma-86	239	1	r	r	NOUN
ma-86	239	2	1/2−h	1/2−h	NUM
ma-86	239	3	j	j	PROPN
ma-86	239	4	(	(	PUNCT
ma-86	239	5	rmk	rmk	PROPN
ma-86	239	6	−	−	PROPN
ma-86	239	7	rj	rj	PROPN
ma-86	239	8	)	)	PUNCT
ma-86	239	9	−1/2−hui(rj)(rj	−1/2−hui(rj)(rj	NOUN
ma-86	239	10	−	−	PROPN
ma-86	239	11	rj−1	rj−1	NOUN
ma-86	239	12	)	)	PUNCT
ma-86	239	13	,	,	PUNCT
ma-86	239	14	(	(	PUNCT
ma-86	239	15	2.11	2.11	NUM
ma-86	239	16	)	)	PUNCT
ma-86	239	17	k	k	NOUN
ma-86	240	1	=	=	SYM
ma-86	240	2	1	1	NUM
ma-86	240	3	,	,	PUNCT
ma-86	240	4	2	2	NUM
ma-86	240	5	,	,	PUNCT
ma-86	240	6	·	·	PUNCT
ma-86	240	7	·	·	PUNCT
ma-86	240	8	·	·	PUNCT
ma-86	240	9	,	,	PUNCT
ma-86	240	10	n.it	n.it	NOUN
ma-86	240	11	is	be	AUX
ma-86	240	12	easy	easy	ADJ
ma-86	240	13	to	to	PART
ma-86	240	14	show	show	VERB
ma-86	240	15	that	that	SCONJ
ma-86	240	16	q̃i(tk)→	q̃i(tk)→	NOUN
ma-86	240	17	qi(t	qi(t	NOUN
ma-86	240	18	)	)	PUNCT
ma-86	240	19	almost	almost	ADV
ma-86	240	20	surely	surely	ADV
ma-86	240	21	as	as	SCONJ
ma-86	240	22	mk	mk	X
ma-86	240	23	→∞	→∞	PROPN
ma-86	240	24	for	for	ADP
ma-86	240	25	each	each	PRON
ma-86	240	26	k	k	NOUN
ma-86	241	1	=	=	SYM
ma-86	241	2	1	1	NUM
ma-86	241	3	,	,	PUNCT
ma-86	241	4	2	2	NUM
ma-86	241	5	,	,	PUNCT
ma-86	241	6	·	·	PUNCT
ma-86	241	7	·	·	PUNCT
ma-86	241	8	·	·	PUNCT
ma-86	241	9	,	,	PUNCT
ma-86	241	10	n.we	n.we	PRON
ma-86	241	11	use	use	VERB
ma-86	241	12	this	this	DET
ma-86	241	13	approximate	approximate	ADJ
ma-86	241	14	observation	observation	NOUN
ma-86	241	15	in	in	ADP
ma-86	241	16	the	the	DET
ma-86	241	17	calculation	calculation	NOUN
ma-86	241	18	of	of	ADP
ma-86	241	19	our	our	PRON
ma-86	241	20	estimators	estimator	NOUN
ma-86	241	21	.	.	PUNCT
ma-86	242	1	thus	thus	ADV
ma-86	242	2	our	our	PRON
ma-86	242	3	observationsare	observationsare	NOUN
ma-86	242	4	ui(t	ui(t	NOUN
ma-86	242	5	)	)	PUNCT
ma-86	243	1	≈	≈	PROPN
ma-86	243	2	∫	∫	PROPN
ma-86	243	3	t	t	PROPN
ma-86	243	4	0	0	NUM
ma-86	243	5	kh(t	kh(t	PROPN
ma-86	243	6	,	,	PUNCT
ma-86	243	7	s)dz̃i(s	s)dz̃i(s	NOUN
ma-86	243	8	)	)	PUNCT
ma-86	243	9	where	where	SCONJ
ma-86	243	10	z̃i(t	z̃i(t	VERB
ma-86	243	11	)	)	PUNCT
ma-86	243	12	=	=	SYM
ma-86	244	1	θ	θ	PROPN
ma-86	244	2	∫	∫	PROPN
ma-86	244	3	t	t	PROPN
ma-86	244	4	0	0	PUNCT
ma-86	245	1	q̃i(s)dvs	q̃i(s)dvs	PROPN
ma-86	246	1	+	+	PROPN
ma-86	246	2	mh	mh	PROPN
ma-86	246	3	t	t	NOUN
ma-86	246	4	.	.	PUNCT
ma-86	247	1	(	(	PUNCT
ma-86	247	2	2.12	2.12	NUM
ma-86	247	3	)	)	PUNCT
ma-86	247	4	observed	observe	VERB
ma-86	247	5	at	at	ADP
ma-86	247	6	poisson	poisson	PROPN
ma-86	247	7	arrivals	arrival	NOUN
ma-86	247	8	t1	t1	PROPN
ma-86	247	9	,	,	PUNCT
ma-86	247	10	t2	t2	NOUN
ma-86	247	11	,	,	PUNCT
ma-86	247	12	.	.	PUNCT
ma-86	247	13	.	.	PUNCT
ma-86	248	1	.	.	PUNCT
ma-86	249	1	,	,	PUNCT
ma-86	249	2	tn	tn	PROPN
ma-86	249	3	.	.	PUNCT
ma-86	250	1	we	we	PRON
ma-86	250	2	observe	observe	VERB
ma-86	250	3	just	just	ADV
ma-86	250	4	one	one	NUM
ma-86	250	5	such	such	ADJ
ma-86	250	6	approximate	approximate	ADJ
ma-86	250	7	fourier	fourier	NOUN
ma-86	250	8	coefficient	coefficient	NOUN
ma-86	250	9	ui(t	ui(t	NOUN
ma-86	250	10	)	)	PUNCT
ma-86	250	11	which	which	PRON
ma-86	250	12	we	we	PRON
ma-86	250	13	denote	denote	VERB
ma-86	250	14	by	by	ADP
ma-86	250	15	u(t	u(t	NOUN
ma-86	250	16	)	)	PUNCT
ma-86	250	17	and	and	CCONJ
ma-86	250	18	the	the	DET
ma-86	250	19	corresponding	corresponding	ADJ
ma-86	250	20	observations	observation	NOUN
ma-86	250	21	are	be	AUX
ma-86	250	22	denoted	denote	VERB
ma-86	250	23	by	by	ADP
ma-86	250	24	ut1	ut1	NOUN
ma-86	250	25	,	,	PUNCT
ma-86	250	26	ut2	ut2	NOUN
ma-86	250	27	,	,	PUNCT
ma-86	250	28	.	.	PUNCT
ma-86	250	29	.	.	PUNCT
ma-86	251	1	.	.	PUNCT
ma-86	252	1	,	,	PUNCT
ma-86	252	2	utnand	utnand	PRON
ma-86	252	3	let	let	VERB
ma-86	252	4	n	n	PRON
ma-86	252	5	→∞.	→∞.	PUNCT
ma-86	253	1	ideally	ideally	ADV
ma-86	253	2	we	we	PRON
ma-86	253	3	are	be	AUX
ma-86	253	4	in	in	ADP
ma-86	253	5	a	a	DET
ma-86	253	6	large	large	ADJ
ma-86	253	7	time	time	NOUN
ma-86	253	8	asymptotic	asymptotic	ADJ
ma-86	253	9	framework.now	framework.now	X
ma-86	253	10	we	we	PRON
ma-86	253	11	focus	focus	VERB
ma-86	253	12	on	on	ADP
ma-86	253	13	the	the	DET
ma-86	253	14	estimation	estimation	NOUN
ma-86	253	15	methodology	methodology	NOUN
ma-86	253	16	.	.	PUNCT
ma-86	254	1	define	define	VERB
ma-86	254	2	ρ	ρ	NOUN
ma-86	254	3	:	:	PUNCT
ma-86	254	4	=	=	SYM
ma-86	254	5	ρ(λ	ρ(λ	PROPN
ma-86	254	6	,	,	PUNCT
ma-86	254	7	θ	θ	NOUN
ma-86	254	8	)	)	PUNCT
ma-86	254	9	=	=	SYM
ma-86	254	10	λ	λ	PROPN
ma-86	254	11	λ−	λ−	PROPN
ma-86	254	12	κ(θ	κ(θ	PROPN
ma-86	254	13	)	)	PUNCT
ma-86	255	1	+	+	CCONJ
ma-86	256	1	β2	β2	ADJ
ma-86	256	2	m	m	NOUN
ma-86	256	3	i	i	PRON
ma-86	256	4	.	.	PUNCT
ma-86	257	1	(	(	PUNCT
ma-86	257	2	2.13	2.13	NUM
ma-86	257	3	)	)	PUNCT
ma-86	257	4	the	the	DET
ma-86	257	5	quasi	quasi	ADJ
ma-86	257	6	likelihood	likelihood	PROPN
ma-86	257	7	estimator	estimator	NOUN
ma-86	257	8	is	be	AUX
ma-86	257	9	the	the	DET
ma-86	257	10	solution	solution	NOUN
ma-86	257	11	of	of	ADP
ma-86	257	12	the	the	DET
ma-86	257	13	estimating	estimate	VERB
ma-86	257	14	equation	equation	NOUN
ma-86	257	15	:	:	PUNCT
ma-86	257	16	g∗n(θ	g∗n(θ	PROPN
ma-86	257	17	)	)	PUNCT
ma-86	258	1	=	=	SYM
ma-86	258	2	0	0	PUNCT
ma-86	258	3	(	(	PUNCT
ma-86	258	4	2.14	2.14	NUM
ma-86	258	5	)	)	PUNCT
ma-86	258	6	where	where	SCONJ
ma-86	258	7	g∗n(θ	g∗n(θ	PROPN
ma-86	258	8	)	)	PUNCT
ma-86	259	1	=	=	PUNCT
ma-86	260	1	β2ν	β2ν	NOUN
ma-86	261	1	i	i	PRON
ma-86	261	2	λ(ρ(λ	λ(ρ(λ	ADV
ma-86	261	3	,	,	PUNCT
ma-86	261	4	θ))2	θ))2	NOUN
ma-86	261	5	ρ(λ	ρ(λ	PROPN
ma-86	261	6	,	,	PUNCT
ma-86	261	7	2θ	2θ	NUM
ma-86	261	8	)	)	PUNCT
ma-86	261	9	n∑	n∑	NOUN
ma-86	261	10	i=1	i=1	X
ma-86	262	1	uti−1	uti−1	PROPN
ma-86	262	2	(	(	PUNCT
ma-86	262	3	(	(	PUNCT
ma-86	262	4	uti−1	uti−1	PROPN
ma-86	262	5	θρ(λ	θρ(λ	NUM
ma-86	262	6	,	,	PUNCT
ma-86	262	7	θ))2	θ))2	NOUN
ma-86	262	8	+	+	CCONJ
ma-86	262	9	λ	λ	NOUN
ma-86	262	10	)	)	PUNCT
ma-86	262	11	−1	−1	NOUN
ma-86	262	12	(	(	PUNCT
ma-86	262	13	uti	uti	PROPN
ma-86	262	14	−	−	PROPN
ma-86	262	15	ρ(λ	ρ(λ	PROPN
ma-86	262	16	,	,	PUNCT
ma-86	262	17	θ)uti−1	θ)uti−1	PROPN
ma-86	262	18	)	)	PUNCT
ma-86	262	19	(	(	PUNCT
ma-86	262	20	2.15	2.15	NUM
ma-86	262	21	)	)	PUNCT
ma-86	262	22	we	we	PRON
ma-86	262	23	call	call	VERB
ma-86	262	24	the	the	DET
ma-86	262	25	solution	solution	NOUN
ma-86	262	26	of	of	ADP
ma-86	262	27	the	the	DET
ma-86	262	28	estimating	estimate	VERB
ma-86	262	29	equation	equation	NOUN
ma-86	262	30	the	the	DET
ma-86	262	31	quasi	quasi	ADJ
ma-86	262	32	likelihood	likelihood	PROPN
ma-86	262	33	estimator	estimator	NOUN
ma-86	262	34	.	.	PUNCT
ma-86	263	1	there	there	PRON
ma-86	263	2	is	be	VERB
ma-86	263	3	no	no	DET
ma-86	263	4	explicitsolution	explicitsolution	NOUN
ma-86	263	5	for	for	ADP
ma-86	263	6	this	this	DET
ma-86	263	7	equation.the	equation.the	DET
ma-86	263	8	optimal	optimal	ADJ
ma-86	263	9	estimating	estimating	NOUN
ma-86	263	10	function	function	NOUN
ma-86	263	11	for	for	ADP
ma-86	263	12	estimation	estimation	NOUN
ma-86	263	13	of	of	ADP
ma-86	263	14	the	the	DET
ma-86	263	15	unknown	unknown	ADJ
ma-86	263	16	parameter	parameter	NOUN
ma-86	263	17	θ	θ	PROPN
ma-86	263	18	is	be	AUX
ma-86	263	19	gn(θ	gn(θ	PUNCT
ma-86	263	20	)	)	PUNCT
ma-86	264	1	=	=	SYM
ma-86	264	2	β2ν	β2ν	NOUN
ma-86	265	1	i	i	PRON
ma-86	265	2	n∑	n∑	INTJ
ma-86	265	3	i=1	i=1	PRON
ma-86	266	1	uti−1	uti−1	PROPN
ma-86	267	1	[	[	X
ma-86	267	2	uti	uti	PROPN
ma-86	267	3	−	−	PROPN
ma-86	267	4	ρ(λ	ρ(λ	PROPN
ma-86	267	5	,	,	PUNCT
ma-86	267	6	θ)uti−1	θ)uti−1	PROPN
ma-86	267	7	]	]	PUNCT
ma-86	267	8	.	.	PUNCT
ma-86	268	1	(	(	PUNCT
ma-86	268	2	2.16	2.16	NUM
ma-86	268	3	)	)	PUNCT
ma-86	268	4	the	the	DET
ma-86	268	5	martingale	martingale	NOUN
ma-86	268	6	estimation	estimation	NOUN
ma-86	268	7	function	function	NOUN
ma-86	268	8	(	(	PUNCT
ma-86	268	9	mef	mef	NOUN
ma-86	268	10	)	)	PUNCT
ma-86	268	11	estimator	estimator	NOUN
ma-86	268	12	of	of	ADP
ma-86	268	13	ρ	ρ	PROPN
ma-86	268	14	is	be	AUX
ma-86	268	15	the	the	DET
ma-86	268	16	solution	solution	NOUN
ma-86	268	17	of	of	ADP
ma-86	268	18	gn(θ	gn(θ	NOUN
ma-86	268	19	)	)	PUNCT
ma-86	269	1	=	=	SYM
ma-86	269	2	0	0	PUNCT
ma-86	269	3	and	and	CCONJ
ma-86	269	4	isgiven	isgiven	VERB
ma-86	269	5	by	by	ADP
ma-86	269	6	ρ̂n	ρ̂n	NOUN
ma-86	269	7	:	:	PUNCT
ma-86	270	1	=	=	SYM
ma-86	270	2	∑n	∑n	PROPN
ma-86	270	3	i=1	i=1	PROPN
ma-86	271	1	uti−1	uti−1	PROPN
ma-86	271	2	uti∑n	uti∑n	NOUN
ma-86	271	3	i=1	i=1	PROPN
ma-86	271	4	u	u	NOUN
ma-86	271	5	2	2	NUM
ma-86	271	6	ti−1	ti−1	NOUN
ma-86	271	7	.	.	PUNCT
ma-86	272	1	(	(	PUNCT
ma-86	272	2	2.17	2.17	NUM
ma-86	272	3	)	)	PUNCT
ma-86	272	4	3	3	NUM
ma-86	272	5	.	.	X
ma-86	272	6	main	main	ADJ
ma-86	272	7	results	result	NOUN
ma-86	272	8	we	we	PRON
ma-86	272	9	do	do	VERB
ma-86	272	10	the	the	DET
ma-86	272	11	parameter	parameter	NOUN
ma-86	272	12	estimation	estimation	NOUN
ma-86	272	13	in	in	ADP
ma-86	272	14	two	two	NUM
ma-86	272	15	steps	step	NOUN
ma-86	272	16	:	:	PUNCT
ma-86	272	17	the	the	DET
ma-86	272	18	rate	rate	NOUN
ma-86	272	19	λ	λ	PROPN
ma-86	272	20	of	of	ADP
ma-86	272	21	the	the	DET
ma-86	272	22	poisson	poisson	NOUN
ma-86	272	23	process	process	NOUN
ma-86	272	24	can	can	AUX
ma-86	272	25	be	be	AUX
ma-86	272	26	estimatedgiven	estimatedgiven	VERB
ma-86	272	27	the	the	DET
ma-86	272	28	arrival	arrival	NOUN
ma-86	272	29	times	time	NOUN
ma-86	272	30	ti	ti	PROPN
ma-86	272	31	,	,	PUNCT
ma-86	272	32	therefore	therefore	ADV
ma-86	272	33	it	it	PRON
ma-86	272	34	is	be	AUX
ma-86	272	35	done	do	VERB
ma-86	272	36	at	at	ADP
ma-86	272	37	a	a	DET
ma-86	272	38	first	first	ADJ
ma-86	272	39	step	step	NOUN
ma-86	272	40	.	.	PUNCT
ma-86	273	1	since	since	SCONJ
ma-86	273	2	we	we	PRON
ma-86	273	3	observe	observe	VERB
ma-86	273	4	total	total	ADJ
ma-86	273	5	number	number	NOUN
ma-86	273	6	ofarrivals	ofarrival	NOUN
ma-86	273	7	n	n	ADP
ma-86	273	8	of	of	ADP
ma-86	273	9	the	the	DET
ma-86	273	10	poisson	poisson	NOUN
ma-86	273	11	process	process	NOUN
ma-86	273	12	over	over	ADP
ma-86	273	13	the	the	DET
ma-86	273	14	t	t	NOUN
ma-86	273	15	intervals	interval	NOUN
ma-86	273	16	of	of	ADP
ma-86	273	17	length	length	NOUN
ma-86	273	18	one	one	NUM
ma-86	273	19	,	,	PUNCT
ma-86	273	20	the	the	DET
ma-86	273	21	mle	mle	NOUN
ma-86	273	22	of	of	ADP
ma-86	273	23	λ	λ	PROPN
ma-86	273	24	is	be	AUX
ma-86	273	25	given	give	VERB
ma-86	273	26	by	by	ADP
ma-86	273	27	λ̂n	λ̂n	PUNCT
ma-86	273	28	:	:	PUNCT
ma-86	273	29	=	=	SYM
ma-86	273	30	n	n	PRON
ma-86	273	31	t	t	NOUN
ma-86	273	32	.	.	PUNCT
ma-86	274	1	(	(	PUNCT
ma-86	274	2	3.1	3.1	NUM
ma-86	274	3	)	)	PUNCT
ma-86	274	4	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	PROPN
ma-86	274	5	eur	eur	PROPN
ma-86	274	6	.	.	PUNCT
ma-86	275	1	j.	j.	PROPN
ma-86	275	2	math	math	PROPN
ma-86	275	3	.	.	PUNCT
ma-86	276	1	anal	anal	PROPN
ma-86	276	2	.	.	PUNCT
ma-86	277	1	10.28924	10.28924	NUM
ma-86	277	2	/	/	SYM
ma-86	277	3	ada	ada	NOUN
ma-86	277	4	/	/	SYM
ma-86	277	5	ma.2.15	ma.2.15	NOUN
ma-86	277	6	11	11	NUM
ma-86	277	7	theorem	theorem	NOUN
ma-86	277	8	3.1	3.1	NUM
ma-86	277	9	we	we	PRON
ma-86	277	10	have	have	VERB
ma-86	277	11	λ̂n	λ̂n	X
ma-86	277	12	→	→	SYM
ma-86	277	13	λ	λ	X
ma-86	277	14	a.s	a.s	PROPN
ma-86	277	15	.	.	PROPN
ma-86	277	16	as	as	ADP
ma-86	277	17	n	n	PROPN
ma-86	277	18	→∞	→∞	PROPN
ma-86	277	19	,	,	PUNCT
ma-86	277	20	√	√	NUM
ma-86	277	21	n(λ̂n	n(λ̂n	PROPN
ma-86	277	22	−	−	PROPN
ma-86	277	23	λ)→d	λ)→d	PROPN
ma-86	277	24	n	n	PROPN
ma-86	277	25	(	(	PUNCT
ma-86	277	26	0	0	NUM
ma-86	277	27	,	,	PUNCT
ma-86	277	28	eλ(1−	eλ(1−	PROPN
ma-86	277	29	e−λ	e−λ	NOUN
ma-86	277	30	)	)	PUNCT
ma-86	277	31	)	)	PUNCT
ma-86	277	32	as	as	ADP
ma-86	277	33	n	n	X
ma-86	277	34	→∞.	→∞.	NOUN
ma-86	277	35	proof	proof	NOUN
ma-86	277	36	.	.	PUNCT
ma-86	278	1	let	let	VERB
ma-86	278	2	vi	vi	NOUN
ma-86	278	3	be	be	AUX
ma-86	278	4	the	the	DET
ma-86	278	5	number	number	NOUN
ma-86	278	6	of	of	ADP
ma-86	278	7	arrivals	arrival	NOUN
ma-86	278	8	in	in	ADP
ma-86	278	9	the	the	DET
ma-86	278	10	interval	interval	NOUN
ma-86	278	11	(	(	PUNCT
ma-86	278	12	i	i	PRON
ma-86	278	13	−	−	PROPN
ma-86	278	14	1	1	NUM
ma-86	278	15	,	,	PUNCT
ma-86	278	16	i	i	PRON
ma-86	278	17	]	]	PUNCT
ma-86	278	18	.	.	PUNCT
ma-86	279	1	then	then	ADV
ma-86	279	2	vi	vi	VERB
ma-86	279	3	,	,	PUNCT
ma-86	279	4	i	i	PRON
ma-86	279	5	=	=	NOUN
ma-86	279	6	1	1	NUM
ma-86	279	7	,	,	PUNCT
ma-86	279	8	2	2	NUM
ma-86	279	9	,	,	PUNCT
ma-86	279	10	.	.	PUNCT
ma-86	279	11	.	.	PUNCT
ma-86	279	12	.	.	PUNCT
ma-86	280	1	,	,	PUNCT
ma-86	280	2	n	n	PRON
ma-86	280	3	are	be	AUX
ma-86	280	4	i.i.d.poisson	i.i.d.poisson	NOUN
ma-86	280	5	distributed	distribute	VERB
ma-86	280	6	with	with	ADP
ma-86	280	7	parameter	parameter	PROPN
ma-86	280	8	λ	λ	PROPN
ma-86	280	9	.	.	PUNCT
ma-86	281	1	since	since	SCONJ
ma-86	281	2	φ	φ	PROPN
ma-86	281	3	is	be	AUX
ma-86	281	4	continuous	continuous	ADJ
ma-86	281	5	,	,	PUNCT
ma-86	281	6	we	we	PRON
ma-86	281	7	have	have	VERB
ma-86	281	8	i{0}(vi	i{0}(vi	NOUN
ma-86	281	9	)	)	PUNCT
ma-86	281	10	=	=	SYM
ma-86	281	11	i{0}(u(ti	i{0}(u(ti	NOUN
ma-86	281	12	)	)	PUNCT
ma-86	281	13	)	)	PUNCT
ma-86	282	1	a.s	a.s	PROPN
ma-86	283	1	.	.	PROPN
ma-86	283	2	i	i	PROPN
ma-86	283	3	=	=	NOUN
ma-86	283	4	1	1	NUM
ma-86	283	5	,	,	PUNCT
ma-86	283	6	2	2	NUM
ma-86	283	7	,	,	PUNCT
ma-86	283	8	.	.	PUNCT
ma-86	283	9	.	.	PUNCT
ma-86	284	1	.	.	PUNCT
ma-86	285	1	,	,	PUNCT
ma-86	285	2	n.	n.	PROPN
ma-86	285	3	note	note	VERB
ma-86	285	4	that	that	SCONJ
ma-86	285	5	1	1	NUM
ma-86	285	6	n	n	NUM
ma-86	285	7	n∑	n∑	NOUN
ma-86	285	8	i=1	i=1	PROPN
ma-86	285	9	i{0}(uti	i{0}(uti	PROPN
ma-86	285	10	)	)	PUNCT
ma-86	286	1	→	→	SYM
ma-86	286	2	a.s	a.s	PROPN
ma-86	286	3	.	.	PROPN
ma-86	286	4	e(i{0}v1	e(i{0}v1	PROPN
ma-86	286	5	)	)	PUNCT
ma-86	287	1	=	=	SYM
ma-86	287	2	p	p	X
ma-86	287	3	(	(	PUNCT
ma-86	287	4	v1	v1	NOUN
ma-86	287	5	=	=	SYM
ma-86	287	6	0	0	NUM
ma-86	287	7	)	)	PUNCT
ma-86	287	8	=	=	PRON
ma-86	287	9	e−λ	e−λ	NOUN
ma-86	287	10	as	as	ADP
ma-86	287	11	n	n	PROPN
ma-86	287	12	→∞.	→∞.	PROPN
ma-86	287	13	lln	lln	PROPN
ma-86	287	14	and	and	CCONJ
ma-86	287	15	clt	clt	PROPN
ma-86	287	16	and	and	CCONJ
ma-86	287	17	delta	delta	NOUN
ma-86	287	18	method	method	NOUN
ma-86	287	19	applied	apply	VERB
ma-86	287	20	to	to	ADP
ma-86	287	21	the	the	DET
ma-86	287	22	sequence	sequence	NOUN
ma-86	287	23	i{0}(uti	i{0}(uti	PROPN
ma-86	287	24	)	)	PUNCT
ma-86	287	25	,	,	PUNCT
ma-86	287	26	i	i	PRON
ma-86	287	27	=	=	NOUN
ma-86	287	28	1	1	NUM
ma-86	287	29	,	,	PUNCT
ma-86	287	30	2	2	NUM
ma-86	287	31	,	,	PUNCT
ma-86	287	32	.	.	PUNCT
ma-86	287	33	.	.	PUNCT
ma-86	288	1	.	.	PUNCT
ma-86	289	1	,	,	PUNCT
ma-86	289	2	n	n	PRON
ma-86	289	3	give	give	VERB
ma-86	289	4	the	the	DET
ma-86	289	5	results	result	NOUN
ma-86	289	6	.	.	PUNCT
ma-86	290	1	the	the	DET
ma-86	290	2	clt	clt	PROPN
ma-86	290	3	result	result	NOUN
ma-86	290	4	above	above	ADV
ma-86	290	5	allows	allow	VERB
ma-86	290	6	us	we	PRON
ma-86	290	7	to	to	PART
ma-86	290	8	construct	construct	VERB
ma-86	290	9	confidence	confidence	NOUN
ma-86	290	10	interval	interval	NOUN
ma-86	290	11	for	for	ADP
ma-86	290	12	the	the	DET
ma-86	290	13	jump	jump	NOUN
ma-86	290	14	rate	rate	NOUN
ma-86	290	15	λ	λ	PROPN
ma-86	290	16	.	.	PUNCT
ma-86	290	17	corollary	corollary	ADJ
ma-86	290	18	3.1	3.1	NUM
ma-86	290	19	a	a	DET
ma-86	290	20	100(1−	100(1−	NUM
ma-86	290	21	α)%	α)%	NOUN
ma-86	290	22	confidence	confidence	NOUN
ma-86	290	23	interval	interval	NOUN
ma-86	290	24	for	for	ADP
ma-86	290	25	λ	λ	PROPN
ma-86	290	26	is	be	AUX
ma-86	290	27	given	give	VERB
ma-86	290	28	by	by	ADP
ma-86	290	29	[	[	PUNCT
ma-86	290	30	n	n	NOUN
ma-86	290	31	t	t	NOUN
ma-86	291	1	−	−	PROPN
ma-86	291	2	z1−α	z1−α	PROPN
ma-86	291	3	2	2	NUM
ma-86	291	4	√	√	ADP
ma-86	291	5	1	1	NUM
ma-86	291	6	n	n	CCONJ
ma-86	291	7	−	−	NUM
ma-86	291	8	1	1	NUM
ma-86	291	9	t	t	NOUN
ma-86	291	10	,	,	PUNCT
ma-86	291	11	n	n	NOUN
ma-86	291	12	t	t	NOUN
ma-86	292	1	+	+	CCONJ
ma-86	292	2	z1−α	z1−α	PROPN
ma-86	292	3	2	2	NUM
ma-86	292	4	√	√	ADP
ma-86	292	5	1	1	NUM
ma-86	292	6	n	n	CCONJ
ma-86	292	7	−	−	NUM
ma-86	292	8	1	1	NUM
ma-86	292	9	t	t	NOUN
ma-86	292	10	]	]	PUNCT
ma-86	292	11	where	where	SCONJ
ma-86	292	12	z1−α	z1−α	PROPN
ma-86	292	13	2	2	NUM
ma-86	292	14	is	be	AUX
ma-86	292	15	the	the	DET
ma-86	292	16	(	(	PUNCT
ma-86	292	17	1−	1−	NUM
ma-86	292	18	α	α	NOUN
ma-86	292	19	2	2	X
ma-86	292	20	)	)	PUNCT
ma-86	292	21	-quantile	-quantile	NOUN
ma-86	292	22	of	of	ADP
ma-86	292	23	the	the	DET
ma-86	292	24	standard	standard	ADJ
ma-86	292	25	normal	normal	ADJ
ma-86	292	26	distribution	distribution	NOUN
ma-86	292	27	.	.	PUNCT
ma-86	293	1	we	we	PRON
ma-86	293	2	obtain	obtain	VERB
ma-86	293	3	the	the	DET
ma-86	293	4	strong	strong	ADJ
ma-86	293	5	consistency	consistency	NOUN
ma-86	293	6	and	and	CCONJ
ma-86	293	7	asymptotic	asymptotic	ADJ
ma-86	293	8	normality	normality	NOUN
ma-86	293	9	of	of	ADP
ma-86	293	10	the	the	DET
ma-86	293	11	mef	mef	NOUN
ma-86	293	12	estimator	estimator	NOUN
ma-86	293	13	.	.	PUNCT
ma-86	294	1	theorem	theorem	VERB
ma-86	294	2	3.2	3.2	NUM
ma-86	294	3	we	we	PRON
ma-86	294	4	have	have	VERB
ma-86	294	5	ρ̂n	ρ̂n	NOUN
ma-86	294	6	→	→	SYM
ma-86	294	7	ρ	ρ	PROPN
ma-86	295	1	a.s	a.s	PROPN
ma-86	295	2	.	.	PROPN
ma-86	295	3	as	as	ADP
ma-86	295	4	n	n	PROPN
ma-86	295	5	→∞	→∞	NOUN
ma-86	295	6	,	,	PUNCT
ma-86	295	7	√	√	PRON
ma-86	295	8	n(ρ̂n	n(ρ̂n	NOUN
ma-86	295	9	−	−	NOUN
ma-86	295	10	ρ)→d	ρ)→d	NOUN
ma-86	295	11	n	n	PROPN
ma-86	295	12	(	(	PUNCT
ma-86	295	13	0	0	NUM
ma-86	295	14	,	,	PUNCT
ma-86	295	15	λ−i(1−	λ−i(1−	X
ma-86	295	16	e−ρ	e−ρ	PROPN
ma-86	295	17	)	)	PUNCT
ma-86	295	18	)	)	PUNCT
ma-86	295	19	as	as	ADP
ma-86	295	20	n	n	X
ma-86	295	21	→∞.	→∞.	SYM
ma-86	295	22	proof	proof	NOUN
ma-86	295	23	:	:	PUNCT
ma-86	295	24	by	by	ADP
ma-86	295	25	using	use	VERB
ma-86	295	26	the	the	DET
ma-86	295	27	fact	fact	NOUN
ma-86	295	28	that	that	SCONJ
ma-86	295	29	every	every	DET
ma-86	295	30	stationary	stationary	ADJ
ma-86	295	31	mixing	mixing	NOUN
ma-86	295	32	process	process	NOUN
ma-86	295	33	is	be	AUX
ma-86	295	34	ergodic	ergodic	ADJ
ma-86	295	35	,	,	PUNCT
ma-86	295	36	it	it	PRON
ma-86	295	37	is	be	AUX
ma-86	295	38	easy	easy	ADJ
ma-86	295	39	to	to	PART
ma-86	295	40	show	show	VERB
ma-86	295	41	thatif	thatif	PROPN
ma-86	295	42	ut	ut	PROPN
ma-86	295	43	is	be	AUX
ma-86	295	44	a	a	DET
ma-86	295	45	stationary	stationary	ADJ
ma-86	295	46	ergodic	ergodic	ADJ
ma-86	295	47	o	o	ADJ
ma-86	295	48	-	-	PUNCT
ma-86	295	49	u	u	NOUN
ma-86	295	50	process	process	NOUN
ma-86	295	51	and	and	CCONJ
ma-86	295	52	ti	ti	NOUN
ma-86	295	53	is	be	AUX
ma-86	295	54	a	a	DET
ma-86	295	55	process	process	NOUN
ma-86	295	56	with	with	ADP
ma-86	295	57	nonnegative	nonnegative	ADJ
ma-86	295	58	i.i.d	i.i.d	PROPN
ma-86	295	59	.	.	PUNCT
ma-86	296	1	incrementswhich	incrementswhich	PROPN
ma-86	296	2	is	be	AUX
ma-86	296	3	independent	independent	ADJ
ma-86	296	4	of	of	ADP
ma-86	296	5	ut	ut	PROPN
ma-86	296	6	,	,	PUNCT
ma-86	296	7	then	then	ADV
ma-86	296	8	{	{	PUNCT
ma-86	296	9	uti	uti	PROPN
ma-86	296	10	,	,	PUNCT
ma-86	296	11	i	i	PRON
ma-86	296	12	≥	≥	VERB
ma-86	296	13	1	1	NUM
ma-86	296	14	}	}	PUNCT
ma-86	296	15	is	be	AUX
ma-86	296	16	a	a	DET
ma-86	296	17	stationary	stationary	ADJ
ma-86	296	18	ergodic	ergodic	ADJ
ma-86	296	19	process	process	NOUN
ma-86	296	20	.	.	PUNCT
ma-86	297	1	hence	hence	ADV
ma-86	297	2	{	{	PUNCT
ma-86	297	3	uti	uti	PROPN
ma-86	297	4	,	,	PUNCT
ma-86	297	5	i	i	PRON
ma-86	297	6	≥	≥	VERB
ma-86	297	7	1	1	NUM
ma-86	297	8	}	}	PUNCT
ma-86	297	9	isa	isa	VERB
ma-86	297	10	stationary	stationary	ADJ
ma-86	297	11	ergodic	ergodic	ADJ
ma-86	297	12	process.observe	process.observe	NOUN
ma-86	297	13	that	that	DET
ma-86	297	14	uθi	uθi	NOUN
ma-86	297	15	(	(	PUNCT
ma-86	297	16	t	t	PROPN
ma-86	297	17	)	)	PUNCT
ma-86	297	18	:	:	PUNCT
ma-86	297	19	=	=	SYM
ma-86	297	20	vi	vi	PROPN
ma-86	297	21	is	be	AUX
ma-86	297	22	stationary	stationary	ADJ
ma-86	297	23	ergodic	ergodic	ADJ
ma-86	297	24	and	and	CCONJ
ma-86	297	25	vi	vi	ADJ
ma-86	297	26	∼	∼	NOUN
ma-86	297	27	n	n	CCONJ
ma-86	297	28	(	(	PUNCT
ma-86	297	29	0	0	NUM
ma-86	297	30	,	,	PUNCT
ma-86	297	31	σ2	σ2	NOUN
ma-86	297	32	)	)	PUNCT
ma-86	297	33	where	where	SCONJ
ma-86	297	34	σ2	σ2	NOUN
ma-86	297	35	is	be	AUX
ma-86	297	36	the	the	DET
ma-86	297	37	variance	variance	NOUN
ma-86	297	38	of	of	ADP
ma-86	297	39	u0	u0	PROPN
ma-86	297	40	.	.	PUNCT
ma-86	298	1	thus	thus	ADV
ma-86	298	2	by	by	ADP
ma-86	298	3	slln	slln	NOUN
ma-86	298	4	for	for	ADP
ma-86	298	5	zero	zero	NUM
ma-86	298	6	mean	mean	PROPN
ma-86	298	7	square	square	PROPN
ma-86	298	8	integrable	integrable	ADJ
ma-86	298	9	martingales	martingale	NOUN
ma-86	298	10	,	,	PUNCT
ma-86	298	11	we	we	PRON
ma-86	298	12	have	have	VERB
ma-86	298	13	as	as	ADP
ma-86	298	14	n	n	PROPN
ma-86	298	15	→∞	→∞	NOUN
ma-86	298	16	,	,	PUNCT
ma-86	298	17	1	1	NUM
ma-86	298	18	n	n	NUM
ma-86	298	19	n∑	n∑	NOUN
ma-86	298	20	i=1	i=1	PROPN
ma-86	299	1	uti−1	uti−1	PROPN
ma-86	299	2	uti	uti	PROPN
ma-86	299	3	→	→	SYM
ma-86	299	4	a.s	a.s	PROPN
ma-86	299	5	.	.	PROPN
ma-86	299	6	e(ut0ut1	e(ut0ut1	ADJ
ma-86	299	7	)	)	PUNCT
ma-86	299	8	=	=	SYM
ma-86	299	9	ρe(u2	ρe(u2	NUM
ma-86	299	10	t0	t0	PROPN
ma-86	299	11	)	)	PUNCT
ma-86	299	12	1	1	NUM
ma-86	300	1	n	n	NUM
ma-86	300	2	n∑	n∑	NOUN
ma-86	300	3	i=1	i=1	PROPN
ma-86	301	1	u2	u2	PROPN
ma-86	301	2	ti−1	ti−1	PROPN
ma-86	301	3	→a.s	→a.s	NUM
ma-86	301	4	.	.	PUNCT
ma-86	302	1	e(u2	e(u2	PROPN
ma-86	302	2	t0	t0	PROPN
ma-86	302	3	)	)	PUNCT
ma-86	302	4	thus	thus	ADV
ma-86	302	5	∑n	∑n	PROPN
ma-86	302	6	i=1	i=1	PROPN
ma-86	303	1	uti−1	uti−1	PROPN
ma-86	303	2	uti∑n	uti∑n	NOUN
ma-86	303	3	i=1	i=1	PROPN
ma-86	303	4	u	u	NOUN
ma-86	303	5	2	2	NUM
ma-86	303	6	ti−1	ti−1	NOUN
ma-86	303	7	→a.s	→a.s	NUM
ma-86	303	8	.	.	PUNCT
ma-86	304	1	ρ	ρ	PROPN
ma-86	304	2	.	.	PUNCT
ma-86	305	1	further	far	ADV
ma-86	305	2	,	,	PUNCT
ma-86	305	3	√	√	PRON
ma-86	305	4	n(ρ̂n	n(ρ̂n	NOUN
ma-86	305	5	−	−	PROPN
ma-86	305	6	ρ	ρ	NOUN
ma-86	305	7	)	)	PUNCT
ma-86	305	8	=	=	VERB
ma-86	306	1	n−1/2	n−1/2	PROPN
ma-86	306	2	∑n	∑n	NOUN
ma-86	306	3	i=1	i=1	PROPN
ma-86	307	1	uti−1	uti−1	PROPN
ma-86	307	2	(	(	PUNCT
ma-86	307	3	uti	uti	PROPN
ma-86	307	4	−	−	PROPN
ma-86	307	5	θuti−1	θuti−1	PROPN
ma-86	307	6	)	)	PUNCT
ma-86	308	1	n−1	n−1	PROPN
ma-86	308	2	∑n	∑n	PROPN
ma-86	308	3	i=1	i=1	PROPN
ma-86	308	4	u	u	NOUN
ma-86	308	5	2	2	NUM
ma-86	308	6	ti−1	ti−1	NOUN
ma-86	308	7	.	.	PUNCT
ma-86	309	1	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	PROPN
ma-86	309	2	eur	eur	PROPN
ma-86	309	3	.	.	PUNCT
ma-86	310	1	j.	j.	PROPN
ma-86	310	2	math	math	PROPN
ma-86	310	3	.	.	PUNCT
ma-86	311	1	anal	anal	PROPN
ma-86	311	2	.	.	PUNCT
ma-86	312	1	10.28924	10.28924	NUM
ma-86	312	2	/	/	SYM
ma-86	312	3	ada	ada	PROPN
ma-86	312	4	/	/	SYM
ma-86	312	5	ma.2.15	ma.2.15	PROPN
ma-86	312	6	12since	12since	X
ma-86	312	7	e(ut1ut2	e(ut1ut2	NOUN
ma-86	312	8	|ut1	|ut1	PUNCT
ma-86	312	9	)	)	PUNCT
ma-86	313	1	=	=	PUNCT
ma-86	313	2	θu2	θu2	NOUN
ma-86	313	3	t1it	t1it	NOUN
ma-86	313	4	follows	follow	VERB
ma-86	313	5	by	by	ADP
ma-86	313	6	lemma	lemma	PROPN
ma-86	313	7	3.1	3.1	NUM
ma-86	313	8	in	in	ADP
ma-86	313	9	bibby	bibby	PROPN
ma-86	313	10	and	and	CCONJ
ma-86	313	11	srensen	srensen	NOUN
ma-86	313	12	[	[	X
ma-86	313	13	2	2	NUM
ma-86	313	14	]	]	PUNCT
ma-86	313	15	n−1/2	n−1/2	PROPN
ma-86	313	16	n∑	n∑	NOUN
ma-86	313	17	i=1	i=1	PROPN
ma-86	314	1	uti−1	uti−1	PROPN
ma-86	314	2	(	(	PUNCT
ma-86	314	3	uti	uti	PROPN
ma-86	314	4	−	−	PROPN
ma-86	314	5	θuti−1	θuti−1	PROPN
ma-86	314	6	)	)	PUNCT
ma-86	314	7	converges	converge	VERB
ma-86	314	8	in	in	ADP
ma-86	314	9	distribution	distribution	NOUN
ma-86	314	10	to	to	ADP
ma-86	314	11	normal	normal	ADJ
ma-86	314	12	distribution	distribution	NOUN
ma-86	314	13	with	with	ADP
ma-86	314	14	mean	mean	NOUN
ma-86	314	15	zero	zero	NUM
ma-86	314	16	and	and	CCONJ
ma-86	314	17	variance	variance	NOUN
ma-86	314	18	equal	equal	ADJ
ma-86	314	19	to	to	ADP
ma-86	314	20	e[(ut1ut2	e[(ut1ut2	NOUN
ma-86	314	21	)	)	PUNCT
ma-86	314	22	−	−	PROPN
ma-86	314	23	e(ut1ut2	e(ut1ut2	NOUN
ma-86	314	24	|ut1	|ut1	PROPN
ma-86	314	25	)	)	PUNCT
ma-86	314	26	]	]	SYM
ma-86	314	27	2	2	X
ma-86	314	28	=	=	SYM
ma-86	314	29	1−	1−	NUM
ma-86	314	30	e2(θ−β1δ){2(β1	e2(θ−β1δ){2(β1	PROPN
ma-86	314	31	−	−	PROPN
ma-86	314	32	θ)(βi	θ)(βi	NOUN
ma-86	315	1	+	+	CCONJ
ma-86	315	2	1)}−1	1)}−1	ADJ
ma-86	315	3	.	.	PUNCT
ma-86	316	1	applying	apply	VERB
ma-86	316	2	delta	delta	NOUN
ma-86	316	3	method	method	NOUN
ma-86	316	4	the	the	DET
ma-86	316	5	result	result	NOUN
ma-86	316	6	follows	follow	VERB
ma-86	316	7	.	.	PUNCT
ma-86	317	1	in	in	ADP
ma-86	317	2	the	the	DET
ma-86	317	3	next	next	ADJ
ma-86	317	4	step	step	NOUN
ma-86	317	5	,	,	PUNCT
ma-86	317	6	we	we	PRON
ma-86	317	7	use	use	VERB
ma-86	317	8	the	the	DET
ma-86	317	9	estimator	estimator	NOUN
ma-86	317	10	of	of	ADP
ma-86	317	11	λ	λ	PROPN
ma-86	317	12	to	to	PART
ma-86	317	13	estimate	estimate	VERB
ma-86	317	14	θ.note	θ.note	PRON
ma-86	317	15	that	that	SCONJ
ma-86	317	16	1	1	NUM
ma-86	317	17	ρ̂n	ρ̂n	NOUN
ma-86	317	18	=	=	SYM
ma-86	317	19	∑n	∑n	PROPN
ma-86	317	20	i=1	i=1	PROPN
ma-86	317	21	u	u	NOUN
ma-86	317	22	2	2	NUM
ma-86	317	23	ti−1∑n	ti−1∑n	NOUN
ma-86	317	24	i=1	i=1	X
ma-86	318	1	uti−1	uti−1	PROPN
ma-86	318	2	uti	uti	PROPN
ma-86	318	3	.	.	PUNCT
ma-86	319	1	hence	hence	ADV
ma-86	319	2	1	1	NUM
ma-86	319	3	+	+	CCONJ
ma-86	319	4	β2	β2	ADJ
ma-86	319	5	m	m	NOUN
ma-86	319	6	1	1	NUM
ma-86	320	1	−	−	PROPN
ma-86	320	2	κ(θ	κ(θ	PROPN
ma-86	320	3	)	)	PUNCT
ma-86	320	4	λ	λ	NOUN
ma-86	320	5	=	=	SYM
ma-86	321	1	∑n	∑n	PROPN
ma-86	321	2	i=1	i=1	PROPN
ma-86	321	3	u	u	NOUN
ma-86	321	4	2	2	NUM
ma-86	321	5	ti−1∑n	ti−1∑n	NOUN
ma-86	321	6	i=1	i=1	X
ma-86	322	1	uti−1	uti−1	PROPN
ma-86	322	2	uti	uti	PROPN
ma-86	322	3	.	.	PUNCT
ma-86	323	1	thus	thus	ADV
ma-86	323	2	β2	β2	VERB
ma-86	323	3	m	m	PROPN
ma-86	323	4	1	1	NUM
ma-86	323	5	−	−	PROPN
ma-86	323	6	κ(θ	κ(θ	PROPN
ma-86	323	7	)	)	PUNCT
ma-86	323	8	λ	λ	NOUN
ma-86	324	1	=	=	SYM
ma-86	324	2	∑n	∑n	PROPN
ma-86	324	3	i=1	i=1	PROPN
ma-86	324	4	u	u	NOUN
ma-86	324	5	2	2	NUM
ma-86	324	6	ti−1∑n	ti−1∑n	NOUN
ma-86	324	7	i=1	i=1	PUNCT
ma-86	325	1	uti−1	uti−1	PROPN
ma-86	325	2	uti	uti	PROPN
ma-86	325	3	−	−	PROPN
ma-86	326	1	1	1	NUM
ma-86	326	2	=	=	SYM
ma-86	326	3	−	−	PROPN
ma-86	326	4	∑n	∑n	PROPN
ma-86	326	5	i=1	i=1	PROPN
ma-86	327	1	uti−1	uti−1	PROPN
ma-86	328	1	[	[	X
ma-86	328	2	uti	uti	PROPN
ma-86	328	3	−	−	PROPN
ma-86	329	1	uti−1	uti−1	PROPN
ma-86	329	2	]	]	X
ma-86	329	3	∑n	∑n	PROPN
ma-86	329	4	i=1	i=1	PROPN
ma-86	330	1	uti−1	uti−1	PROPN
ma-86	330	2	uti	uti	PROPN
ma-86	330	3	.	.	PUNCT
ma-86	331	1	now	now	ADV
ma-86	331	2	replace	replace	VERB
ma-86	331	3	λ	λ	NOUN
ma-86	331	4	by	by	ADP
ma-86	331	5	its	its	PRON
ma-86	331	6	estimator	estimator	NOUN
ma-86	331	7	mle	mle	PROPN
ma-86	331	8	λ̂n	λ̂n	PROPN
ma-86	331	9	.	.	PUNCT
ma-86	332	1	β2	β2	PROPN
ma-86	332	2	m	m	PROPN
ma-86	332	3	1	1	NUM
ma-86	332	4	−	−	PROPN
ma-86	332	5	κ(θ	κ(θ	PROPN
ma-86	332	6	)	)	PUNCT
ma-86	333	1	=	=	PUNCT
ma-86	334	1	−	−	PROPN
ma-86	334	2	∑n	∑n	PROPN
ma-86	334	3	i=1	i=1	PROPN
ma-86	335	1	uti−1	uti−1	PROPN
ma-86	336	1	[	[	X
ma-86	336	2	uti	uti	PROPN
ma-86	336	3	−	−	PROPN
ma-86	337	1	uti−1	uti−1	PROPN
ma-86	337	2	]	]	PUNCT
ma-86	337	3	t	t	PROPN
ma-86	337	4	n	n	PROPN
ma-86	337	5	∑n	∑n	PROPN
ma-86	337	6	i=1	i=1	PROPN
ma-86	338	1	uti−1	uti−1	PROPN
ma-86	338	2	uti	uti	PROPN
ma-86	338	3	.	.	PUNCT
ma-86	339	1	thus	thus	ADV
ma-86	339	2	θ̂n	θ̂n	ADP
ma-86	339	3	=	=	PUNCT
ma-86	339	4	κ−1	κ−1	PROPN
ma-86	339	5	(	(	PUNCT
ma-86	339	6	β2	β2	VERB
ma-86	339	7	m	m	PROPN
ma-86	339	8	1	1	NUM
ma-86	339	9	+	+	NUM
ma-86	339	10	∑n	∑n	PROPN
ma-86	339	11	i=1	i=1	X
ma-86	340	1	uti−1	uti−1	PROPN
ma-86	341	1	[	[	X
ma-86	341	2	uti	uti	PROPN
ma-86	341	3	−	−	PROPN
ma-86	342	1	uti−1	uti−1	PROPN
ma-86	342	2	]	]	PUNCT
ma-86	342	3	t	t	PROPN
ma-86	342	4	n	n	PROPN
ma-86	342	5	∑n	∑n	PROPN
ma-86	342	6	i=1	i=1	PROPN
ma-86	343	1	uti−1	uti−1	PROPN
ma-86	343	2	uti	uti	PROPN
ma-86	343	3	)	)	PUNCT
ma-86	343	4	.	.	PUNCT
ma-86	344	1	since	since	SCONJ
ma-86	344	2	the	the	DET
ma-86	344	3	function	function	NOUN
ma-86	344	4	κ−1	κ−1	PROPN
ma-86	344	5	(	(	PUNCT
ma-86	344	6	·	·	PUNCT
ma-86	344	7	)	)	PUNCT
ma-86	344	8	is	be	AUX
ma-86	344	9	a	a	DET
ma-86	344	10	continuous	continuous	ADJ
ma-86	344	11	function	function	NOUN
ma-86	344	12	,	,	PUNCT
ma-86	344	13	by	by	ADP
ma-86	344	14	application	application	NOUN
ma-86	344	15	of	of	ADP
ma-86	344	16	delta	delta	PROPN
ma-86	344	17	method	method	NOUN
ma-86	344	18	,	,	PUNCT
ma-86	344	19	the	the	DET
ma-86	344	20	followingresult	followingresult	NOUN
ma-86	344	21	is	be	AUX
ma-86	344	22	a	a	DET
ma-86	344	23	consequence	consequence	NOUN
ma-86	344	24	of	of	ADP
ma-86	344	25	theorem	theorem	ADJ
ma-86	344	26	3.2	3.2	NUM
ma-86	344	27	.	.	PUNCT
ma-86	345	1	theorem	theorem	VERB
ma-86	345	2	3.3	3.3	NUM
ma-86	345	3	θ̂n	θ̂n	ADP
ma-86	345	4	→a.s	→a.s	X
ma-86	345	5	.	.	PUNCT
ma-86	346	1	θ	θ	PROPN
ma-86	346	2	as	as	ADP
ma-86	346	3	n	n	PROPN
ma-86	346	4	→∞	→∞	PROPN
ma-86	346	5	,	,	PUNCT
ma-86	346	6	√	√	PROPN
ma-86	346	7	n(θ̂n	n(θ̂n	NUM
ma-86	346	8	−	−	PROPN
ma-86	346	9	θ)→d	θ)→d	NOUN
ma-86	346	10	n	n	X
ma-86	346	11	(	(	PUNCT
ma-86	346	12	0	0	NUM
ma-86	346	13	,	,	PUNCT
ma-86	346	14	(	(	PUNCT
ma-86	346	15	κ′(θ))−2λ2(1−	κ′(θ))−2λ2(1−	NUM
ma-86	346	16	e−2λ−1(κ(θ)−β2	e−2λ−1(κ(θ)−β2	NUM
ma-86	346	17	m	m	NOUN
ma-86	346	18	1	1	NUM
ma-86	346	19	)	)	PUNCT
ma-86	346	20	)	)	PUNCT
ma-86	346	21	)	)	PUNCT
ma-86	346	22	as	as	ADP
ma-86	346	23	n	n	PROPN
ma-86	346	24	→∞.in	→∞.in	PROPN
ma-86	346	25	the	the	DET
ma-86	346	26	second	second	ADJ
ma-86	346	27	stage	stage	NOUN
ma-86	346	28	,	,	PUNCT
ma-86	346	29	we	we	PRON
ma-86	346	30	plug	plug	VERB
ma-86	346	31	-	-	PUNCT
ma-86	346	32	in	in	ADP
ma-86	346	33	λ	λ	NOUN
ma-86	346	34	by	by	ADP
ma-86	346	35	its	its	PRON
ma-86	346	36	estimator	estimator	NOUN
ma-86	346	37	λ̂n	λ̂n	PROPN
ma-86	346	38	.	.	PUNCT
ma-86	346	39	remark	remark	PROPN
ma-86	346	40	sub	sub	ADJ
ma-86	346	41	-	-	ADJ
ma-86	346	42	fractional	fractional	ADJ
ma-86	346	43	brownian	brownian	ADJ
ma-86	346	44	motion	motion	NOUN
ma-86	346	45	,	,	PUNCT
ma-86	346	46	which	which	PRON
ma-86	346	47	has	have	VERB
ma-86	346	48	main	main	ADJ
ma-86	346	49	properties	property	NOUN
ma-86	346	50	of	of	ADP
ma-86	346	51	the	the	DET
ma-86	346	52	fractional	fractional	ADJ
ma-86	346	53	brownianmotion	brownianmotion	NOUN
ma-86	346	54	,	,	PUNCT
ma-86	346	55	excluding	exclude	VERB
ma-86	346	56	the	the	DET
ma-86	346	57	stationarity	stationarity	NOUN
ma-86	346	58	of	of	ADP
ma-86	346	59	increments	increment	NOUN
ma-86	346	60	,	,	PUNCT
ma-86	346	61	has	have	VERB
ma-86	346	62	the	the	DET
ma-86	346	63	covariance	covariance	NOUN
ma-86	346	64	function	function	NOUN
ma-86	346	65	ch(s	ch(s	PROPN
ma-86	346	66	,	,	PUNCT
ma-86	346	67	t	t	PROPN
ma-86	346	68	)	)	PUNCT
ma-86	347	1	=	=	PUNCT
ma-86	348	1	s2h	s2h	NOUN
ma-86	348	2	+	+	PROPN
ma-86	348	3	t2h	t2h	PROPN
ma-86	348	4	−	−	PROPN
ma-86	348	5	1	1	NUM
ma-86	348	6	2	2	NUM
ma-86	348	7	[	[	PUNCT
ma-86	348	8	(	(	PUNCT
ma-86	348	9	s	s	NOUN
ma-86	348	10	+	+	NOUN
ma-86	348	11	t)2h	t)2h	NOUN
ma-86	348	12	+	+	CCONJ
ma-86	348	13	|s	|s	PROPN
ma-86	348	14	−	−	PROPN
ma-86	348	15	t|2h	t|2h	NOUN
ma-86	348	16	]	]	PUNCT
ma-86	348	17	,	,	PUNCT
ma-86	348	18	s	s	X
ma-86	348	19	,	,	PUNCT
ma-86	348	20	t	t	X
ma-86	348	21	>	>	X
ma-86	348	22	0	0	X
ma-86	348	23	.	.	PUNCT
ma-86	349	1	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	PROPN
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ma-86	349	3	.	.	PUNCT
ma-86	350	1	j.	j.	PROPN
ma-86	350	2	math	math	PROPN
ma-86	350	3	.	.	PUNCT
ma-86	351	1	anal	anal	PROPN
ma-86	351	2	.	.	PUNCT
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ma-86	352	2	/	/	SYM
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ma-86	352	6	13one	13one	PROPN
ma-86	352	7	can	can	AUX
ma-86	352	8	gereneralize	gereneralize	VERB
ma-86	352	9	this	this	PRON
ma-86	352	10	to	to	ADP
ma-86	352	11	sub	sub	ADJ
ma-86	352	12	-	-	ADJ
ma-86	352	13	fractional	fractional	ADJ
ma-86	352	14	levy	levy	NOUN
ma-86	352	15	process	process	NOUN
ma-86	352	16	by	by	ADP
ma-86	352	17	plug	plug	NOUN
ma-86	352	18	-	-	PUNCT
ma-86	352	19	in	in	ADP
ma-86	352	20	method	method	NOUN
ma-86	352	21	which	which	PRON
ma-86	352	22	would	would	AUX
ma-86	352	23	havenonstationary	havenonstationary	VERB
ma-86	352	24	increments	increment	NOUN
ma-86	352	25	and	and	CCONJ
ma-86	352	26	corresponding	corresponding	ADJ
ma-86	352	27	spde	spde	NOUN
ma-86	352	28	models	model	NOUN
ma-86	352	29	could	could	AUX
ma-86	352	30	be	be	AUX
ma-86	352	31	used	use	VERB
ma-86	352	32	for	for	ADP
ma-86	352	33	modeling	modeling	NOUN
ma-86	352	34	in	in	ADP
ma-86	352	35	financeand	financeand	NOUN
ma-86	352	36	biology	biology	NOUN
ma-86	352	37	.	.	PUNCT
ma-86	353	1	references	reference	NOUN
ma-86	353	2	[	[	X
ma-86	353	3	1	1	NUM
ma-86	353	4	]	]	X
ma-86	353	5	o.e	o.e	PROPN
ma-86	353	6	.	.	NOUN
ma-86	353	7	barndorff	barndorff	PROPN
ma-86	353	8	-	-	PUNCT
ma-86	353	9	nielsen	nielsen	PROPN
ma-86	353	10	,	,	PUNCT
ma-86	353	11	n.	n.	PROPN
ma-86	353	12	shephard	shephard	PROPN
ma-86	353	13	,	,	PUNCT
ma-86	353	14	non	non	ADJ
ma-86	353	15	-	-	ADJ
ma-86	353	16	gaussian	gaussian	ADJ
ma-86	353	17	ornstein	ornstein	PROPN
ma-86	353	18	-	-	PUNCT
ma-86	353	19	uhlenbeck	uhlenbeck	ADV
ma-86	353	20	-	-	PUNCT
ma-86	353	21	based	base	VERB
ma-86	353	22	models	model	NOUN
ma-86	353	23	and	and	CCONJ
ma-86	353	24	some	some	PRON
ma-86	353	25	of	of	ADP
ma-86	353	26	their	their	PRON
ma-86	353	27	uses	use	NOUN
ma-86	353	28	infinancial	infinancial	ADJ
ma-86	353	29	economics	economic	NOUN
ma-86	353	30	,	,	PUNCT
ma-86	353	31	j.	j.	PROPN
ma-86	353	32	r.	r.	PROPN
ma-86	353	33	stat	stat	PROPN
ma-86	353	34	.	.	PUNCT
ma-86	354	1	soc	soc	PROPN
ma-86	354	2	.	.	PUNCT
ma-86	355	1	b.	b.	PROPN
ma-86	355	2	63	63	NUM
ma-86	355	3	(	(	PUNCT
ma-86	355	4	2001	2001	NUM
ma-86	355	5	)	)	PUNCT
ma-86	355	6	167–241	167–241	NUM
ma-86	355	7	.	.	PUNCT
ma-86	356	1	https://doi.org/10.1111/1467-9868.00282.[2	https://doi.org/10.1111/1467-9868.00282.[2	NOUN
ma-86	356	2	]	]	PUNCT
ma-86	356	3	b.m	b.m	PROPN
ma-86	356	4	.	.	PROPN
ma-86	356	5	bibby	bibby	PROPN
ma-86	356	6	,	,	PUNCT
ma-86	356	7	m.	m.	NOUN
ma-86	356	8	sørensen	sørensen	NOUN
ma-86	356	9	,	,	PUNCT
ma-86	356	10	m.	m.	PROPN
ma-86	356	11	sorensen	sorensen	PROPN
ma-86	356	12	,	,	PUNCT
ma-86	356	13	martingale	martingale	ADJ
ma-86	356	14	estimation	estimation	NOUN
ma-86	356	15	functions	function	NOUN
ma-86	356	16	for	for	ADP
ma-86	356	17	discretely	discretely	ADV
ma-86	356	18	observed	observe	VERB
ma-86	356	19	diffusion	diffusion	NOUN
ma-86	356	20	processes	process	NOUN
ma-86	356	21	,	,	PUNCT
ma-86	356	22	bernoulli	bernoulli	PROPN
ma-86	356	23	.	.	PUNCT
ma-86	357	1	1	1	NUM
ma-86	357	2	(	(	PUNCT
ma-86	357	3	1995	1995	NUM
ma-86	357	4	)	)	PUNCT
ma-86	357	5	17	17	NUM
ma-86	357	6	-	-	SYM
ma-86	357	7	39	39	NUM
ma-86	357	8	.	.	PUNCT
ma-86	358	1	https://doi.org/10.2307/3318679.[3	https://doi.org/10.2307/3318679.[3	PRON
ma-86	358	2	]	]	PUNCT
ma-86	358	3	j.p.n	j.p.n	PROPN
ma-86	358	4	.	.	PROPN
ma-86	358	5	bishwal	bishwal	PROPN
ma-86	358	6	,	,	PUNCT
ma-86	358	7	bayes	bayes	PROPN
ma-86	358	8	and	and	CCONJ
ma-86	358	9	sequential	sequential	ADJ
ma-86	358	10	estimation	estimation	NOUN
ma-86	358	11	in	in	ADP
ma-86	358	12	hilbert	hilbert	NOUN
ma-86	358	13	space	space	NOUN
ma-86	358	14	valued	value	VERB
ma-86	358	15	stochastic	stochastic	ADJ
ma-86	358	16	differential	differential	ADJ
ma-86	358	17	equations	equation	NOUN
ma-86	358	18	,	,	PUNCT
ma-86	358	19	j.	j.	PROPN
ma-86	358	20	koreanstat	koreanstat	PROPN
ma-86	358	21	.	.	PUNCT
ma-86	359	1	soc	soc	PROPN
ma-86	359	2	.	.	PUNCT
ma-86	360	1	28	28	NUM
ma-86	360	2	(	(	PUNCT
ma-86	360	3	1999	1999	NUM
ma-86	360	4	)	)	PUNCT
ma-86	360	5	93	93	NUM
ma-86	360	6	-	-	SYM
ma-86	360	7	106.[4	106.[4	NUM
ma-86	360	8	]	]	PUNCT
ma-86	360	9	j.p.n	j.p.n	PROPN
ma-86	360	10	.	.	PROPN
ma-86	360	11	bishwal	bishwal	PROPN
ma-86	360	12	,	,	PUNCT
ma-86	360	13	the	the	DET
ma-86	360	14	bernstein	bernstein	PROPN
ma-86	360	15	-	-	PUNCT
ma-86	360	16	von	von	PROPN
ma-86	360	17	mises	mises	PROPN
ma-86	360	18	theorem	theorem	VERB
ma-86	360	19	and	and	CCONJ
ma-86	360	20	spectral	spectral	ADJ
ma-86	360	21	asymptotics	asymptotic	NOUN
ma-86	360	22	of	of	ADP
ma-86	360	23	bayes	bayes	NOUN
ma-86	360	24	estimators	estimator	NOUN
ma-86	360	25	for	for	ADP
ma-86	360	26	parabolic	parabolic	ADJ
ma-86	360	27	spdes	spde	NOUN
ma-86	360	28	,	,	PUNCT
ma-86	360	29	j.	j.	PROPN
ma-86	360	30	aust	aust	PROPN
ma-86	360	31	.	.	PUNCT
ma-86	360	32	math	math	PROPN
ma-86	360	33	.	.	PUNCT
ma-86	361	1	soc	soc	PROPN
ma-86	361	2	.	.	PUNCT
ma-86	362	1	72	72	NUM
ma-86	362	2	(	(	PUNCT
ma-86	362	3	2002	2002	NUM
ma-86	362	4	)	)	PUNCT
ma-86	363	1	287–298	287–298	NUM
ma-86	363	2	.	.	PUNCT
ma-86	364	1	https://doi.org/10.1017/s1446788700003906.[5	https://doi.org/10.1017/s1446788700003906.[5	PROPN
ma-86	364	2	]	]	PUNCT
ma-86	364	3	j.p.n	j.p.n	PROPN
ma-86	364	4	.	.	PROPN
ma-86	364	5	bishwal	bishwal	PROPN
ma-86	364	6	,	,	PUNCT
ma-86	364	7	parameter	parameter	NOUN
ma-86	364	8	estimation	estimation	NOUN
ma-86	364	9	in	in	ADP
ma-86	364	10	stochastic	stochastic	ADJ
ma-86	364	11	differential	differential	ADJ
ma-86	364	12	equations	equation	NOUN
ma-86	364	13	,	,	PUNCT
ma-86	364	14	lecture	lecture	NOUN
ma-86	364	15	notes	note	NOUN
ma-86	364	16	in	in	ADP
ma-86	364	17	mathematics	mathematic	NOUN
ma-86	364	18	,	,	PUNCT
ma-86	364	19	1923,springer	1923,springer	NUM
ma-86	364	20	-	-	PUNCT
ma-86	364	21	verlag	verlag	NOUN
ma-86	364	22	,	,	PUNCT
ma-86	364	23	(	(	PUNCT
ma-86	364	24	2008).[6	2008).[6	NOUN
ma-86	364	25	]	]	PUNCT
ma-86	364	26	j.p.n	j.p.n	PROPN
ma-86	364	27	.	.	PROPN
ma-86	364	28	bishwal	bishwal	PROPN
ma-86	364	29	,	,	PUNCT
ma-86	364	30	maximum	maximum	ADJ
ma-86	364	31	quasi	quasi	ADJ
ma-86	364	32	-	-	ADJ
ma-86	364	33	likelihood	likelihood	ADJ
ma-86	364	34	estimation	estimation	NOUN
ma-86	364	35	in	in	ADP
ma-86	364	36	fractional	fractional	ADJ
ma-86	364	37	levy	levy	NOUN
ma-86	364	38	stochastic	stochastic	ADJ
ma-86	364	39	volatility	volatility	NOUN
ma-86	364	40	model	model	NOUN
ma-86	364	41	,	,	PUNCT
ma-86	364	42	j.	j.	PROPN
ma-86	364	43	math	math	PROPN
ma-86	364	44	.	.	PUNCT
ma-86	365	1	finance.1	finance.1	PROPN
ma-86	365	2	(	(	PUNCT
ma-86	365	3	2011	2011	NUM
ma-86	365	4	)	)	PUNCT
ma-86	366	1	58–62	58–62	NUM
ma-86	366	2	.	.	PUNCT
ma-86	367	1	https://doi.org/10.4236/jmf.2011.13008.[7	https://doi.org/10.4236/jmf.2011.13008.[7	PROPN
ma-86	367	2	]	]	PUNCT
ma-86	367	3	j.p.n	j.p.n	PROPN
ma-86	367	4	.	.	PROPN
ma-86	367	5	bishwal	bishwal	NOUN
ma-86	367	6	,	,	PUNCT
ma-86	367	7	berry	berry	NOUN
ma-86	367	8	-	-	PUNCT
ma-86	367	9	esseen	esseen	PROPN
ma-86	367	10	inequalities	inequality	NOUN
ma-86	367	11	for	for	ADP
ma-86	367	12	the	the	DET
ma-86	367	13	discretely	discretely	ADV
ma-86	367	14	observed	observe	VERB
ma-86	367	15	ornstein	ornstein	NOUN
ma-86	367	16	-	-	PUNCT
ma-86	367	17	uhlenbeck	uhlenbeck	ADJ
ma-86	367	18	-	-	PUNCT
ma-86	367	19	gamma	gamma	NOUN
ma-86	367	20	process	process	NOUN
ma-86	367	21	,	,	PUNCT
ma-86	367	22	markovprocesses	markovprocesse	NOUN
ma-86	367	23	and	and	CCONJ
ma-86	367	24	related	related	ADJ
ma-86	367	25	fields	field	NOUN
ma-86	367	26	.	.	PUNCT
ma-86	368	1	17	17	NUM
ma-86	368	2	(	(	PUNCT
ma-86	368	3	2011b	2011b	NUM
ma-86	368	4	)	)	PUNCT
ma-86	368	5	119	119	NUM
ma-86	368	6	-	-	SYM
ma-86	368	7	150.[8	150.[8	NUM
ma-86	368	8	]	]	PUNCT
ma-86	368	9	j.	j.	PROPN
ma-86	368	10	bishwal	bishwal	PROPN
ma-86	368	11	,	,	PUNCT
ma-86	368	12	minimum	minimum	ADJ
ma-86	368	13	contrast	contrast	NOUN
ma-86	368	14	estimation	estimation	NOUN
ma-86	368	15	in	in	ADP
ma-86	368	16	fractional	fractional	PROPN
ma-86	368	17	ornstein	ornstein	PROPN
ma-86	368	18	-	-	PUNCT
ma-86	368	19	uhlenbeck	uhlenbeck	PROPN
ma-86	368	20	process	process	NOUN
ma-86	368	21	:	:	PUNCT
ma-86	368	22	continuous	continuous	ADJ
ma-86	368	23	and	and	CCONJ
ma-86	368	24	discrete	discrete	ADJ
ma-86	368	25	sam	sam	PROPN
ma-86	368	26	-	-	PUNCT
ma-86	368	27	pling	pling	NOUN
ma-86	368	28	,	,	PUNCT
ma-86	368	29	fract	fract	NOUN
ma-86	368	30	.	.	PUNCT
ma-86	369	1	calc	calc	PROPN
ma-86	369	2	.	.	PUNCT
ma-86	370	1	appl	appl	PROPN
ma-86	370	2	.	.	PUNCT
ma-86	371	1	anal	anal	PROPN
ma-86	371	2	.	.	PUNCT
ma-86	372	1	14	14	NUM
ma-86	372	2	(	(	PUNCT
ma-86	372	3	2011	2011	NUM
ma-86	372	4	)	)	PUNCT
ma-86	373	1	375–410	375–410	NUM
ma-86	373	2	.	.	PUNCT
ma-86	374	1	https://doi.org/10.2478/s13540-011-0024-6.[9	https://doi.org/10.2478/s13540-011-0024-6.[9	NOUN
ma-86	374	2	]	]	PUNCT
ma-86	374	3	j.p.n	j.p.n	PROPN
ma-86	374	4	.	.	PROPN
ma-86	374	5	bishwal	bishwal	PROPN
ma-86	374	6	,	,	PUNCT
ma-86	374	7	benstein	benstein	PROPN
ma-86	374	8	-	-	PUNCT
ma-86	374	9	von	von	PROPN
ma-86	374	10	mises	mises	PROPN
ma-86	374	11	theorem	theorem	VERB
ma-86	374	12	and	and	CCONJ
ma-86	374	13	small	small	ADJ
ma-86	374	14	noise	noise	NOUN
ma-86	374	15	bayesian	bayesian	NOUN
ma-86	374	16	asymptotics	asymptotic	NOUN
ma-86	374	17	for	for	ADP
ma-86	374	18	parabolic	parabolic	ADJ
ma-86	374	19	stochastic	stochastic	ADJ
ma-86	374	20	partialdifferential	partialdifferential	ADJ
ma-86	374	21	equations	equation	NOUN
ma-86	374	22	,	,	PUNCT
ma-86	374	23	theory	theory	NOUN
ma-86	374	24	stoch	stoch	NOUN
ma-86	374	25	.	.	PUNCT
ma-86	375	1	proc	proc	PROPN
ma-86	375	2	.	.	PUNCT
ma-86	376	1	23	23	NUM
ma-86	376	2	(	(	PUNCT
ma-86	376	3	2018	2018	NUM
ma-86	376	4	)	)	PUNCT
ma-86	376	5	6	6	NUM
ma-86	376	6	-	-	SYM
ma-86	376	7	17.[10	17.[10	NUM
ma-86	376	8	]	]	PUNCT
ma-86	376	9	m.	m.	NOUN
ma-86	376	10	huebner	huebner	PROPN
ma-86	376	11	,	,	PUNCT
ma-86	376	12	a	a	DET
ma-86	376	13	characterization	characterization	NOUN
ma-86	376	14	of	of	ADP
ma-86	376	15	asymptotic	asymptotic	ADJ
ma-86	376	16	behaviour	behaviour	NOUN
ma-86	376	17	of	of	ADP
ma-86	376	18	maximum	maximum	ADJ
ma-86	376	19	likelihood	likelihood	NOUN
ma-86	376	20	estimators	estimator	NOUN
ma-86	376	21	for	for	ADP
ma-86	376	22	stochastic	stochastic	ADJ
ma-86	376	23	pde’s	pde’s	NOUN
ma-86	376	24	,	,	PUNCT
ma-86	376	25	math	math	NOUN
ma-86	376	26	.	.	PUNCT
ma-86	377	1	methods	method	NOUN
ma-86	377	2	stat	stat	PROPN
ma-86	377	3	.	.	PUNCT
ma-86	378	1	6	6	NUM
ma-86	378	2	(	(	PUNCT
ma-86	378	3	1997	1997	NUM
ma-86	378	4	)	)	PUNCT
ma-86	378	5	395	395	NUM
ma-86	378	6	-	-	SYM
ma-86	378	7	415.[11	415.[11	NUM
ma-86	378	8	]	]	PUNCT
ma-86	378	9	m.	m.	NOUN
ma-86	378	10	huebner	huebner	PROPN
ma-86	378	11	,	,	PUNCT
ma-86	378	12	asymptotic	asymptotic	ADJ
ma-86	378	13	properties	property	NOUN
ma-86	378	14	of	of	ADP
ma-86	378	15	the	the	DET
ma-86	378	16	maximum	maximum	ADJ
ma-86	378	17	likelihood	likelihood	NOUN
ma-86	378	18	estimator	estimator	NOUN
ma-86	378	19	for	for	ADP
ma-86	378	20	stochastic	stochastic	ADJ
ma-86	378	21	pdes	pde	NOUN
ma-86	378	22	disturbed	disturb	VERB
ma-86	378	23	by	by	ADP
ma-86	378	24	smallnoise	smallnoise	ADJ
ma-86	378	25	,	,	PUNCT
ma-86	378	26	stat	stat	PROPN
ma-86	378	27	.	.	PUNCT
ma-86	379	1	inference	inference	NOUN
ma-86	379	2	stoch	stoch	NOUN
ma-86	379	3	.	.	PUNCT
ma-86	380	1	processes	process	VERB
ma-86	380	2	2	2	NUM
ma-86	380	3	(	(	PUNCT
ma-86	380	4	1999	1999	NUM
ma-86	380	5	)	)	PUNCT
ma-86	380	6	57–68	57–68	NUM
ma-86	380	7	.	.	PUNCT
ma-86	381	1	https://doi.org/10.1023/a:1009990504925.[12	https://doi.org/10.1023/a:1009990504925.[12	NOUN
ma-86	381	2	]	]	X
ma-86	381	3	m.	m.	NOUN
ma-86	381	4	hübner	hübner	NOUN
ma-86	381	5	,	,	PUNCT
ma-86	381	6	r.	r.	PROPN
ma-86	381	7	khasminskii	khasminskii	PROPN
ma-86	381	8	,	,	PUNCT
ma-86	381	9	b.l	b.l	PROPN
ma-86	381	10	.	.	PROPN
ma-86	381	11	rozovskii	rozovskii	PROPN
ma-86	381	12	,	,	PUNCT
ma-86	381	13	two	two	NUM
ma-86	381	14	examples	example	NOUN
ma-86	381	15	of	of	ADP
ma-86	381	16	parameter	parameter	NOUN
ma-86	381	17	estimation	estimation	NOUN
ma-86	381	18	for	for	ADP
ma-86	381	19	stochastic	stochastic	ADJ
ma-86	381	20	partial	partial	ADJ
ma-86	381	21	differentialequations	differentialequation	NOUN
ma-86	381	22	,	,	PUNCT
ma-86	381	23	in	in	ADP
ma-86	381	24	:	:	PUNCT
ma-86	381	25	s.	s.	PROPN
ma-86	381	26	cambanis	cambanis	PROPN
ma-86	381	27	,	,	PUNCT
ma-86	381	28	j.k	j.k	PROPN
ma-86	381	29	.	.	PROPN
ma-86	381	30	ghosh	ghosh	PROPN
ma-86	381	31	,	,	PUNCT
ma-86	381	32	r.l	r.l	PROPN
ma-86	381	33	.	.	PROPN
ma-86	381	34	karandikar	karandikar	PROPN
ma-86	381	35	,	,	PUNCT
ma-86	381	36	p.k	p.k	PROPN
ma-86	381	37	.	.	PROPN
ma-86	381	38	sen	sen	PROPN
ma-86	381	39	(	(	PUNCT
ma-86	381	40	eds	eds	PROPN
ma-86	381	41	.	.	PUNCT
ma-86	381	42	)	)	PUNCT
ma-86	381	43	,	,	PUNCT
ma-86	381	44	stochastic	stochastic	NOUN
ma-86	381	45	processes	process	NOUN
ma-86	381	46	,	,	PUNCT
ma-86	381	47	springer	springer	NOUN
ma-86	381	48	new	new	PROPN
ma-86	381	49	york	york	PROPN
ma-86	381	50	,	,	PUNCT
ma-86	381	51	new	new	PROPN
ma-86	381	52	york	york	PROPN
ma-86	381	53	,	,	PUNCT
ma-86	381	54	ny	ny	PROPN
ma-86	381	55	,	,	PUNCT
ma-86	381	56	1993	1993	NUM
ma-86	381	57	:	:	PUNCT
ma-86	381	58	pp	pp	ADP
ma-86	381	59	.	.	PUNCT
ma-86	382	1	149–160	149–160	NUM
ma-86	382	2	.	.	PUNCT
ma-86	382	3	https://doi.org/10.1007/978-1-4615-7909-0_18.[13	https://doi.org/10.1007/978-1-4615-7909-0_18.[13	PROPN
ma-86	382	4	]	]	X
ma-86	382	5	m.	m.	NOUN
ma-86	382	6	huebner	huebner	PROPN
ma-86	382	7	,	,	PUNCT
ma-86	382	8	b.l	b.l	PROPN
ma-86	382	9	.	.	PROPN
ma-86	382	10	rozovskii	rozovskii	PROPN
ma-86	382	11	,	,	PUNCT
ma-86	382	12	on	on	ADP
ma-86	382	13	asymptotic	asymptotic	ADJ
ma-86	382	14	properties	property	NOUN
ma-86	382	15	of	of	ADP
ma-86	382	16	maximum	maximum	ADJ
ma-86	382	17	likelihood	likelihood	NOUN
ma-86	382	18	estimators	estimator	NOUN
ma-86	382	19	for	for	ADP
ma-86	382	20	parabolic	parabolic	ADJ
ma-86	382	21	stochasticpde	stochasticpde	NOUN
ma-86	382	22	’s	’s	PART
ma-86	382	23	,	,	PUNCT
ma-86	382	24	probab	probab	PROPN
ma-86	382	25	.	.	PUNCT
ma-86	383	1	theory	theory	NOUN
ma-86	383	2	related	relate	VERB
ma-86	383	3	fields	field	NOUN
ma-86	383	4	.	.	PUNCT
ma-86	384	1	103	103	NUM
ma-86	384	2	(	(	PUNCT
ma-86	384	3	1995	1995	NUM
ma-86	384	4	)	)	PUNCT
ma-86	384	5	143–163	143–163	NUM
ma-86	384	6	.	.	PUNCT
ma-86	385	1	https://doi.org/10.1007/bf01204212.[14	https://doi.org/10.1007/bf01204212.[14	PROPN
ma-86	385	2	]	]	X
ma-86	385	3	i.a	i.a	PROPN
ma-86	385	4	.	.	PROPN
ma-86	385	5	ibragimov	ibragimov	PROPN
ma-86	385	6	,	,	PUNCT
ma-86	385	7	r.z	r.z	PROPN
ma-86	385	8	.	.	PROPN
ma-86	385	9	khas’minskii	khas’minskii	PROPN
ma-86	385	10	,	,	PUNCT
ma-86	385	11	some	some	DET
ma-86	385	12	estimation	estimation	NOUN
ma-86	385	13	problems	problem	NOUN
ma-86	385	14	for	for	ADP
ma-86	385	15	stochastic	stochastic	ADJ
ma-86	385	16	partial	partial	ADJ
ma-86	385	17	differential	differential	NOUN
ma-86	385	18	equations	equation	NOUN
ma-86	385	19	,	,	PUNCT
ma-86	385	20	dokl	dokl	NOUN
ma-86	385	21	.	.	PUNCT
ma-86	386	1	akad.nauk	akad.nauk	NUM
ma-86	386	2	,	,	PUNCT
ma-86	386	3	353	353	NUM
ma-86	386	4	(	(	PUNCT
ma-86	386	5	1997	1997	NUM
ma-86	386	6	)	)	PUNCT
ma-86	386	7	300–302.[15	300–302.[15	PROPN
ma-86	386	8	]	]	X
ma-86	386	9	a.n	a.n	PROPN
ma-86	386	10	.	.	PROPN
ma-86	386	11	kolmogorov	kolmogorov	PROPN
ma-86	386	12	,	,	PUNCT
ma-86	386	13	wiener	wiener	NOUN
ma-86	386	14	skewline	skewline	NOUN
ma-86	386	15	and	and	CCONJ
ma-86	386	16	other	other	ADJ
ma-86	386	17	interesting	interesting	ADJ
ma-86	386	18	curves	curve	NOUN
ma-86	386	19	in	in	ADP
ma-86	386	20	hilbert	hilbert	NOUN
ma-86	386	21	space	space	NOUN
ma-86	386	22	,	,	PUNCT
ma-86	386	23	dokl	dokl	NOUN
ma-86	386	24	.	.	PUNCT
ma-86	386	25	akad	akad	PROPN
ma-86	386	26	.	.	PUNCT
ma-86	387	1	nauk	nauk	PROPN
ma-86	387	2	,	,	PUNCT
ma-86	387	3	26	26	NUM
ma-86	387	4	(	(	PUNCT
ma-86	387	5	1940)115	1940)115	PROPN
ma-86	387	6	-	-	SYM
ma-86	387	7	118.[16	118.[16	PROPN
ma-86	387	8	]	]	PUNCT
ma-86	387	9	m.	m.	NOUN
ma-86	387	10	kleptsyna	kleptsyna	PROPN
ma-86	387	11	,	,	PUNCT
ma-86	387	12	a.	a.	PROPN
ma-86	387	13	le	le	PROPN
ma-86	387	14	breton	breton	PROPN
ma-86	387	15	,	,	PUNCT
ma-86	387	16	statistical	statistical	ADJ
ma-86	387	17	analysis	analysis	NOUN
ma-86	387	18	of	of	ADP
ma-86	387	19	the	the	DET
ma-86	387	20	fractional	fractional	PROPN
ma-86	387	21	ornstein	ornstein	PROPN
ma-86	387	22	–	–	PUNCT
ma-86	387	23	uhlenbeck	uhlenbeck	ADJ
ma-86	387	24	type	type	NOUN
ma-86	387	25	process	process	NOUN
ma-86	387	26	.	.	PUNCT
ma-86	388	1	stat	stat	PROPN
ma-86	388	2	.	.	PUNCT
ma-86	389	1	inferencestoch	inferencestoch	PROPN
ma-86	389	2	.	.	PUNCT
ma-86	390	1	processes	process	NOUN
ma-86	390	2	.	.	PUNCT
ma-86	391	1	5	5	NUM
ma-86	391	2	(	(	PUNCT
ma-86	391	3	2002	2002	NUM
ma-86	391	4	)	)	PUNCT
ma-86	392	1	229–248	229–248	NUM
ma-86	392	2	.	.	PUNCT
ma-86	393	1	https://doi.org/10.1023/a:1021220818545.[17	https://doi.org/10.1023/a:1021220818545.[17	PROPN
ma-86	393	2	]	]	X
ma-86	393	3	t.	t.	PROPN
ma-86	393	4	koski	koski	PROPN
ma-86	393	5	,	,	PUNCT
ma-86	393	6	w.	w.	PROPN
ma-86	393	7	loges	loges	PROPN
ma-86	393	8	,	,	PUNCT
ma-86	393	9	asymptotic	asymptotic	ADJ
ma-86	393	10	statistical	statistical	ADJ
ma-86	393	11	inference	inference	NOUN
ma-86	393	12	for	for	ADP
ma-86	393	13	a	a	DET
ma-86	393	14	stochastic	stochastic	ADJ
ma-86	393	15	heat	heat	NOUN
ma-86	393	16	flow	flow	NOUN
ma-86	393	17	problem	problem	NOUN
ma-86	393	18	,	,	PUNCT
ma-86	393	19	stat	stat	PROPN
ma-86	393	20	.	.	PUNCT
ma-86	394	1	probab	probab	PROPN
ma-86	394	2	.	.	PUNCT
ma-86	395	1	lett	lett	PROPN
ma-86	395	2	.	.	PROPN
ma-86	396	1	3	3	NUM
ma-86	396	2	(	(	PUNCT
ma-86	396	3	1985)185–189	1985)185–189	NUM
ma-86	396	4	.	.	PUNCT
ma-86	397	1	https://doi.org/10.1016/0167-7152(85)90015-x.[18	https://doi.org/10.1016/0167-7152(85)90015-x.[18	PROPN
ma-86	397	2	]	]	PUNCT
ma-86	397	3	t.	t.	PROPN
ma-86	397	4	koski	koski	PROPN
ma-86	397	5	,	,	PUNCT
ma-86	397	6	w.	w.	PROPN
ma-86	397	7	loges	loges	PROPN
ma-86	397	8	,	,	PUNCT
ma-86	397	9	on	on	ADP
ma-86	397	10	minimum	minimum	ADJ
ma-86	397	11	-	-	PUNCT
ma-86	397	12	contrast	contrast	NOUN
ma-86	397	13	estimation	estimation	NOUN
ma-86	397	14	for	for	ADP
ma-86	397	15	hilbert	hilbert	PROPN
ma-86	397	16	space	space	NOUN
ma-86	397	17	-	-	PUNCT
ma-86	397	18	valued	value	VERB
ma-86	397	19	stochastic	stochastic	ADJ
ma-86	397	20	differential	differential	ADJ
ma-86	397	21	equations	equation	NOUN
ma-86	397	22	,	,	PUNCT
ma-86	397	23	stochastics	stochastic	NOUN
ma-86	397	24	.	.	PUNCT
ma-86	398	1	16	16	NUM
ma-86	398	2	(	(	PUNCT
ma-86	398	3	1986	1986	NUM
ma-86	398	4	)	)	PUNCT
ma-86	399	1	217–225	217–225	NUM
ma-86	399	2	.	.	PUNCT
ma-86	400	1	https://doi.org/10.1080/17442508608833374.[19	https://doi.org/10.1080/17442508608833374.[19	NOUN
ma-86	400	2	]	]	X
ma-86	400	3	p.	p.	PROPN
ma-86	400	4	lévy	lévy	NOUN
ma-86	400	5	,	,	PUNCT
ma-86	400	6	processus	processus	PROPN
ma-86	400	7	stochastiques	stochastique	NOUN
ma-86	400	8	et	et	PROPN
ma-86	400	9	mouvement	mouvement	PROPN
ma-86	400	10	brownien	brownien	PROPN
ma-86	400	11	,	,	PUNCT
ma-86	400	12	gauthier	gauthier	NOUN
ma-86	400	13	-	-	PUNCT
ma-86	400	14	villars	villar	NOUN
ma-86	400	15	,	,	PUNCT
ma-86	400	16	paris	paris	PROPN
ma-86	400	17	,	,	PUNCT
ma-86	400	18	1948	1948	NUM
ma-86	400	19	.	.	PUNCT
ma-86	401	1	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	VERB
ma-86	401	2	https://doi.org/10.1111/1467-9868.00282	https://doi.org/10.1111/1467-9868.00282	PROPN
ma-86	401	3	https://doi.org/10.2307/3318679	https://doi.org/10.2307/3318679	NOUN
ma-86	401	4	https://doi.org/10.1017/s1446788700003906	https://doi.org/10.1017/s1446788700003906	NUM
ma-86	401	5	https://doi.org/10.4236/jmf.2011.13008	https://doi.org/10.4236/jmf.2011.13008	NOUN
ma-86	401	6	https://doi.org/10.2478/s13540-011-0024-6	https://doi.org/10.2478/s13540-011-0024-6	NOUN
ma-86	401	7	https://doi.org/10.1023/a:1009990504925	https://doi.org/10.1023/a:1009990504925	NOUN
ma-86	401	8	https://doi.org/10.1007/978-1-4615-7909-0_18	https://doi.org/10.1007/978-1-4615-7909-0_18	NOUN
ma-86	401	9	https://doi.org/10.1007/bf01204212	https://doi.org/10.1007/bf01204212	NOUN
ma-86	401	10	https://doi.org/10.1023/a:1021220818545	https://doi.org/10.1023/a:1021220818545	NOUN
ma-86	401	11	https://doi.org/10.1016/0167-7152(85)90015-x	https://doi.org/10.1016/0167-7152(85)90015-x	PROPN
ma-86	401	12	https://doi.org/10.1080/17442508608833374	https://doi.org/10.1080/17442508608833374	AUX
ma-86	401	13	eur	eur	PROPN
ma-86	401	14	.	.	PUNCT
ma-86	402	1	j.	j.	PROPN
ma-86	402	2	math	math	PROPN
ma-86	402	3	.	.	PUNCT
ma-86	403	1	anal	anal	PROPN
ma-86	403	2	.	.	PUNCT
ma-86	404	1	10.28924	10.28924	NUM
ma-86	404	2	/	/	SYM
ma-86	404	3	ada	ada	NOUN
ma-86	404	4	/	/	SYM
ma-86	404	5	ma.2.15	ma.2.15	NOUN
ma-86	404	6	14	14	NUM
ma-86	404	7	[	[	SYM
ma-86	404	8	20	20	NUM
ma-86	404	9	]	]	PUNCT
ma-86	404	10	w.	w.	PROPN
ma-86	404	11	loges	loges	PROPN
ma-86	404	12	,	,	PUNCT
ma-86	404	13	girsanov	girsanov	PROPN
ma-86	404	14	’s	’s	PART
ma-86	404	15	theorem	theorem	NOUN
ma-86	404	16	in	in	ADP
ma-86	404	17	hilbert	hilbert	NOUN
ma-86	404	18	space	space	NOUN
ma-86	404	19	and	and	CCONJ
ma-86	404	20	an	an	DET
ma-86	404	21	application	application	NOUN
ma-86	404	22	to	to	ADP
ma-86	404	23	the	the	DET
ma-86	404	24	statistics	statistic	NOUN
ma-86	404	25	of	of	ADP
ma-86	404	26	hilbert	hilbert	PROPN
ma-86	404	27	spacevalued	spacevalue	VERB
ma-86	404	28	stochasticdifferential	stochasticdifferential	ADJ
ma-86	404	29	equations	equation	NOUN
ma-86	404	30	,	,	PUNCT
ma-86	404	31	stoch	stoch	NOUN
ma-86	404	32	.	.	PUNCT
ma-86	405	1	processes	process	VERB
ma-86	405	2	appl	appl	NOUN
ma-86	405	3	.	.	PUNCT
ma-86	406	1	17	17	NUM
ma-86	406	2	(	(	PUNCT
ma-86	406	3	1984	1984	NUM
ma-86	406	4	)	)	PUNCT
ma-86	406	5	243–263	243–263	NUM
ma-86	406	6	.	.	PUNCT
ma-86	406	7	https://doi.org/10.1016/0304-4149(84	https://doi.org/10.1016/0304-4149(84	NOUN
ma-86	406	8	)	)	PUNCT
ma-86	406	9	90004	90004	NUM
ma-86	406	10	-	-	SYM
ma-86	406	11	8.[21	8.[21	NUM
ma-86	406	12	]	]	X
ma-86	406	13	s.v	s.v	PROPN
ma-86	406	14	.	.	PROPN
ma-86	406	15	lototsky	lototsky	PROPN
ma-86	406	16	,	,	PUNCT
ma-86	406	17	b.l	b.l	PROPN
ma-86	406	18	.	.	PROPN
ma-86	406	19	rosovskii	rosovskii	PROPN
ma-86	406	20	,	,	PUNCT
ma-86	406	21	spectral	spectral	ADJ
ma-86	406	22	asymptotics	asymptotic	NOUN
ma-86	406	23	of	of	ADP
ma-86	406	24	some	some	DET
ma-86	406	25	functionals	functional	NOUN
ma-86	406	26	arising	arise	VERB
ma-86	406	27	in	in	ADP
ma-86	406	28	statistical	statistical	ADJ
ma-86	406	29	inference	inference	NOUN
ma-86	406	30	for	for	ADP
ma-86	406	31	spdes	spde	NOUN
ma-86	406	32	,	,	PUNCT
ma-86	406	33	stoch	stoch	NOUN
ma-86	406	34	.	.	PUNCT
ma-86	407	1	processes	process	VERB
ma-86	407	2	appl	appl	NOUN
ma-86	407	3	.	.	PUNCT
ma-86	408	1	79	79	NUM
ma-86	408	2	(	(	PUNCT
ma-86	408	3	1999	1999	NUM
ma-86	408	4	)	)	PUNCT
ma-86	408	5	69–94	69–94	NOUN
ma-86	408	6	.	.	PUNCT
ma-86	409	1	https://doi.org/10.1016/s0304-4149(98)00079-9.[22	https://doi.org/10.1016/s0304-4149(98)00079-9.[22	PROPN
ma-86	409	2	]	]	X
ma-86	409	3	i.s	i.s	PROPN
ma-86	409	4	.	.	PROPN
ma-86	409	5	mishura	mishura	PROPN
ma-86	409	6	,	,	PUNCT
ma-86	409	7	stochastic	stochastic	ADJ
ma-86	409	8	calculus	calculus	NOUN
ma-86	409	9	for	for	ADP
ma-86	409	10	fractional	fractional	ADJ
ma-86	409	11	brownian	brownian	ADJ
ma-86	409	12	motion	motion	NOUN
ma-86	409	13	and	and	CCONJ
ma-86	409	14	related	related	ADJ
ma-86	409	15	processes	process	NOUN
ma-86	409	16	,	,	PUNCT
ma-86	409	17	springer	springer	NOUN
ma-86	409	18	-	-	PUNCT
ma-86	409	19	verlag	verlag	PROPN
ma-86	409	20	,	,	PUNCT
ma-86	409	21	berlin	berlin	PROPN
ma-86	409	22	,	,	PUNCT
ma-86	409	23	new	new	PROPN
ma-86	409	24	york	york	PROPN
ma-86	409	25	,	,	PUNCT
ma-86	409	26	2008.[23	2008.[23	PROPN
ma-86	409	27	]	]	X
ma-86	409	28	i.	i.	PROPN
ma-86	409	29	norros	norros	PROPN
ma-86	409	30	,	,	PUNCT
ma-86	409	31	e.	e.	PROPN
ma-86	409	32	valkeila	valkeila	PROPN
ma-86	409	33	,	,	PUNCT
ma-86	409	34	j.	j.	PROPN
ma-86	409	35	virtamo	virtamo	PROPN
ma-86	409	36	,	,	PUNCT
ma-86	409	37	an	an	DET
ma-86	409	38	elementary	elementary	ADJ
ma-86	409	39	approach	approach	NOUN
ma-86	409	40	to	to	ADP
ma-86	409	41	a	a	DET
ma-86	409	42	girsanov	girsanov	NOUN
ma-86	409	43	formula	formula	NOUN
ma-86	409	44	and	and	CCONJ
ma-86	409	45	other	other	ADJ
ma-86	409	46	analytical	analytical	ADJ
ma-86	409	47	results	result	NOUN
ma-86	409	48	onfractional	onfractional	ADJ
ma-86	409	49	brownian	brownian	ADJ
ma-86	409	50	motions	motion	NOUN
ma-86	409	51	,	,	PUNCT
ma-86	409	52	bernoulli	bernoulli	PROPN
ma-86	409	53	.	.	PUNCT
ma-86	410	1	5	5	NUM
ma-86	410	2	(	(	PUNCT
ma-86	410	3	1999	1999	NUM
ma-86	410	4	)	)	PUNCT
ma-86	410	5	571	571	NUM
ma-86	410	6	-	-	SYM
ma-86	410	7	587	587	NUM
ma-86	410	8	.	.	PUNCT
ma-86	411	1	https://doi.org/10.2307/3318691.[24	https://doi.org/10.2307/3318691.[24	PROPN
ma-86	411	2	]	]	PUNCT
ma-86	411	3	s.	s.	PROPN
ma-86	411	4	peszat	peszat	PROPN
ma-86	411	5	,	,	PUNCT
ma-86	411	6	j.	j.	PROPN
ma-86	411	7	zabczyk	zabczyk	PROPN
ma-86	411	8	,	,	PUNCT
ma-86	411	9	stochastic	stochastic	ADJ
ma-86	411	10	partial	partial	ADJ
ma-86	411	11	differential	differential	ADJ
ma-86	411	12	equations	equation	NOUN
ma-86	411	13	with	with	ADP
ma-86	411	14	levy	levy	NOUN
ma-86	411	15	noise	noise	NOUN
ma-86	411	16	:	:	PUNCT
ma-86	411	17	evolution	evolution	NOUN
ma-86	411	18	equations	equation	NOUN
ma-86	411	19	approach	approach	PROPN
ma-86	411	20	,	,	PUNCT
ma-86	411	21	cambridge	cambridge	PROPN
ma-86	411	22	university	university	PROPN
ma-86	411	23	press	press	PROPN
ma-86	411	24	,	,	PUNCT
ma-86	411	25	cambridge	cambridge	PROPN
ma-86	411	26	,	,	PUNCT
ma-86	411	27	england	england	PROPN
ma-86	411	28	,	,	PUNCT
ma-86	411	29	(	(	PUNCT
ma-86	411	30	2007).[25	2007).[25	NUM
ma-86	411	31	]	]	X
ma-86	411	32	d.	d.	PROPN
ma-86	411	33	straumann	straumann	PROPN
ma-86	411	34	,	,	PUNCT
ma-86	411	35	estimation	estimation	NOUN
ma-86	411	36	in	in	ADP
ma-86	411	37	conditionally	conditionally	ADV
ma-86	411	38	heteroscedastic	heteroscedastic	ADJ
ma-86	411	39	time	time	NOUN
ma-86	411	40	series	series	NOUN
ma-86	411	41	models	model	NOUN
ma-86	411	42	,	,	PUNCT
ma-86	411	43	lecture	lecture	NOUN
ma-86	411	44	notes	note	NOUN
ma-86	411	45	in	in	ADP
ma-86	411	46	statistics	statistic	NOUN
ma-86	411	47	,	,	PUNCT
ma-86	411	48	181,springer	181,springer	NUM
ma-86	411	49	-	-	PUNCT
ma-86	411	50	verlag	verlag	NOUN
ma-86	411	51	,	,	PUNCT
ma-86	411	52	berlin	berlin	PROPN
ma-86	411	53	,	,	PUNCT
ma-86	411	54	(	(	PUNCT
ma-86	411	55	2005).[26	2005).[26	NUM
ma-86	411	56	]	]	X
ma-86	411	57	c.a	c.a	PROPN
ma-86	411	58	.	.	PROPN
ma-86	411	59	tudor	tudor	PROPN
ma-86	411	60	,	,	PUNCT
ma-86	411	61	f.g	f.g	PROPN
ma-86	411	62	.	.	PROPN
ma-86	411	63	viens	vien	NOUN
ma-86	411	64	,	,	PUNCT
ma-86	411	65	statistical	statistical	ADJ
ma-86	411	66	aspects	aspect	NOUN
ma-86	411	67	of	of	ADP
ma-86	411	68	the	the	DET
ma-86	411	69	fractional	fractional	ADJ
ma-86	411	70	stochastic	stochastic	NOUN
ma-86	411	71	calculus	calculus	NOUN
ma-86	411	72	,	,	PUNCT
ma-86	411	73	ann	ann	PROPN
ma-86	411	74	.	.	PROPN
ma-86	411	75	stat	stat	PROPN
ma-86	411	76	.	.	PUNCT
ma-86	412	1	35	35	NUM
ma-86	412	2	(	(	PUNCT
ma-86	412	3	2007	2007	NUM
ma-86	412	4	)	)	PUNCT
ma-86	412	5	1183	1183	NUM
ma-86	412	6	-	-	SYM
ma-86	412	7	1212	1212	NUM
ma-86	412	8	.	.	PUNCT
ma-86	413	1	https://doi.org/10.1214/009053606000001541.[27	https://doi.org/10.1214/009053606000001541.[27	PROPN
ma-86	413	2	]	]	X
ma-86	413	3	b.b	b.b	PROPN
ma-86	413	4	.	.	PROPN
ma-86	413	5	mandelbrot	mandelbrot	PROPN
ma-86	413	6	,	,	PUNCT
ma-86	413	7	j.w	j.w	PROPN
ma-86	413	8	.	.	PROPN
ma-86	413	9	van	van	PROPN
ma-86	413	10	ness	ness	NOUN
ma-86	413	11	,	,	PUNCT
ma-86	413	12	fractional	fractional	ADJ
ma-86	413	13	brownian	brownian	ADJ
ma-86	413	14	motions	motion	NOUN
ma-86	413	15	,	,	PUNCT
ma-86	413	16	fractional	fractional	ADJ
ma-86	413	17	noises	noise	NOUN
ma-86	413	18	and	and	CCONJ
ma-86	413	19	applications	application	NOUN
ma-86	413	20	,	,	PUNCT
ma-86	413	21	siam	siam	PROPN
ma-86	413	22	rev	rev	PROPN
ma-86	413	23	.	.	PROPN
ma-86	413	24	10(1968	10(1968	NUM
ma-86	413	25	)	)	PUNCT
ma-86	414	1	422–437	422–437	NUM
ma-86	414	2	.	.	PUNCT
ma-86	415	1	https://doi.org/10.1137/1010093	https://doi.org/10.1137/1010093	X
ma-86	415	2	.	.	PUNCT
ma-86	416	1	https://doi.org/10.28924/ada/ma.2.15	https://doi.org/10.28924/ada/ma.2.15	VERB
ma-86	416	2	https://doi.org/10.1016/0304-4149(84)90004-8	https://doi.org/10.1016/0304-4149(84)90004-8	PROPN
ma-86	416	3	https://doi.org/10.1016/0304-4149(84)90004-8	https://doi.org/10.1016/0304-4149(84)90004-8	PUNCT
ma-86	416	4	https://doi.org/10.1016/s0304-4149(98)00079-9	https://doi.org/10.1016/s0304-4149(98)00079-9	PROPN
ma-86	417	1	https://doi.org/10.2307/3318691	https://doi.org/10.2307/3318691	NOUN
ma-86	418	1	https://doi.org/10.1214/009053606000001541	https://doi.org/10.1214/009053606000001541	X
ma-86	419	1	https://doi.org/10.1137/1010093	https://doi.org/10.1137/1010093	NUM
ma-86	419	2	references	reference	NOUN