id	sid	tid	token	lemma	pos
ma-203	1	1	2024	2024	NUM
ma-203	1	2	ada	ada	PROPN
ma-203	1	3	academica	academica	PROPN
ma-203	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-203	1	5	.	.	PUNCT
ma-203	2	1	j.	j.	PROPN
ma-203	2	2	math	math	PROPN
ma-203	2	3	.	.	PUNCT
ma-203	3	1	anal	anal	ADJ
ma-203	3	2	.	.	PUNCT
ma-203	4	1	4	4	NUM
ma-203	4	2	(	(	PUNCT
ma-203	4	3	2024	2024	NUM
ma-203	4	4	)	)	PUNCT
ma-203	4	5	12doi	12doi	NUM
ma-203	4	6	:	:	PUNCT
ma-203	4	7	10.28924	10.28924	NUM
ma-203	4	8	/	/	SYM
ma-203	4	9	ada	ada	NOUN
ma-203	4	10	/	/	SYM
ma-203	4	11	ma.4.12	ma.4.12	NOUN
ma-203	4	12	conditional	conditional	ADJ
ma-203	4	13	least	least	ADJ
ma-203	4	14	squares	square	NOUN
ma-203	4	15	estimation	estimation	NOUN
ma-203	4	16	for	for	ADP
ma-203	4	17	fractional	fractional	ADJ
ma-203	4	18	super	super	ADJ
ma-203	4	19	levy	levy	NOUN
ma-203	4	20	processes	process	NOUN
ma-203	4	21	in	in	ADP
ma-203	4	22	nonlinear	nonlinear	ADJ
ma-203	4	23	spdes	spdes	PROPN
ma-203	4	24	jaya	jaya	PROPN
ma-203	4	25	p.	p.	PROPN
ma-203	4	26	n.	n.	PROPN
ma-203	4	27	bishwal	bishwal	PROPN
ma-203	4	28	department	department	PROPN
ma-203	4	29	of	of	ADP
ma-203	4	30	mathematics	mathematics	PROPN
ma-203	4	31	and	and	CCONJ
ma-203	4	32	statistics	statistic	NOUN
ma-203	4	33	,	,	PUNCT
ma-203	4	34	university	university	PROPN
ma-203	4	35	of	of	ADP
ma-203	4	36	north	north	PROPN
ma-203	4	37	carolina	carolina	PROPN
ma-203	4	38	at	at	ADP
ma-203	4	39	charlotte	charlotte	PROPN
ma-203	4	40	,	,	PUNCT
ma-203	4	41	376	376	NUM
ma-203	4	42	fretwell	fretwell	NOUN
ma-203	4	43	bldg,9201	bldg,9201	NOUN
ma-203	4	44	university	university	NOUN
ma-203	4	45	city	city	NOUN
ma-203	4	46	blvd	blvd	PROPN
ma-203	4	47	.	.	PUNCT
ma-203	5	1	charlotte	charlotte	PROPN
ma-203	5	2	,	,	PUNCT
ma-203	5	3	nc	nc	PROPN
ma-203	5	4	28223	28223	NUM
ma-203	5	5	-	-	PUNCT
ma-203	5	6	0001	0001	NUM
ma-203	5	7	,	,	PUNCT
ma-203	5	8	usaj.bishwal@uncc.edu	usaj.bishwal@uncc.edu	NOUN
ma-203	5	9	abstract	abstract	NOUN
ma-203	5	10	.	.	PUNCT
ma-203	6	1	we	we	PRON
ma-203	6	2	consider	consider	VERB
ma-203	6	3	infinite	infinite	ADJ
ma-203	6	4	dimensional	dimensional	ADJ
ma-203	6	5	extension	extension	NOUN
ma-203	6	6	of	of	ADP
ma-203	6	7	affine	affine	NOUN
ma-203	6	8	models	model	NOUN
ma-203	6	9	as	as	SCONJ
ma-203	6	10	super	super	ADJ
ma-203	6	11	levy	levy	NOUN
ma-203	6	12	processes	process	NOUN
ma-203	6	13	sat	sat	AUX
ma-203	6	14	-	-	PUNCT
ma-203	6	15	isfying	isfye	VERB
ma-203	6	16	a	a	DET
ma-203	6	17	nonlinear	nonlinear	ADJ
ma-203	6	18	spde	spde	NOUN
ma-203	6	19	.	.	PUNCT
ma-203	7	1	we	we	PRON
ma-203	7	2	obtain	obtain	VERB
ma-203	7	3	the	the	DET
ma-203	7	4	asymptotics	asymptotic	NOUN
ma-203	7	5	of	of	ADP
ma-203	7	6	the	the	DET
ma-203	7	7	conditional	conditional	ADJ
ma-203	7	8	least	least	ADJ
ma-203	7	9	squares	square	NOUN
ma-203	7	10	estimators.finally	estimators.finally	ADV
ma-203	7	11	we	we	PRON
ma-203	7	12	obtain	obtain	VERB
ma-203	7	13	the	the	DET
ma-203	7	14	berry	berry	NOUN
ma-203	7	15	-	-	PUNCT
ma-203	7	16	esseen	esseen	PROPN
ma-203	7	17	inequality	inequality	NOUN
ma-203	7	18	.	.	PUNCT
ma-203	8	1	1	1	X
ma-203	8	2	.	.	X
ma-203	8	3	introduction	introduction	NOUN
ma-203	8	4	and	and	CCONJ
ma-203	8	5	preliminaries	preliminary	NOUN
ma-203	8	6	parameter	parameter	NOUN
ma-203	8	7	estimation	estimation	NOUN
ma-203	8	8	in	in	ADP
ma-203	8	9	finite	finite	ADJ
ma-203	8	10	dimensional	dimensional	ADJ
ma-203	8	11	diffusions	diffusion	NOUN
ma-203	8	12	is	be	AUX
ma-203	8	13	now	now	ADV
ma-203	8	14	classical	classical	ADJ
ma-203	8	15	.	.	PUNCT
ma-203	9	1	bishwal	bishwal	NOUN
ma-203	10	1	[	[	X
ma-203	10	2	7	7	NUM
ma-203	10	3	]	]	PUNCT
ma-203	10	4	studied	study	VERB
ma-203	10	5	a	a	DET
ma-203	10	6	newestimating	newestimating	NOUN
ma-203	10	7	function	function	NOUN
ma-203	10	8	for	for	ADP
ma-203	10	9	discretely	discretely	ADV
ma-203	10	10	sampled	sample	VERB
ma-203	10	11	diffusions	diffusion	NOUN
ma-203	10	12	.	.	PUNCT
ma-203	11	1	bishwal	bishwal	NOUN
ma-203	12	1	[	[	X
ma-203	12	2	8	8	NUM
ma-203	12	3	]	]	PUNCT
ma-203	12	4	studied	study	VERB
ma-203	12	5	asymptotic	asymptotic	ADJ
ma-203	12	6	theory	theory	NOUN
ma-203	12	7	of	of	ADP
ma-203	12	8	like	like	ADP
ma-203	12	9	-	-	PUNCT
ma-203	12	10	lihood	lihood	NOUN
ma-203	12	11	method	method	NOUN
ma-203	12	12	and	and	CCONJ
ma-203	12	13	bayesian	bayesian	NOUN
ma-203	12	14	method	method	NOUN
ma-203	12	15	for	for	ADP
ma-203	12	16	drift	drift	NOUN
ma-203	12	17	estimation	estimation	NOUN
ma-203	12	18	of	of	ADP
ma-203	12	19	finite	finite	ADJ
ma-203	12	20	dimensional	dimensional	ADJ
ma-203	12	21	stochastic	stochastic	ADJ
ma-203	12	22	differentialequations	differentialequation	NOUN
ma-203	12	23	.	.	PUNCT
ma-203	13	1	bishwal	bishwal	NOUN
ma-203	14	1	[	[	X
ma-203	14	2	12	12	NUM
ma-203	14	3	]	]	PUNCT
ma-203	14	4	studied	study	VERB
ma-203	14	5	applications	application	NOUN
ma-203	14	6	of	of	ADP
ma-203	14	7	levy	levy	NOUN
ma-203	14	8	processes	process	NOUN
ma-203	14	9	in	in	ADP
ma-203	14	10	stochastic	stochastic	ADJ
ma-203	14	11	volatility	volatility	NOUN
ma-203	14	12	models	model	NOUN
ma-203	14	13	infinance	infinance	NOUN
ma-203	14	14	.	.	PUNCT
ma-203	15	1	bishwal	bishwal	NOUN
ma-203	16	1	[	[	X
ma-203	16	2	13	13	NUM
ma-203	16	3	]	]	PUNCT
ma-203	16	4	studied	study	VERB
ma-203	16	5	parameter	parameter	NOUN
ma-203	16	6	estimation	estimation	NOUN
ma-203	16	7	for	for	ADP
ma-203	16	8	spdes	spde	NOUN
ma-203	16	9	driven	drive	VERB
ma-203	16	10	by	by	ADP
ma-203	16	11	cylindrical	cylindrical	ADJ
ma-203	16	12	stable	stable	ADJ
ma-203	16	13	pro	pro	ADJ
ma-203	16	14	-	-	NOUN
ma-203	16	15	cesses	cesse	NOUN
ma-203	16	16	.	.	PUNCT
ma-203	17	1	bishwal	bishwal	NOUN
ma-203	18	1	[	[	X
ma-203	18	2	6	6	NUM
ma-203	18	3	]	]	PUNCT
ma-203	18	4	studied	study	VERB
ma-203	18	5	the	the	DET
ma-203	18	6	bernstein	bernstein	PROPN
ma-203	18	7	-	-	PUNCT
ma-203	18	8	von	von	PROPN
ma-203	18	9	mises	mises	PROPN
ma-203	18	10	theorem	theorem	VERB
ma-203	18	11	and	and	CCONJ
ma-203	18	12	spectral	spectral	ADJ
ma-203	18	13	asymptotics	asymptotic	NOUN
ma-203	18	14	of	of	ADP
ma-203	18	15	bayesestimators	bayesestimator	NOUN
ma-203	18	16	for	for	ADP
ma-203	18	17	parabolic	parabolic	ADJ
ma-203	18	18	spdes	spde	NOUN
ma-203	18	19	when	when	SCONJ
ma-203	18	20	the	the	DET
ma-203	18	21	number	number	NOUN
ma-203	18	22	of	of	ADP
ma-203	18	23	fourier	fourier	ADJ
ma-203	18	24	coefficients	coefficient	NOUN
ma-203	18	25	becomes	become	VERB
ma-203	18	26	large	large	ADJ
ma-203	18	27	.	.	PUNCT
ma-203	19	1	in	in	ADP
ma-203	19	2	thiscase	thiscase	NOUN
ma-203	19	3	,	,	PUNCT
ma-203	19	4	the	the	DET
ma-203	19	5	measures	measure	NOUN
ma-203	19	6	generated	generate	VERB
ma-203	19	7	by	by	ADP
ma-203	19	8	the	the	DET
ma-203	19	9	process	process	NOUN
ma-203	19	10	for	for	ADP
ma-203	19	11	different	different	ADJ
ma-203	19	12	parameters	parameter	NOUN
ma-203	19	13	are	be	AUX
ma-203	19	14	singular	singular	ADJ
ma-203	19	15	.	.	PUNCT
ma-203	20	1	bishwal	bishwal	NOUN
ma-203	21	1	[	[	X
ma-203	21	2	11]studied	11]studied	NUM
ma-203	21	3	bernstein	bernstein	PROPN
ma-203	21	4	-	-	PUNCT
ma-203	21	5	von	von	PROPN
ma-203	21	6	mises	mises	PROPN
ma-203	21	7	theorem	theorem	VERB
ma-203	21	8	and	and	CCONJ
ma-203	21	9	small	small	ADJ
ma-203	21	10	noise	noise	NOUN
ma-203	21	11	bayesian	bayesian	NOUN
ma-203	21	12	asymptotics	asymptotic	NOUN
ma-203	21	13	for	for	ADP
ma-203	21	14	parabolic	parabolic	ADJ
ma-203	21	15	stochas	stochas	ADJ
ma-203	21	16	-	-	PUNCT
ma-203	21	17	tic	tic	ADJ
ma-203	21	18	partial	partial	ADJ
ma-203	21	19	differential	differential	NOUN
ma-203	21	20	equations	equation	NOUN
ma-203	21	21	.	.	PUNCT
ma-203	22	1	bishwal	bishwal	NOUN
ma-203	23	1	[	[	X
ma-203	23	2	10	10	NUM
ma-203	23	3	]	]	PUNCT
ma-203	23	4	studied	study	VERB
ma-203	23	5	hypothesis	hypothesis	NOUN
ma-203	23	6	testing	testing	NOUN
ma-203	23	7	for	for	ADP
ma-203	23	8	fractional	fractional	ADJ
ma-203	23	9	stochasticpartial	stochasticpartial	ADJ
ma-203	23	10	differential	differential	ADJ
ma-203	23	11	equations	equation	NOUN
ma-203	23	12	with	with	ADP
ma-203	23	13	applications	application	NOUN
ma-203	23	14	to	to	ADP
ma-203	23	15	neurophysiology	neurophysiology	NOUN
ma-203	23	16	and	and	CCONJ
ma-203	23	17	finance.consider	finance.consider	NUM
ma-203	23	18	the	the	DET
ma-203	23	19	nonlinear	nonlinear	ADJ
ma-203	23	20	spde	spde	NOUN
ma-203	23	21	dx(t	dx(t	PROPN
ma-203	23	22	,	,	PUNCT
ma-203	23	23	x	x	X
ma-203	23	24	)	)	PUNCT
ma-203	23	25	=	=	SYM
ma-203	23	26	1	1	NUM
ma-203	23	27	2	2	NUM
ma-203	23	28	∆x(t	∆x(t	NOUN
ma-203	23	29	,	,	PUNCT
ma-203	23	30	x)dt	x)dt	PROPN
ma-203	23	31	+	+	CCONJ
ma-203	23	32	√	√	PROPN
ma-203	23	33	x(t	x(t	PROPN
ma-203	23	34	,	,	PUNCT
ma-203	23	35	x)dw	x)dw	PROPN
ma-203	23	36	(	(	PUNCT
ma-203	23	37	t	t	PROPN
ma-203	23	38	,	,	PUNCT
ma-203	23	39	x	x	NOUN
ma-203	23	40	)	)	PUNCT
ma-203	23	41	(	(	PUNCT
ma-203	23	42	1.1	1.1	NUM
ma-203	23	43	)	)	PUNCT
ma-203	23	44	where	where	SCONJ
ma-203	23	45	w	w	PROPN
ma-203	23	46	(	(	PUNCT
ma-203	23	47	t	t	PROPN
ma-203	23	48	,	,	PUNCT
ma-203	23	49	x	x	NOUN
ma-203	23	50	)	)	PUNCT
ma-203	23	51	a	a	DET
ma-203	23	52	cylindrical	cylindrical	ADJ
ma-203	23	53	brownian	brownian	ADJ
ma-203	23	54	motion	motion	NOUN
ma-203	23	55	.	.	PUNCT
ma-203	24	1	konno	konno	NOUN
ma-203	24	2	and	and	CCONJ
ma-203	24	3	shiga	shiga	ADJ
ma-203	25	1	[	[	X
ma-203	25	2	26	26	NUM
ma-203	25	3	]	]	PUNCT
ma-203	25	4	studied	study	VERB
ma-203	25	5	the	the	DET
ma-203	25	6	existence	existence	NOUN
ma-203	25	7	andweak	andweak	NOUN
ma-203	25	8	uniqueness	uniqueness	NOUN
ma-203	25	9	of	of	ADP
ma-203	25	10	the	the	DET
ma-203	25	11	above	above	ADJ
ma-203	25	12	equation	equation	NOUN
ma-203	25	13	as	as	ADP
ma-203	25	14	a	a	DET
ma-203	25	15	martingale	martingale	ADJ
ma-203	25	16	problem	problem	NOUN
ma-203	25	17	for	for	ADP
ma-203	25	18	the	the	DET
ma-203	25	19	associated	associated	ADJ
ma-203	25	20	super	super	NOUN
ma-203	25	21	-	-	NOUN
ma-203	25	22	brownianmotion	brownianmotion	NOUN
ma-203	25	23	.	.	PUNCT
ma-203	26	1	the	the	DET
ma-203	26	2	pathwise	pathwise	NOUN
ma-203	26	3	uniqueness	uniqueness	NOUN
ma-203	26	4	of	of	ADP
ma-203	26	5	nonnegative	nonnegative	ADJ
ma-203	26	6	solution	solution	NOUN
ma-203	26	7	still	still	ADV
ma-203	26	8	remains	remain	VERB
ma-203	26	9	open	open	ADJ
ma-203	26	10	.	.	PUNCT
ma-203	27	1	the	the	DET
ma-203	27	2	main	main	ADJ
ma-203	27	3	difficultycomes	difficultycome	NOUN
ma-203	27	4	from	from	ADP
ma-203	27	5	the	the	DET
ma-203	27	6	unbounded	unbounded	ADJ
ma-203	27	7	drift	drift	NOUN
ma-203	27	8	coefficient	coefficient	NOUN
ma-203	27	9	and	and	CCONJ
ma-203	27	10	non	non	ADJ
ma-203	27	11	-	-	ADJ
ma-203	27	12	lipschitz	lipschitz	ADJ
ma-203	27	13	diffusion	diffusion	NOUN
ma-203	27	14	coefficient	coefficient	NOUN
ma-203	27	15	.	.	PUNCT
ma-203	28	1	wang	wang	PROPN
ma-203	28	2	et	et	PROPN
ma-203	28	3	al	al	PROPN
ma-203	28	4	.	.	PUNCT
ma-203	29	1	[	[	X
ma-203	29	2	39]studied	39]studied	NUM
ma-203	29	3	a	a	DET
ma-203	29	4	comparison	comparison	NOUN
ma-203	29	5	theorem	theorem	VERB
ma-203	29	6	and	and	CCONJ
ma-203	29	7	showed	show	VERB
ma-203	29	8	that	that	SCONJ
ma-203	29	9	the	the	DET
ma-203	29	10	solution	solution	NOUN
ma-203	29	11	of	of	ADP
ma-203	29	12	the	the	DET
ma-203	29	13	nonlinear	nonlinear	ADJ
ma-203	29	14	spde	spde	NOUN
ma-203	29	15	is	be	AUX
ma-203	29	16	distribution	distribution	NOUN
ma-203	29	17	received	receive	VERB
ma-203	29	18	:	:	PUNCT
ma-203	29	19	4	4	NUM
ma-203	29	20	dec	dec	PROPN
ma-203	29	21	2023	2023	NUM
ma-203	29	22	.	.	PUNCT
ma-203	30	1	key	key	ADJ
ma-203	30	2	words	word	NOUN
ma-203	30	3	and	and	CCONJ
ma-203	30	4	phrases	phrase	NOUN
ma-203	30	5	.	.	PUNCT
ma-203	31	1	nonlinear	nonlinear	ADJ
ma-203	31	2	stochastic	stochastic	ADJ
ma-203	31	3	partial	partial	ADJ
ma-203	31	4	differential	differential	NOUN
ma-203	31	5	equations	equation	NOUN
ma-203	31	6	,	,	PUNCT
ma-203	31	7	super	super	ADJ
ma-203	31	8	processes	process	NOUN
ma-203	31	9	,	,	PUNCT
ma-203	31	10	fractional	fractional	PROPN
ma-203	31	11	cox	cox	PROPN
ma-203	31	12	-	-	PUNCT
ma-203	31	13	ingersollross	ingersollross	PROPN
ma-203	31	14	model	model	NOUN
ma-203	31	15	,	,	PUNCT
ma-203	31	16	conditional	conditional	ADJ
ma-203	31	17	least	least	ADJ
ma-203	31	18	squares	square	NOUN
ma-203	31	19	estimator	estimator	NOUN
ma-203	31	20	,	,	PUNCT
ma-203	31	21	branching	branch	VERB
ma-203	31	22	interacting	interact	VERB
ma-203	31	23	particle	particle	NOUN
ma-203	31	24	system	system	NOUN
ma-203	31	25	,	,	PUNCT
ma-203	31	26	berry	berry	NOUN
ma-203	31	27	-	-	PUNCT
ma-203	31	28	esseen	esseen	PROPN
ma-203	31	29	inequality.1	inequality.1	PROPN
ma-203	31	30	https://adac.ee	https://adac.ee	PROPN
ma-203	31	31	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	VERB
ma-203	31	32	eur	eur	PROPN
ma-203	31	33	.	.	PUNCT
ma-203	32	1	j.	j.	PROPN
ma-203	32	2	math	math	PROPN
ma-203	32	3	.	.	PUNCT
ma-203	33	1	anal	anal	PROPN
ma-203	33	2	.	.	PUNCT
ma-203	34	1	10.28924	10.28924	NUM
ma-203	34	2	/	/	SYM
ma-203	34	3	ada	ada	NOUN
ma-203	34	4	/	/	SYM
ma-203	34	5	ma.4.12	ma.4.12	NOUN
ma-203	34	6	2function	2function	NUM
ma-203	34	7	valued	value	VERB
ma-203	34	8	.	.	PUNCT
ma-203	35	1	they	they	PRON
ma-203	35	2	also	also	ADV
ma-203	35	3	established	establish	VERB
ma-203	35	4	pathwise	pathwise	NOUN
ma-203	35	5	uniqueness	uniqueness	NOUN
ma-203	35	6	.	.	PUNCT
ma-203	36	1	as	as	ADP
ma-203	36	2	application	application	NOUN
ma-203	36	3	they	they	PRON
ma-203	36	4	obtained	obtain	VERB
ma-203	36	5	well	well	ADV
ma-203	36	6	-	-	PUNCT
ma-203	36	7	posedness	posedness	NOUN
ma-203	36	8	of	of	ADP
ma-203	36	9	martingale	martingale	ADJ
ma-203	36	10	problems	problem	NOUN
ma-203	36	11	for	for	ADP
ma-203	36	12	two	two	NUM
ma-203	36	13	classes	class	NOUN
ma-203	36	14	of	of	ADP
ma-203	36	15	measure	measure	NOUN
ma-203	36	16	-	-	PUNCT
ma-203	36	17	valued	value	VERB
ma-203	36	18	diffusions	diffusion	NOUN
ma-203	36	19	:	:	PUNCT
ma-203	36	20	interacting	interact	VERB
ma-203	36	21	super	super	ADJ
ma-203	36	22	-	-	ADJ
ma-203	36	23	brownian	brownian	ADJ
ma-203	36	24	motions	motion	NOUN
ma-203	36	25	and	and	CCONJ
ma-203	36	26	interacting	interact	VERB
ma-203	36	27	fleming	fleming	NOUN
ma-203	36	28	-	-	PUNCT
ma-203	36	29	viot	viot	NOUN
ma-203	36	30	processes	process	NOUN
ma-203	36	31	.	.	PUNCT
ma-203	37	1	he	he	PRON
ma-203	37	2	et	et	PROPN
ma-203	37	3	al	al	PROPN
ma-203	37	4	.	.	PUNCT
ma-203	38	1	[	[	X
ma-203	38	2	21	21	NUM
ma-203	38	3	]	]	PUNCT
ma-203	38	4	obtained	obtain	VERB
ma-203	38	5	pathwise	pathwise	NOUN
ma-203	38	6	uniquesolution	uniquesolution	NOUN
ma-203	38	7	to	to	ADP
ma-203	38	8	nonlinear	nonlinear	ADJ
ma-203	38	9	spde	spde	NOUN
ma-203	38	10	with	with	ADP
ma-203	38	11	super	super	ADJ
ma-203	38	12	levy	levy	NOUN
ma-203	38	13	process	process	NOUN
ma-203	38	14	,	,	PUNCT
ma-203	38	15	which	which	PRON
ma-203	38	16	is	be	AUX
ma-203	38	17	a	a	DET
ma-203	38	18	combination	combination	NOUN
ma-203	38	19	of	of	ADP
ma-203	38	20	space	space	NOUN
ma-203	38	21	-	-	PUNCT
ma-203	38	22	time	time	NOUN
ma-203	38	23	gaussianwhite	gaussianwhite	PROPN
ma-203	38	24	noises	noise	NOUN
ma-203	38	25	and	and	CCONJ
ma-203	38	26	poisson	poisson	NOUN
ma-203	38	27	random	random	ADJ
ma-203	38	28	measures	measure	NOUN
ma-203	38	29	which	which	PRON
ma-203	38	30	is	be	AUX
ma-203	38	31	a	a	DET
ma-203	38	32	generalization	generalization	NOUN
ma-203	38	33	of	of	ADP
ma-203	38	34	work	work	NOUN
ma-203	38	35	of	of	ADP
ma-203	38	36	xiong	xiong	PROPN
ma-203	39	1	[	[	X
ma-203	39	2	40	40	NUM
ma-203	39	3	]	]	PUNCT
ma-203	39	4	wherethe	wherethe	PROPN
ma-203	39	5	result	result	NOUN
ma-203	39	6	for	for	ADP
ma-203	39	7	a	a	DET
ma-203	39	8	super	super	ADJ
ma-203	39	9	-	-	ADJ
ma-203	39	10	brownian	brownian	ADJ
ma-203	39	11	motion	motion	NOUN
ma-203	39	12	with	with	ADP
ma-203	39	13	binary	binary	ADJ
ma-203	39	14	branching	branching	NOUN
ma-203	39	15	mechanism	mechanism	NOUN
ma-203	39	16	was	be	AUX
ma-203	39	17	obtained	obtain	VERB
ma-203	39	18	.	.	PUNCT
ma-203	40	1	usingan	usingan	PROPN
ma-203	40	2	extended	extended	ADJ
ma-203	40	3	yamada	yamada	PROPN
ma-203	40	4	-	-	PUNCT
ma-203	40	5	watanabe	watanabe	PROPN
ma-203	40	6	argument	argument	NOUN
ma-203	40	7	,	,	PUNCT
ma-203	40	8	xiong	xiong	PROPN
ma-203	41	1	[	[	X
ma-203	41	2	40	40	NUM
ma-203	41	3	]	]	PUNCT
ma-203	41	4	established	establish	VERB
ma-203	41	5	strong	strong	ADJ
ma-203	41	6	existence	existence	NOUN
ma-203	41	7	and	and	CCONJ
ma-203	41	8	uniquenessof	uniquenessof	VERB
ma-203	41	9	the	the	DET
ma-203	41	10	solution	solution	NOUN
ma-203	41	11	to	to	ADP
ma-203	41	12	the	the	DET
ma-203	41	13	spde	spde	NOUN
ma-203	41	14	.	.	PUNCT
ma-203	42	1	super	super	ADJ
ma-203	42	2	-	-	ADJ
ma-203	42	3	brownian	brownian	ADJ
ma-203	42	4	motion	motion	NOUN
ma-203	42	5	(	(	PUNCT
ma-203	42	6	sbm	sbm	PROPN
ma-203	42	7	)	)	PUNCT
ma-203	42	8	,	,	PUNCT
ma-203	42	9	also	also	ADV
ma-203	42	10	called	call	VERB
ma-203	42	11	the	the	DET
ma-203	42	12	dawson	dawson	PROPN
ma-203	42	13	-	-	PUNCT
ma-203	42	14	watanabeprocess	watanabeprocess	NOUN
ma-203	42	15	introduced	introduce	VERB
ma-203	42	16	by	by	ADP
ma-203	42	17	dawson	dawson	PROPN
ma-203	42	18	and	and	CCONJ
ma-203	42	19	watanabe	watanabe	PROPN
ma-203	42	20	is	be	AUX
ma-203	42	21	a	a	DET
ma-203	42	22	measure	measure	NOUN
ma-203	42	23	valued	value	VERB
ma-203	42	24	process	process	NOUN
ma-203	42	25	arising	arise	VERB
ma-203	42	26	as	as	ADP
ma-203	42	27	the	the	DET
ma-203	42	28	limit	limit	NOUN
ma-203	42	29	ofempirical	ofempirical	ADJ
ma-203	42	30	measure	measure	NOUN
ma-203	42	31	process	process	NOUN
ma-203	42	32	of	of	ADP
ma-203	42	33	a	a	DET
ma-203	42	34	branching	branch	VERB
ma-203	42	35	particle	particle	NOUN
ma-203	42	36	system	system	NOUN
ma-203	42	37	.	.	PUNCT
ma-203	43	1	sbm	sbm	PROPN
ma-203	43	2	satisfies	satisfy	VERB
ma-203	43	3	a	a	DET
ma-203	43	4	martingale	martingale	NOUN
ma-203	43	5	problem.when	problem.when	SCONJ
ma-203	43	6	the	the	DET
ma-203	43	7	state	state	NOUN
ma-203	43	8	space	space	NOUN
ma-203	43	9	is	be	AUX
ma-203	43	10	r	r	NOUN
ma-203	43	11	,	,	PUNCT
ma-203	43	12	sbm	sbm	PROPN
ma-203	43	13	has	have	VERB
ma-203	43	14	a	a	DET
ma-203	43	15	density	density	NOUN
ma-203	43	16	w.r.t	w.r.t	NOUN
ma-203	43	17	.	.	PUNCT
ma-203	44	1	lebesgue	lebesgue	NOUN
ma-203	44	2	measure	measure	NOUN
ma-203	44	3	and	and	CCONJ
ma-203	44	4	this	this	DET
ma-203	44	5	density	density	NOUN
ma-203	44	6	valuedprocess	valuedprocess	NOUN
ma-203	44	7	x(t	x(t	PROPN
ma-203	44	8	,	,	PUNCT
ma-203	44	9	x	x	X
ma-203	44	10	)	)	PUNCT
ma-203	44	11	satisfies	satisfy	VERB
ma-203	44	12	the	the	DET
ma-203	44	13	above	above	ADJ
ma-203	44	14	spde	spde	NOUN
ma-203	44	15	.	.	PUNCT
ma-203	45	1	when	when	SCONJ
ma-203	45	2	the	the	DET
ma-203	45	3	space	space	NOUN
ma-203	45	4	r	r	NOUN
ma-203	45	5	is	be	AUX
ma-203	45	6	s	s	NOUN
ma-203	45	7	single	single	ADJ
ma-203	45	8	point	point	NOUN
ma-203	45	9	,	,	PUNCT
ma-203	45	10	the	the	DET
ma-203	45	11	spde	spde	NOUN
ma-203	45	12	becomesan	becomesan	PROPN
ma-203	45	13	sde	sde	PROPN
ma-203	45	14	which	which	PRON
ma-203	45	15	is	be	AUX
ma-203	45	16	cir	cir	NOUN
ma-203	45	17	diffusion	diffusion	NOUN
ma-203	45	18	dxt	dxt	PROPN
ma-203	45	19	=	=	PUNCT
ma-203	45	20	√	√	PROPN
ma-203	45	21	xtdwt	xtdwt	NOUN
ma-203	45	22	whose	whose	DET
ma-203	45	23	uniqueness	uniqueness	NOUN
ma-203	45	24	is	be	AUX
ma-203	45	25	established	establish	VERB
ma-203	45	26	using	use	VERB
ma-203	45	27	the	the	DET
ma-203	45	28	yamada	yamada	PROPN
ma-203	45	29	-	-	PUNCT
ma-203	45	30	watanabe	watanabe	PROPN
ma-203	45	31	argument	argument	NOUN
ma-203	45	32	.	.	PUNCT
ma-203	46	1	xiong	xiong	PROPN
ma-203	46	2	and	and	CCONJ
ma-203	46	3	yang	yang	PROPN
ma-203	46	4	(	(	PUNCT
ma-203	46	5	2019	2019	NUM
ma-203	46	6	)	)	PUNCT
ma-203	46	7	studied	study	VERB
ma-203	46	8	existence	existence	NOUN
ma-203	46	9	and	and	CCONJ
ma-203	46	10	pathwise	pathwise	NOUN
ma-203	46	11	uniqueness	uniqueness	NOUN
ma-203	46	12	to	to	PART
ma-203	46	13	anspde	anspde	VERB
ma-203	46	14	with	with	ADP
ma-203	46	15	hölder	hölder	PROPN
ma-203	46	16	continuous	continuous	ADJ
ma-203	46	17	coefficient	coefficient	NOUN
ma-203	46	18	driven	drive	VERB
ma-203	46	19	by	by	ADP
ma-203	46	20	α	α	VERB
ma-203	46	21	-	-	ADJ
ma-203	46	22	stable	stable	ADJ
ma-203	46	23	colored	colored	ADJ
ma-203	46	24	noise	noise	NOUN
ma-203	46	25	.	.	PUNCT
ma-203	47	1	the	the	DET
ma-203	47	2	existence	existence	NOUN
ma-203	47	3	of	of	ADP
ma-203	47	4	thesolution	thesolution	NOUN
ma-203	47	5	is	be	AUX
ma-203	47	6	shown	show	VERB
ma-203	47	7	by	by	ADP
ma-203	47	8	considering	consider	VERB
ma-203	47	9	the	the	DET
ma-203	47	10	weak	weak	ADJ
ma-203	47	11	limit	limit	NOUN
ma-203	47	12	of	of	ADP
ma-203	47	13	a	a	DET
ma-203	47	14	sequence	sequence	NOUN
ma-203	47	15	of	of	ADP
ma-203	47	16	sde	sde	PROPN
ma-203	47	17	system	system	NOUN
ma-203	47	18	which	which	PRON
ma-203	47	19	is	be	AUX
ma-203	47	20	obtained	obtain	VERB
ma-203	47	21	byreplacing	byreplace	VERB
ma-203	47	22	the	the	DET
ma-203	47	23	laplacian	laplacian	ADJ
ma-203	47	24	operator	operator	NOUN
ma-203	47	25	in	in	ADP
ma-203	47	26	the	the	DET
ma-203	47	27	spde	spde	NOUN
ma-203	47	28	by	by	ADP
ma-203	47	29	its	its	PRON
ma-203	47	30	discrete	discrete	ADJ
ma-203	47	31	version	version	NOUN
ma-203	47	32	.	.	PUNCT
ma-203	48	1	the	the	DET
ma-203	48	2	pathwise	pathwise	NOUN
ma-203	48	3	uniqueness	uniqueness	NOUN
ma-203	48	4	isshown	isshown	ADJ
ma-203	48	5	by	by	ADP
ma-203	48	6	using	use	VERB
ma-203	48	7	a	a	DET
ma-203	48	8	backward	backward	ADJ
ma-203	48	9	doubly	doubly	ADV
ma-203	48	10	stochastic	stochastic	ADJ
ma-203	48	11	differential	differential	ADJ
ma-203	48	12	equation	equation	NOUN
ma-203	48	13	to	to	PART
ma-203	48	14	take	take	VERB
ma-203	48	15	care	care	NOUN
ma-203	48	16	of	of	ADP
ma-203	48	17	the	the	DET
ma-203	48	18	laplacian.in	laplacian.in	NOUN
ma-203	48	19	the	the	DET
ma-203	48	20	case	case	NOUN
ma-203	48	21	of	of	ADP
ma-203	48	22	d	d	PROPN
ma-203	48	23	=	=	SYM
ma-203	48	24	1	1	NUM
ma-203	48	25	,	,	PUNCT
ma-203	48	26	the	the	DET
ma-203	48	27	pathwise	pathwise	NOUN
ma-203	48	28	uniqueness	uniqueness	NOUN
ma-203	48	29	of	of	ADP
ma-203	48	30	a	a	DET
ma-203	48	31	nonnegative	nonnegative	ADJ
ma-203	48	32	solution	solution	NOUN
ma-203	48	33	to	to	ADP
ma-203	48	34	the	the	DET
ma-203	48	35	correspondingequation	correspondingequation	NOUN
ma-203	48	36	was	be	AUX
ma-203	48	37	established	establish	VERB
ma-203	48	38	by	by	ADP
ma-203	48	39	yang	yang	PROPN
ma-203	48	40	and	and	CCONJ
ma-203	48	41	zhou	zhou	PROPN
ma-203	49	1	[	[	X
ma-203	49	2	42	42	NUM
ma-203	49	3	]	]	PUNCT
ma-203	49	4	for	for	ADP
ma-203	49	5	1	1	NUM
ma-203	49	6	<	<	X
ma-203	49	7	α	α	X
ma-203	49	8	<	<	X
ma-203	49	9	√	√	PROPN
ma-203	49	10	5−	5−	NUM
ma-203	49	11	1	1	NUM
ma-203	49	12	and	and	CCONJ
ma-203	49	13	pathwise	pathwise	NOUN
ma-203	49	14	uniqueness	uniqueness	NOUN
ma-203	49	15	for	for	ADP
ma-203	49	16	√	√	PROPN
ma-203	49	17	5−	5−	NUM
ma-203	49	18	1	1	NUM
ma-203	49	19	<	<	X
ma-203	49	20	α	α	X
ma-203	49	21	<	<	X
ma-203	49	22	2	2	NUM
ma-203	49	23	is	be	AUX
ma-203	49	24	still	still	ADV
ma-203	49	25	open.the	open.the	DET
ma-203	49	26	existence	existence	NOUN
ma-203	49	27	and	and	CCONJ
ma-203	49	28	pathwise	pathwise	NOUN
ma-203	49	29	uniqueness	uniqueness	NOUN
ma-203	49	30	of	of	ADP
ma-203	49	31	solutions	solution	NOUN
ma-203	49	32	to	to	ADP
ma-203	49	33	the	the	DET
ma-203	49	34	sdes	sde	NOUN
ma-203	49	35	with	with	ADP
ma-203	49	36	non	non	ADJ
ma-203	49	37	-	-	ADJ
ma-203	49	38	lipschitz	lipschitz	ADJ
ma-203	49	39	coefficientdriven	coefficientdriven	NOUN
ma-203	49	40	by	by	ADP
ma-203	49	41	spectrally	spectrally	ADV
ma-203	49	42	positive	positive	ADJ
ma-203	49	43	levy	levy	NOUN
ma-203	49	44	processes	process	NOUN
ma-203	49	45	were	be	AUX
ma-203	49	46	studied	study	VERB
ma-203	49	47	in	in	ADP
ma-203	49	48	fu	fu	NOUN
ma-203	49	49	and	and	CCONJ
ma-203	49	50	li	li	NOUN
ma-203	50	1	[	[	X
ma-203	50	2	20].consider	20].consider	NUM
ma-203	50	3	the	the	DET
ma-203	50	4	spde	spde	NOUN
ma-203	50	5	with	with	ADP
ma-203	50	6	multiplicative	multiplicative	ADJ
ma-203	50	7	noise	noise	NOUN
ma-203	50	8	:	:	PUNCT
ma-203	50	9	duθ(t	duθ(t	PROPN
ma-203	50	10	,	,	PUNCT
ma-203	50	11	x	x	NOUN
ma-203	50	12	)	)	PUNCT
ma-203	50	13	=	=	SYM
ma-203	50	14	(	(	PUNCT
ma-203	50	15	a0	a0	PROPN
ma-203	50	16	+	+	CCONJ
ma-203	50	17	θa1)uθ(t	θa1)uθ(t	PROPN
ma-203	50	18	,	,	PUNCT
ma-203	50	19	x)dt	x)dt	PROPN
ma-203	50	20	+	+	PROPN
ma-203	50	21	muθ(t	muθ(t	PROPN
ma-203	50	22	,	,	PUNCT
ma-203	50	23	x)dz(t	x)dz(t	PROPN
ma-203	50	24	,	,	PUNCT
ma-203	50	25	x	x	X
ma-203	50	26	)	)	PUNCT
ma-203	50	27	,	,	PUNCT
ma-203	50	28	t	t	PROPN
ma-203	50	29	≥	≥	NUM
ma-203	50	30	0	0	NUM
ma-203	50	31	,	,	PUNCT
ma-203	50	32	x	x	SYM
ma-203	50	33	∈	∈	PROPN
ma-203	51	1	[	[	X
ma-203	51	2	0	0	NUM
ma-203	51	3	,	,	PUNCT
ma-203	51	4	1	1	NUM
ma-203	51	5	]	]	PUNCT
ma-203	51	6	(	(	PUNCT
ma-203	51	7	1.2	1.2	NUM
ma-203	51	8	)	)	PUNCT
ma-203	51	9	where	where	SCONJ
ma-203	51	10	m	m	NOUN
ma-203	51	11	is	be	AUX
ma-203	51	12	a	a	DET
ma-203	51	13	known	know	VERB
ma-203	51	14	nonlinear	nonlinear	NOUN
ma-203	51	15	operator.priola	operator.priola	INTJ
ma-203	51	16	et	et	NOUN
ma-203	51	17	al	al	PROPN
ma-203	51	18	.	.	PUNCT
ma-203	52	1	[	[	X
ma-203	52	2	32	32	NUM
ma-203	52	3	]	]	PUNCT
ma-203	52	4	obtained	obtain	VERB
ma-203	52	5	exponential	exponential	ADJ
ma-203	52	6	convergence	convergence	NOUN
ma-203	52	7	to	to	ADP
ma-203	52	8	the	the	DET
ma-203	52	9	invariant	invariant	ADJ
ma-203	52	10	measure	measure	NOUN
ma-203	52	11	,	,	PUNCT
ma-203	52	12	in	in	ADP
ma-203	52	13	the	the	DET
ma-203	52	14	total	total	ADJ
ma-203	52	15	variationnorm	variationnorm	NOUN
ma-203	52	16	,	,	PUNCT
ma-203	52	17	for	for	ADP
ma-203	52	18	solutions	solution	NOUN
ma-203	52	19	to	to	ADP
ma-203	52	20	sdes	sde	NOUN
ma-203	52	21	driven	drive	VERB
ma-203	52	22	by	by	ADP
ma-203	52	23	α	α	NOUN
ma-203	52	24	-	-	ADJ
ma-203	52	25	stable	stable	ADJ
ma-203	52	26	noises	noise	NOUN
ma-203	52	27	in	in	ADP
ma-203	52	28	finite	finite	NOUN
ma-203	52	29	and	and	CCONJ
ma-203	52	30	infinite	infinite	ADJ
ma-203	52	31	dimensions	dimension	NOUN
ma-203	52	32	using	use	VERB
ma-203	52	33	twoapproaches	twoapproache	NOUN
ma-203	52	34	:	:	PUNCT
ma-203	52	35	lyapounov	lyapounov	PROPN
ma-203	52	36	’s	’s	PART
ma-203	52	37	function	function	NOUN
ma-203	52	38	approach	approach	NOUN
ma-203	52	39	by	by	ADP
ma-203	52	40	harris	harris	PROPN
ma-203	52	41	and	and	CCONJ
ma-203	52	42	doeblin	doeblin	PROPN
ma-203	52	43	’s	’s	PART
ma-203	52	44	coupling	coupling	NOUN
ma-203	52	45	argument	argument	NOUN
ma-203	52	46	.	.	PUNCT
ma-203	53	1	in	in	ADP
ma-203	53	2	bothapproaches	bothapproache	NOUN
ma-203	53	3	irreducibility	irreducibility	NOUN
ma-203	53	4	and	and	CCONJ
ma-203	53	5	uniform	uniform	ADJ
ma-203	53	6	strong	strong	ADJ
ma-203	53	7	feller	feller	NOUN
ma-203	53	8	property	property	NOUN
ma-203	53	9	play	play	VERB
ma-203	53	10	crucial	crucial	ADJ
ma-203	53	11	role.equation	role.equation	PROPN
ma-203	53	12	(	(	PUNCT
ma-203	53	13	1.2	1.2	NUM
ma-203	53	14	)	)	PUNCT
ma-203	53	15	is	be	AUX
ma-203	53	16	called	call	VERB
ma-203	53	17	diagonalizable	diagonalizable	ADJ
ma-203	53	18	if	if	SCONJ
ma-203	53	19	a0	a0	PROPN
ma-203	53	20	,	,	PUNCT
ma-203	53	21	a1	a1	NOUN
ma-203	53	22	and	and	CCONJ
ma-203	53	23	m	m	VERB
ma-203	53	24	have	have	AUX
ma-203	53	25	point	point	NOUN
ma-203	53	26	spectrum	spectrum	NOUN
ma-203	53	27	and	and	CCONJ
ma-203	53	28	a	a	DET
ma-203	53	29	commonsystem	commonsystem	NOUN
ma-203	53	30	of	of	ADP
ma-203	53	31	eigenfunction	eigenfunction	NOUN
ma-203	53	32	{	{	PUNCT
ma-203	53	33	hj	hj	PROPN
ma-203	53	34	,	,	PUNCT
ma-203	53	35	j	j	PROPN
ma-203	53	36	≥	≥	PROPN
ma-203	53	37	1	1	NUM
ma-203	53	38	}	}	PUNCT
ma-203	53	39	.	.	PUNCT
ma-203	54	1	denote	denote	VERB
ma-203	54	2	by	by	ADP
ma-203	54	3	ρk	ρk	PRON
ma-203	54	4	,	,	PUNCT
ma-203	54	5	νk	νk	NOUN
ma-203	54	6	and	and	CCONJ
ma-203	54	7	µk	µk	INTJ
ma-203	54	8	,	,	PUNCT
ma-203	54	9	the	the	DET
ma-203	54	10	eigenvalues	eigenvalue	NOUN
ma-203	54	11	of	of	ADP
ma-203	54	12	the	the	DET
ma-203	54	13	operators	operator	NOUN
ma-203	54	14	a0	a0	PROPN
ma-203	54	15	,	,	PUNCT
ma-203	54	16	a1	a1	NOUN
ma-203	54	17	and	and	CCONJ
ma-203	54	18	m	m	NOUN
ma-203	54	19	respectively	respectively	ADV
ma-203	54	20	.	.	PUNCT
ma-203	55	1	then	then	ADV
ma-203	55	2	uθ(t	uθ(t	VERB
ma-203	55	3	,	,	PUNCT
ma-203	55	4	x	x	NOUN
ma-203	55	5	)	)	PUNCT
ma-203	55	6	=	=	PUNCT
ma-203	56	1	∞∑	∞∑	NUM
ma-203	56	2	j=1	j=1	PROPN
ma-203	56	3	uj	uj	PROPN
ma-203	56	4	,	,	PUNCT
ma-203	56	5	thj	thj	PROPN
ma-203	56	6	.	.	PUNCT
ma-203	57	1	(	(	PUNCT
ma-203	57	2	1.3	1.3	NUM
ma-203	57	3	)	)	PUNCT
ma-203	57	4	we	we	PRON
ma-203	57	5	consider	consider	VERB
ma-203	57	6	fractional	fractional	ADJ
ma-203	57	7	stable	stable	ADJ
ma-203	57	8	cir	cir	NOUN
ma-203	57	9	model	model	NOUN
ma-203	57	10	as	as	ADP
ma-203	57	11	example.using	example.use	VERB
ma-203	57	12	fractional	fractional	ADJ
ma-203	57	13	levy	levy	NOUN
ma-203	57	14	process	process	NOUN
ma-203	57	15	as	as	ADP
ma-203	57	16	the	the	DET
ma-203	57	17	driving	drive	VERB
ma-203	57	18	term	term	NOUN
ma-203	57	19	,	,	PUNCT
ma-203	57	20	maximum	maximum	ADJ
ma-203	57	21	quasi	quasi	ADJ
ma-203	57	22	-	-	ADJ
ma-203	57	23	likelihood	likelihood	ADJ
ma-203	57	24	estimation	estimation	NOUN
ma-203	57	25	in	in	ADP
ma-203	57	26	frac	frac	ADJ
ma-203	57	27	-	-	PUNCT
ma-203	57	28	tional	tional	ADJ
ma-203	57	29	levy	levy	NOUN
ma-203	57	30	stochastic	stochastic	ADJ
ma-203	57	31	volatility	volatility	NOUN
ma-203	57	32	model	model	NOUN
ma-203	57	33	was	be	AUX
ma-203	57	34	studied	study	VERB
ma-203	57	35	in	in	ADP
ma-203	57	36	bishwal	bishwal	NOUN
ma-203	57	37	[	[	X
ma-203	57	38	9	9	NUM
ma-203	57	39	]	]	SYM
ma-203	57	40	.	.	PUNCT
ma-203	58	1	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	58	2	eur	eur	PROPN
ma-203	58	3	.	.	PUNCT
ma-203	59	1	j.	j.	PROPN
ma-203	59	2	math	math	PROPN
ma-203	59	3	.	.	PUNCT
ma-203	60	1	anal	anal	PROPN
ma-203	60	2	.	.	PUNCT
ma-203	61	1	10.28924	10.28924	NUM
ma-203	61	2	/	/	SYM
ma-203	61	3	ada	ada	NOUN
ma-203	61	4	/	/	SYM
ma-203	61	5	ma.4.12	ma.4.12	NOUN
ma-203	61	6	3fractional	3fractional	NUM
ma-203	61	7	levy	levy	NOUN
ma-203	61	8	process	process	NOUN
ma-203	61	9	(	(	PUNCT
ma-203	61	10	flp	flp	NOUN
ma-203	61	11	)	)	PUNCT
ma-203	61	12	is	be	AUX
ma-203	61	13	defined	define	VERB
ma-203	61	14	as	as	ADP
ma-203	61	15	mh	mh	PROPN
ma-203	61	16	,	,	PUNCT
ma-203	61	17	t	t	PROPN
ma-203	61	18	=	=	SYM
ma-203	61	19	1	1	NUM
ma-203	61	20	γ(h	γ(h	NOUN
ma-203	61	21	+	+	CCONJ
ma-203	61	22	1	1	NUM
ma-203	61	23	2	2	NUM
ma-203	61	24	)	)	PUNCT
ma-203	61	25	∫	∫	NOUN
ma-203	62	1	r	r	NOUN
ma-203	62	2	[	[	X
ma-203	62	3	(	(	PUNCT
ma-203	62	4	t	t	PROPN
ma-203	62	5	−	−	PROPN
ma-203	62	6	s	s	PART
ma-203	62	7	)	)	PUNCT
ma-203	62	8	h−1/2	h−1/2	PROPN
ma-203	62	9	+	+	CCONJ
ma-203	62	10	−	−	PROPN
ma-203	62	11	(	(	PUNCT
ma-203	62	12	−s	−s	NOUN
ma-203	62	13	)	)	PUNCT
ma-203	62	14	h−1/2	h−1/2	NOUN
ma-203	63	1	+	+	CCONJ
ma-203	63	2	]	]	X
ma-203	63	3	dls	dls	PROPN
ma-203	63	4	,	,	PUNCT
ma-203	63	5	t	t	PROPN
ma-203	63	6	∈	∈	PROPN
ma-203	63	7	r	r	NOUN
ma-203	63	8	(	(	PUNCT
ma-203	63	9	1.4	1.4	NUM
ma-203	63	10	)	)	PUNCT
ma-203	63	11	where	where	SCONJ
ma-203	63	12	{	{	PUNCT
ma-203	63	13	lt	lt	INTJ
ma-203	63	14	,	,	PUNCT
ma-203	63	15	t	t	PROPN
ma-203	63	16	∈	∈	PROPN
ma-203	63	17	r	r	X
ma-203	63	18	}	}	PUNCT
ma-203	63	19	is	be	AUX
ma-203	63	20	a	a	DET
ma-203	63	21	levy	levy	NOUN
ma-203	63	22	process	process	NOUN
ma-203	63	23	on	on	ADP
ma-203	63	24	r	r	NOUN
ma-203	63	25	with	with	ADP
ma-203	63	26	e(l1	e(l1	NOUN
ma-203	63	27	)	)	PUNCT
ma-203	64	1	=	=	SYM
ma-203	64	2	0	0	NUM
ma-203	64	3	,	,	PUNCT
ma-203	64	4	e(l2	e(l2	NOUN
ma-203	64	5	1	1	NUM
ma-203	64	6	)	)	PUNCT
ma-203	65	1	<	<	X
ma-203	65	2	∞.here	∞.here	ADV
ma-203	65	3	are	be	AUX
ma-203	65	4	some	some	DET
ma-203	65	5	properties	property	NOUN
ma-203	65	6	of	of	ADP
ma-203	65	7	the	the	DET
ma-203	65	8	fractional	fractional	ADJ
ma-203	65	9	levy	levy	NOUN
ma-203	65	10	process:1	process:1	VERB
ma-203	65	11	)	)	PUNCT
ma-203	65	12	the	the	DET
ma-203	65	13	covariance	covariance	NOUN
ma-203	65	14	of	of	ADP
ma-203	65	15	the	the	DET
ma-203	65	16	process	process	NOUN
ma-203	65	17	is	be	AUX
ma-203	65	18	given	give	VERB
ma-203	65	19	by	by	ADP
ma-203	65	20	cov(mh	cov(mh	NOUN
ma-203	65	21	,	,	PUNCT
ma-203	65	22	t	t	PROPN
ma-203	65	23	,	,	PUNCT
ma-203	65	24	mh	mh	PROPN
ma-203	65	25	,	,	PUNCT
ma-203	65	26	s	s	PART
ma-203	65	27	)	)	PUNCT
ma-203	65	28	=	=	SYM
ma-203	65	29	e(l2	e(l2	NOUN
ma-203	65	30	1	1	NUM
ma-203	65	31	)	)	PUNCT
ma-203	65	32	2γ(2h	2γ(2h	NUM
ma-203	65	33	+	+	CCONJ
ma-203	65	34	1	1	NUM
ma-203	65	35	)	)	PUNCT
ma-203	65	36	sin(πh	sin(πh	NOUN
ma-203	65	37	)	)	PUNCT
ma-203	66	1	[	[	X
ma-203	66	2	|t|2h	|t|2h	ADJ
ma-203	66	3	+	+	CCONJ
ma-203	66	4	|s|2h	|s|2h	ADJ
ma-203	66	5	−	−	PROPN
ma-203	66	6	|t	|t	NOUN
ma-203	66	7	−	−	PROPN
ma-203	66	8	s|2h	s|2h	ADJ
ma-203	66	9	]	]	PUNCT
ma-203	66	10	.	.	PUNCT
ma-203	67	1	(	(	PUNCT
ma-203	67	2	1.5	1.5	NUM
ma-203	67	3	)	)	PUNCT
ma-203	67	4	2	2	NUM
ma-203	67	5	)	)	PUNCT
ma-203	67	6	mh	mh	PROPN
ma-203	67	7	is	be	AUX
ma-203	67	8	not	not	PART
ma-203	67	9	a	a	DET
ma-203	67	10	martingale	martingale	NOUN
ma-203	67	11	.	.	PUNCT
ma-203	68	1	for	for	ADP
ma-203	68	2	a	a	DET
ma-203	68	3	large	large	ADJ
ma-203	68	4	class	class	NOUN
ma-203	68	5	of	of	ADP
ma-203	68	6	levy	levy	NOUN
ma-203	68	7	processes	process	NOUN
ma-203	68	8	,	,	PUNCT
ma-203	68	9	mh	mh	PROPN
ma-203	68	10	is	be	AUX
ma-203	68	11	neither	neither	CCONJ
ma-203	68	12	a	a	DET
ma-203	68	13	semimartingale.3)mh	semimartingale.3)mh	PRON
ma-203	68	14	is	be	AUX
ma-203	68	15	hölder	hölder	NOUN
ma-203	68	16	continuous	continuous	ADJ
ma-203	68	17	of	of	ADP
ma-203	68	18	any	any	DET
ma-203	68	19	order	order	NOUN
ma-203	68	20	β	β	X
ma-203	68	21	less	less	ADJ
ma-203	68	22	than	than	ADP
ma-203	68	23	h	h	NOUN
ma-203	68	24	−	−	NOUN
ma-203	68	25	1	1	NUM
ma-203	68	26	2	2	NUM
ma-203	68	27	.	.	PUNCT
ma-203	69	1	4	4	X
ma-203	69	2	)	)	PUNCT
ma-203	69	3	mh	mh	PROPN
ma-203	69	4	has	have	VERB
ma-203	69	5	stationary	stationary	ADJ
ma-203	69	6	increments	increment	NOUN
ma-203	69	7	.	.	PUNCT
ma-203	70	1	5	5	X
ma-203	70	2	)	)	PUNCT
ma-203	70	3	mh	mh	PROPN
ma-203	70	4	is	be	AUX
ma-203	70	5	symmetric	symmetric	ADJ
ma-203	70	6	.	.	PUNCT
ma-203	71	1	6	6	NUM
ma-203	71	2	)	)	PUNCT
ma-203	71	3	l	l	NOUN
ma-203	71	4	is	be	AUX
ma-203	71	5	self	self	NOUN
ma-203	71	6	-	-	PUNCT
ma-203	71	7	similar	similar	ADJ
ma-203	71	8	,	,	PUNCT
ma-203	71	9	but	but	CCONJ
ma-203	71	10	mh	mh	PROPN
ma-203	71	11	is	be	AUX
ma-203	71	12	not	not	PART
ma-203	71	13	self	self	NOUN
ma-203	71	14	-	-	PUNCT
ma-203	71	15	similar	similar	ADJ
ma-203	71	16	.	.	PUNCT
ma-203	72	1	7	7	X
ma-203	72	2	)	)	PUNCT
ma-203	72	3	mh	mh	PROPN
ma-203	72	4	has	have	AUX
ma-203	72	5	infinite	infinite	VERB
ma-203	72	6	total	total	ADJ
ma-203	72	7	variationon	variationon	NOUN
ma-203	72	8	compacts.thus	compacts.thus	X
ma-203	72	9	flp	flp	NOUN
ma-203	72	10	is	be	AUX
ma-203	72	11	a	a	DET
ma-203	72	12	generalization	generalization	NOUN
ma-203	72	13	and	and	CCONJ
ma-203	72	14	a	a	DET
ma-203	72	15	natural	natural	ADJ
ma-203	72	16	counterpart	counterpart	NOUN
ma-203	72	17	of	of	ADP
ma-203	72	18	fbm	fbm	PROPN
ma-203	72	19	.	.	PUNCT
ma-203	73	1	fractional	fractional	ADJ
ma-203	73	2	stable	stable	ADJ
ma-203	73	3	motion	motion	NOUN
ma-203	73	4	is	be	AUX
ma-203	73	5	aspecial	aspecial	ADJ
ma-203	73	6	case	case	NOUN
ma-203	73	7	of	of	ADP
ma-203	73	8	flp	flp	PROPN
ma-203	73	9	.	.	PUNCT
ma-203	74	1	2	2	X
ma-203	74	2	.	.	X
ma-203	74	3	conditional	conditional	ADJ
ma-203	74	4	least	least	ADJ
ma-203	74	5	squares	square	NOUN
ma-203	74	6	estimation	estimation	NOUN
ma-203	74	7	let	let	VERB
ma-203	74	8	h	h	PRON
ma-203	74	9	be	be	AUX
ma-203	74	10	a	a	DET
ma-203	74	11	real	real	ADJ
ma-203	74	12	separable	separable	ADJ
ma-203	74	13	hilbert	hilbert	NOUN
ma-203	74	14	space	space	NOUN
ma-203	74	15	with	with	ADP
ma-203	74	16	inner	inner	ADJ
ma-203	74	17	product	product	NOUN
ma-203	74	18	〈	〈	PROPN
ma-203	74	19	·	·	SYM
ma-203	74	20	〉	〉	PROPN
ma-203	74	21	and	and	CCONJ
ma-203	74	22	norm	norm	NOUN
ma-203	74	23	|	|	ADV
ma-203	74	24	·	·	PUNCT
ma-203	74	25	|	|	INTJ
ma-203	74	26	.	.	PUNCT
ma-203	75	1	by	by	ADP
ma-203	75	2	l(h	l(h	PROPN
ma-203	75	3	)	)	PUNCT
ma-203	75	4	we	we	PRON
ma-203	75	5	denotethe	denotethe	VERB
ma-203	75	6	banach	banach	NOUN
ma-203	75	7	space	space	NOUN
ma-203	75	8	of	of	ADP
ma-203	75	9	bounded	bounded	ADJ
ma-203	75	10	linear	linear	PROPN
ma-203	75	11	operators	operator	NOUN
ma-203	75	12	from	from	ADP
ma-203	75	13	h	h	NOUN
ma-203	75	14	into	into	ADP
ma-203	75	15	h	h	NOUN
ma-203	75	16	endowed	endow	VERB
ma-203	75	17	with	with	ADP
ma-203	75	18	the	the	DET
ma-203	75	19	operator	operator	NOUN
ma-203	75	20	norm	norm	NOUN
ma-203	75	21	‖	‖	PROPN
ma-203	75	22	·	·	PUNCT
ma-203	75	23	‖l(h	‖l(h	NUM
ma-203	75	24	)	)	PUNCT
ma-203	75	25	.	.	PUNCT
ma-203	76	1	we	we	PRON
ma-203	76	2	fix	fix	VERB
ma-203	76	3	an	an	DET
ma-203	76	4	orthonormal	orthonormal	ADJ
ma-203	76	5	basis	basis	NOUN
ma-203	76	6	(	(	PUNCT
ma-203	76	7	en	en	X
ma-203	76	8	)	)	PUNCT
ma-203	76	9	in	in	ADP
ma-203	76	10	h.	h.	PROPN
ma-203	76	11	through	through	ADP
ma-203	76	12	the	the	DET
ma-203	76	13	basis	basis	NOUN
ma-203	76	14	(	(	PUNCT
ma-203	76	15	en	en	X
ma-203	76	16	)	)	PUNCT
ma-203	76	17	we	we	PRON
ma-203	76	18	will	will	AUX
ma-203	76	19	often	often	ADV
ma-203	76	20	identify	identify	VERB
ma-203	76	21	hin	hin	PRON
ma-203	76	22	l2	l2	NOUN
ma-203	76	23	.	.	PUNCT
ma-203	77	1	more	more	ADV
ma-203	77	2	generally	generally	ADV
ma-203	77	3	,	,	PUNCT
ma-203	77	4	for	for	ADP
ma-203	77	5	a	a	DET
ma-203	77	6	given	give	VERB
ma-203	77	7	sequence	sequence	NOUN
ma-203	77	8	ρ	ρ	NOUN
ma-203	77	9	=	=	SYM
ma-203	77	10	(	(	PUNCT
ma-203	77	11	ρn	ρn	INTJ
ma-203	77	12	)	)	PUNCT
ma-203	77	13	of	of	ADP
ma-203	77	14	real	real	ADJ
ma-203	77	15	numbers	number	NOUN
ma-203	77	16	we	we	PRON
ma-203	77	17	set	set	VERB
ma-203	77	18	l2ρ	l2ρ	PROPN
ma-203	77	19	=	=	SYM
ma-203	77	20	{	{	PUNCT
ma-203	77	21	(	(	PUNCT
ma-203	77	22	xn	xn	X
ma-203	77	23	)	)	PUNCT
ma-203	77	24	∈	∈	NOUN
ma-203	77	25	r∞	r∞	NOUN
ma-203	77	26	:	:	PUNCT
ma-203	77	27	∑	∑	PUNCT
ma-203	77	28	n≥1	n≥1	VERB
ma-203	77	29	x2	x2	PROPN
ma-203	77	30	nρ	nρ	PROPN
ma-203	77	31	2	2	NUM
ma-203	77	32	n	n	CCONJ
ma-203	77	33	<	<	X
ma-203	77	34	∞	∞	NUM
ma-203	77	35	}	}	PUNCT
ma-203	77	36	.	.	PUNCT
ma-203	78	1	where	where	SCONJ
ma-203	78	2	r∞	r∞	PROPN
ma-203	78	3	=	=	SYM
ma-203	78	4	rn	rn	PROPN
ma-203	78	5	.	.	PUNCT
ma-203	79	1	the	the	DET
ma-203	79	2	space	space	NOUN
ma-203	79	3	l2ρ	l2ρ	PROPN
ma-203	79	4	becomes	become	VERB
ma-203	79	5	a	a	DET
ma-203	79	6	separable	separable	ADJ
ma-203	79	7	hilbert	hilbert	NOUN
ma-203	79	8	space	space	NOUN
ma-203	79	9	with	with	ADP
ma-203	79	10	the	the	DET
ma-203	79	11	inner	inner	ADJ
ma-203	79	12	product	product	NOUN
ma-203	79	13	:	:	PUNCT
ma-203	79	14	〈	〈	PROPN
ma-203	79	15	x	x	X
ma-203	79	16	,	,	PUNCT
ma-203	79	17	y	y	PROPN
ma-203	79	18	〉	〉	NUM
ma-203	79	19	=	=	NOUN
ma-203	79	20	∑	∑	PROPN
ma-203	79	21	n≥1	n≥1	NOUN
ma-203	79	22	xnynρ	xnynρ	NOUN
ma-203	79	23	2	2	NUM
ma-203	79	24	n	n	NOUN
ma-203	79	25	for	for	ADP
ma-203	79	26	x	x	SYM
ma-203	79	27	=	=	SYM
ma-203	79	28	(	(	PUNCT
ma-203	79	29	xn	xn	PROPN
ma-203	79	30	)	)	PUNCT
ma-203	79	31	,	,	PUNCT
ma-203	79	32	y	y	PROPN
ma-203	79	33	=	=	SYM
ma-203	79	34	(	(	PUNCT
ma-203	79	35	yn	yn	NOUN
ma-203	79	36	)	)	PUNCT
ma-203	79	37	∈	∈	PROPN
ma-203	79	38	l2ρ	l2ρ	PROPN
ma-203	79	39	.	.	PUNCT
ma-203	80	1	let	let	VERB
ma-203	80	2	us	we	PRON
ma-203	80	3	fix	fix	VERB
ma-203	80	4	θ0	θ0	NOUN
ma-203	80	5	,	,	PUNCT
ma-203	80	6	the	the	DET
ma-203	80	7	unknown	unknown	ADJ
ma-203	80	8	true	true	ADJ
ma-203	80	9	value	value	NOUN
ma-203	80	10	of	of	ADP
ma-203	80	11	the	the	DET
ma-203	80	12	parameter	parameter	NOUN
ma-203	80	13	θ.let	θ.let	ADV
ma-203	80	14	(	(	PUNCT
ma-203	80	15	ω	ω	PROPN
ma-203	80	16	,	,	PUNCT
ma-203	80	17	f	f	PROPN
ma-203	80	18	,	,	PUNCT
ma-203	80	19	p	p	NOUN
ma-203	80	20	)	)	PUNCT
ma-203	80	21	be	be	AUX
ma-203	80	22	a	a	DET
ma-203	80	23	complete	complete	ADJ
ma-203	80	24	probability	probability	NOUN
ma-203	80	25	space	space	NOUN
ma-203	80	26	and	and	CCONJ
ma-203	80	27	z(t	z(t	NOUN
ma-203	80	28	,	,	PUNCT
ma-203	80	29	x	x	PRON
ma-203	80	30	)	)	PUNCT
ma-203	80	31	be	be	AUX
ma-203	80	32	a	a	DET
ma-203	80	33	process	process	NOUN
ma-203	80	34	on	on	ADP
ma-203	80	35	this	this	DET
ma-203	80	36	space	space	NOUN
ma-203	80	37	with	with	ADP
ma-203	80	38	valuesin	valuesin	NOUN
ma-203	80	39	the	the	DET
ma-203	80	40	schwarz	schwarz	PROPN
ma-203	80	41	space	space	NOUN
ma-203	80	42	of	of	ADP
ma-203	80	43	distributions	distribution	NOUN
ma-203	80	44	d′(g	d′(g	PROPN
ma-203	80	45	)	)	PUNCT
ma-203	80	46	such	such	ADJ
ma-203	80	47	that	that	PRON
ma-203	80	48	for	for	ADP
ma-203	80	49	φ	φ	PROPN
ma-203	80	50	,	,	PUNCT
ma-203	81	1	ψ	ψ	X
ma-203	81	2	∈	∈	ADP
ma-203	81	3	c∞0	c∞0	X
ma-203	81	4	(	(	PUNCT
ma-203	81	5	g	g	NOUN
ma-203	81	6	)	)	PUNCT
ma-203	81	7	,	,	PUNCT
ma-203	81	8	‖φ‖−1	‖φ‖−1	PROPN
ma-203	81	9	l2(g	l2(g	NOUN
ma-203	81	10	)	)	PUNCT
ma-203	81	11	〈	〈	PROPN
ma-203	81	12	w	w	PROPN
ma-203	81	13	(	(	PUNCT
ma-203	81	14	t	t	PROPN
ma-203	81	15	,	,	PUNCT
ma-203	81	16	·	·	PUNCT
ma-203	81	17	)	)	PUNCT
ma-203	81	18	,	,	PUNCT
ma-203	81	19	φ(·)〉is	φ(·)〉is	VERB
ma-203	81	20	a	a	DET
ma-203	81	21	one	one	NUM
ma-203	81	22	dimensional	dimensional	ADJ
ma-203	81	23	stable	stable	ADJ
ma-203	81	24	process.this	process.this	NOUN
ma-203	81	25	process	process	NOUN
ma-203	81	26	is	be	AUX
ma-203	81	27	usually	usually	ADV
ma-203	81	28	referred	refer	VERB
ma-203	81	29	to	to	ADP
ma-203	81	30	as	as	ADP
ma-203	81	31	the	the	DET
ma-203	81	32	cylindrical	cylindrical	ADJ
ma-203	81	33	α	α	ADJ
ma-203	81	34	-	-	ADJ
ma-203	81	35	stable	stable	ADJ
ma-203	81	36	process	process	NOUN
ma-203	81	37	(	(	PUNCT
ma-203	81	38	c.s.p	c.s.p	NOUN
ma-203	81	39	.	.	PUNCT
ma-203	81	40	)	)	PUNCT
ma-203	81	41	,	,	PUNCT
ma-203	81	42	α	α	PROPN
ma-203	81	43	∈	∈	PROPN
ma-203	81	44	(	(	PUNCT
ma-203	81	45	0	0	NUM
ma-203	81	46	,	,	PUNCT
ma-203	81	47	2	2	NUM
ma-203	81	48	)	)	PUNCT
ma-203	81	49	.	.	PUNCT
ma-203	82	1	weassume	weassume	VERB
ma-203	82	2	that	that	SCONJ
ma-203	82	3	there	there	PRON
ma-203	82	4	exists	exist	VERB
ma-203	82	5	a	a	DET
ma-203	82	6	complete	complete	ADJ
ma-203	82	7	orthonormal	orthonormal	ADJ
ma-203	82	8	system	system	NOUN
ma-203	82	9	{	{	PUNCT
ma-203	82	10	hi}∞i=1	hi}∞i=1	X
ma-203	82	11	in	in	ADP
ma-203	82	12	l2(g	l2(g	NOUN
ma-203	82	13	)	)	PUNCT
ma-203	82	14	)	)	PUNCT
ma-203	82	15	such	such	ADJ
ma-203	82	16	that	that	PRON
ma-203	82	17	for	for	ADP
ma-203	82	18	every	every	DET
ma-203	82	19	i	i	NOUN
ma-203	82	20	=	=	NOUN
ma-203	82	21	1	1	NUM
ma-203	82	22	,	,	PUNCT
ma-203	82	23	2	2	NUM
ma-203	82	24	,	,	PUNCT
ma-203	82	25	.	.	PUNCT
ma-203	82	26	.	.	PUNCT
ma-203	83	1	.	.	PUNCT
ma-203	84	1	,	,	PUNCT
ma-203	84	2	hi	hi	INTJ
ma-203	84	3	∈	∈	PROPN
ma-203	84	4	zm,20	zm,20	PROPN
ma-203	84	5	(	(	PUNCT
ma-203	84	6	g	g	NOUN
ma-203	84	7	)	)	PUNCT
ma-203	84	8	∩	∩	NOUN
ma-203	84	9	c∞(g	c∞(g	PROPN
ma-203	84	10	)	)	PUNCT
ma-203	84	11	and	and	CCONJ
ma-203	84	12	λθhi	λθhi	NOUN
ma-203	84	13	=	=	SYM
ma-203	84	14	βi(θ)hi	βi(θ)hi	NOUN
ma-203	84	15	,	,	PUNCT
ma-203	84	16	and	and	CCONJ
ma-203	84	17	lθhi	lθhi	PROPN
ma-203	84	18	=	=	PUNCT
ma-203	84	19	µi(θ)hi	µi(θ)hi	PROPN
ma-203	84	20	for	for	ADP
ma-203	84	21	all	all	DET
ma-203	84	22	θ	θ	PRON
ma-203	84	23	∈	∈	NOUN
ma-203	84	24	θ	θ	NOUN
ma-203	84	25	where	where	SCONJ
ma-203	84	26	lθ	lθ	NOUN
ma-203	84	27	is	be	AUX
ma-203	84	28	a	a	DET
ma-203	84	29	closed	closed	ADJ
ma-203	84	30	self	self	NOUN
ma-203	84	31	adjoint	adjoint	NOUN
ma-203	84	32	extension	extension	NOUN
ma-203	84	33	of	of	ADP
ma-203	84	34	aθ	aθ	NOUN
ma-203	84	35	,	,	PUNCT
ma-203	84	36	λθ	λθ	X
ma-203	84	37	:	:	PUNCT
ma-203	84	38	=	=	SYM
ma-203	84	39	(	(	PUNCT
ma-203	84	40	k(θ)i	k(θ)i	PROPN
ma-203	84	41	−	−	PROPN
ma-203	84	42	lθ)1/2	lθ)1/2	PROPN
ma-203	84	43	m	m	PROPN
ma-203	84	44	,	,	PUNCT
ma-203	84	45	k(θ	k(θ	PROPN
ma-203	84	46	)	)	PUNCT
ma-203	84	47	is	be	AUX
ma-203	84	48	a	a	DET
ma-203	84	49	constantand	constantand	NOUN
ma-203	84	50	the	the	DET
ma-203	84	51	spectrum	spectrum	NOUN
ma-203	84	52	of	of	ADP
ma-203	84	53	the	the	DET
ma-203	84	54	operator	operator	NOUN
ma-203	84	55	λθ	λθ	ADP
ma-203	84	56	consists	consist	NOUN
ma-203	84	57	of	of	ADP
ma-203	84	58	eigenvalues	eigenvalue	NOUN
ma-203	84	59	{	{	PUNCT
ma-203	84	60	βi(θ)}∞i=1	βi(θ)}∞i=1	NUM
ma-203	84	61	of	of	ADP
ma-203	84	62	finite	finite	PROPN
ma-203	84	63	multiplicities	multiplicity	NOUN
ma-203	84	64	and	and	CCONJ
ma-203	85	1	µi	µi	PROPN
ma-203	85	2	=	=	PROPN
ma-203	85	3	−β2	−β2	PROPN
ma-203	85	4	m	m	VERB
ma-203	85	5	i	i	PRON
ma-203	85	6	+	+	X
ma-203	85	7	k(θ	k(θ	NOUN
ma-203	85	8	)	)	PUNCT
ma-203	85	9	.	.	PUNCT
ma-203	86	1	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	86	2	eur	eur	PROPN
ma-203	86	3	.	.	PUNCT
ma-203	87	1	j.	j.	PROPN
ma-203	87	2	math	math	PROPN
ma-203	87	3	.	.	PUNCT
ma-203	88	1	anal	anal	PROPN
ma-203	88	2	.	.	PUNCT
ma-203	89	1	10.28924	10.28924	NUM
ma-203	89	2	/	/	SYM
ma-203	89	3	ada	ada	PROPN
ma-203	89	4	/	/	SYM
ma-203	89	5	ma.4.12	ma.4.12	NOUN
ma-203	89	6	4a	4a	NOUN
ma-203	89	7	levy	levy	NOUN
ma-203	89	8	process	process	NOUN
ma-203	89	9	(	(	PUNCT
ma-203	89	10	zt	zt	PROPN
ma-203	89	11	)	)	PUNCT
ma-203	89	12	with	with	ADP
ma-203	89	13	values	value	NOUN
ma-203	89	14	in	in	ADP
ma-203	89	15	h	h	NOUN
ma-203	89	16	is	be	AUX
ma-203	89	17	an	an	DET
ma-203	89	18	h	h	NOUN
ma-203	89	19	-	-	PUNCT
ma-203	89	20	valued	value	VERB
ma-203	89	21	process	process	NOUN
ma-203	89	22	defined	define	VERB
ma-203	89	23	on	on	ADP
ma-203	89	24	some	some	DET
ma-203	89	25	stochastic	stochastic	ADJ
ma-203	89	26	basis	basis	NOUN
ma-203	89	27	(	(	PUNCT
ma-203	89	28	ω	ω	NOUN
ma-203	89	29	,	,	PUNCT
ma-203	89	30	f	f	PROPN
ma-203	89	31	,	,	PUNCT
ma-203	89	32	(	(	PUNCT
ma-203	89	33	ft)t≥0	ft)t≥0	ADJ
ma-203	89	34	,	,	PUNCT
ma-203	89	35	p	p	NOUN
ma-203	89	36	)	)	PUNCT
ma-203	89	37	having	have	VERB
ma-203	89	38	stationary	stationary	ADJ
ma-203	89	39	independent	independent	ADJ
ma-203	89	40	increments	increment	NOUN
ma-203	89	41	,	,	PUNCT
ma-203	89	42	cadlag	cadlag	NOUN
ma-203	89	43	trajectories	trajectorie	VERB
ma-203	89	44	such	such	ADJ
ma-203	89	45	that	that	PRON
ma-203	89	46	z0	z0	PROPN
ma-203	89	47	=	=	SYM
ma-203	89	48	0,p	0,p	PROPN
ma-203	89	49	-	-	PUNCT
ma-203	89	50	a.s	a.s	PROPN
ma-203	89	51	.	.	PROPN
ma-203	89	52	one	one	NUM
ma-203	89	53	has	have	VERB
ma-203	89	54	that	that	SCONJ
ma-203	89	55	e[e	e[e	ADJ
ma-203	89	56	i〈zt	i〈zt	PROPN
ma-203	89	57	,	,	PUNCT
ma-203	89	58	s	s	PROPN
ma-203	89	59	〉	〉	NOUN
ma-203	89	60	]	]	PUNCT
ma-203	89	61	=	=	SYM
ma-203	89	62	exp(−tψ(s	exp(−tψ(s	PROPN
ma-203	89	63	)	)	PUNCT
ma-203	89	64	)	)	PUNCT
ma-203	89	65	,	,	PUNCT
ma-203	89	66	s	s	AUX
ma-203	89	67	∈	∈	PROPN
ma-203	89	68	hwhere	hwhere	ADV
ma-203	89	69	ψ	ψ	X
ma-203	89	70	:	:	PUNCT
ma-203	89	71	h	h	NOUN
ma-203	89	72	→	→	SYM
ma-203	89	73	c	c	NOUN
ma-203	89	74	is	be	AUX
ma-203	89	75	sazonov	sazonov	ADJ
ma-203	89	76	continuous	continuous	ADJ
ma-203	89	77	,	,	PUNCT
ma-203	89	78	negative	negative	ADJ
ma-203	89	79	definite	definite	ADJ
ma-203	89	80	function	function	NOUN
ma-203	89	81	such	such	ADJ
ma-203	89	82	that	that	DET
ma-203	89	83	ψ(0	ψ(0	NOUN
ma-203	89	84	)	)	PUNCT
ma-203	89	85	=	=	SYM
ma-203	90	1	0	0	X
ma-203	90	2	.	.	PUNCT
ma-203	91	1	thefunction	thefunction	NOUN
ma-203	91	2	ψ	ψ	PROPN
ma-203	91	3	is	be	AUX
ma-203	91	4	called	call	VERB
ma-203	91	5	the	the	DET
ma-203	91	6	exponent	exponent	NOUN
ma-203	91	7	of	of	ADP
ma-203	91	8	(	(	PUNCT
ma-203	91	9	zt).the	zt).the	PROPN
ma-203	91	10	exponent	exponent	NOUN
ma-203	91	11	ψ	ψ	X
ma-203	91	12	can	can	AUX
ma-203	91	13	be	be	AUX
ma-203	91	14	expressed	express	VERB
ma-203	91	15	by	by	ADP
ma-203	91	16	the	the	DET
ma-203	91	17	infinite	infinite	ADJ
ma-203	91	18	dimensional	dimensional	ADJ
ma-203	91	19	levy	levy	NOUN
ma-203	91	20	-	-	PUNCT
ma-203	91	21	khintchine	khintchine	NOUN
ma-203	91	22	formula	formula	NOUN
ma-203	92	1	ψ(s	ψ(s	PROPN
ma-203	92	2	)	)	PUNCT
ma-203	92	3	=	=	SYM
ma-203	92	4	1	1	NUM
ma-203	92	5	2	2	NUM
ma-203	92	6	〈	〈	NOUN
ma-203	92	7	qs	qs	X
ma-203	92	8	,	,	PUNCT
ma-203	92	9	s	s	PROPN
ma-203	92	10	〉	〉	NOUN
ma-203	92	11	−	−	PROPN
ma-203	92	12	i〈a	i〈a	X
ma-203	92	13	,	,	PUNCT
ma-203	92	14	s	s	PROPN
ma-203	92	15	〉	〉	NUM
ma-203	92	16	−	−	PROPN
ma-203	92	17	∫	∫	PROPN
ma-203	92	18	h	h	PROPN
ma-203	92	19	(	(	PUNCT
ma-203	92	20	e	e	NOUN
ma-203	92	21	i〈s	i〈s	PROPN
ma-203	92	22	,	,	PUNCT
ma-203	92	23	y	y	PROPN
ma-203	92	24	〉	〉	PROPN
ma-203	92	25	−	−	PROPN
ma-203	92	26	1−	1−	NUM
ma-203	92	27	i〈s	i〈s	ADP
ma-203	92	28	,	,	PUNCT
ma-203	92	29	y	y	PROPN
ma-203	92	30	〉	〉	PROPN
ma-203	92	31	1	1	NUM
ma-203	92	32	+	+	CCONJ
ma-203	92	33	|y	|y	NOUN
ma-203	92	34	|2	|2	X
ma-203	92	35	)	)	PUNCT
ma-203	92	36	ν(dy	ν(dy	NUM
ma-203	92	37	)	)	PUNCT
ma-203	92	38	,	,	PUNCT
ma-203	92	39	s	s	VERB
ma-203	92	40	∈	∈	PROPN
ma-203	92	41	h	h	NOUN
ma-203	92	42	where	where	SCONJ
ma-203	92	43	q	q	NOUN
ma-203	92	44	is	be	AUX
ma-203	92	45	the	the	DET
ma-203	92	46	non	non	ADJ
ma-203	92	47	-	-	ADJ
ma-203	92	48	negative	negative	ADJ
ma-203	92	49	trace	trace	NOUN
ma-203	92	50	class	class	NOUN
ma-203	92	51	operator	operator	NOUN
ma-203	92	52	on	on	ADP
ma-203	92	53	h	h	NOUN
ma-203	92	54	,	,	PUNCT
ma-203	92	55	a	a	DET
ma-203	92	56	∈	∈	PROPN
ma-203	92	57	h	h	NOUN
ma-203	92	58	and	and	CCONJ
ma-203	92	59	ν	ν	NOUN
ma-203	92	60	is	be	AUX
ma-203	92	61	the	the	DET
ma-203	92	62	levy	levy	NOUN
ma-203	92	63	measure	measure	NOUN
ma-203	92	64	or	or	CCONJ
ma-203	92	65	thejump	thejump	NOUN
ma-203	92	66	intensity	intensity	NOUN
ma-203	92	67	measure	measure	NOUN
ma-203	92	68	associated	associate	VERB
ma-203	92	69	to	to	ADP
ma-203	92	70	(	(	PUNCT
ma-203	92	71	zt).cylindrical	zt).cylindrical	PROPN
ma-203	92	72	α	α	NOUN
ma-203	92	73	-	-	ADJ
ma-203	92	74	stable	stable	ADJ
ma-203	92	75	process	process	NOUN
ma-203	92	76	(	(	PUNCT
ma-203	92	77	c.s.p	c.s.p	NOUN
ma-203	92	78	.	.	PUNCT
ma-203	92	79	)	)	PUNCT
ma-203	92	80	is	be	AUX
ma-203	92	81	a	a	DET
ma-203	92	82	levy	levy	NOUN
ma-203	92	83	process	process	NOUN
ma-203	92	84	taking	take	VERB
ma-203	92	85	values	value	NOUN
ma-203	92	86	in	in	ADP
ma-203	92	87	the	the	DET
ma-203	92	88	hilbert	hilbert	NOUN
ma-203	92	89	space	space	NOUN
ma-203	92	90	h	h	NOUN
ma-203	92	91	=	=	PUNCT
ma-203	92	92	l2ρ	l2ρ	PROPN
ma-203	92	93	,	,	PUNCT
ma-203	92	94	with	with	ADP
ma-203	92	95	a	a	DET
ma-203	92	96	properly	properly	ADV
ma-203	92	97	chosen	choose	VERB
ma-203	92	98	weight	weight	NOUN
ma-203	92	99	ρ.consider	ρ.consider	NOUN
ma-203	92	100	the	the	DET
ma-203	92	101	linear	linear	ADJ
ma-203	92	102	spde	spde	NOUN
ma-203	92	103	dxt	dxt	PROPN
ma-203	93	1	=	=	PUNCT
ma-203	93	2	θaxtdt	θaxtdt	NOUN
ma-203	93	3	+	+	CCONJ
ma-203	93	4	dzt	dzt	NOUN
ma-203	93	5	,	,	PUNCT
ma-203	93	6	x	x	PUNCT
ma-203	93	7	∈	∈	PROPN
ma-203	93	8	h	h	NOUN
ma-203	93	9	c.s.p	c.s.p	PROPN
ma-203	93	10	.	.	PUNCT
ma-203	94	1	z(t	z(t	NOUN
ma-203	94	2	)	)	PUNCT
ma-203	94	3	is	be	AUX
ma-203	94	4	a	a	DET
ma-203	94	5	cylindrical	cylindrical	ADJ
ma-203	94	6	α	α	ADJ
ma-203	94	7	-	-	ADJ
ma-203	94	8	stable	stable	ADJ
ma-203	94	9	process	process	NOUN
ma-203	94	10	,	,	PUNCT
ma-203	94	11	α	α	PROPN
ma-203	94	12	∈	∈	PROPN
ma-203	94	13	(	(	PUNCT
ma-203	94	14	0	0	NUM
ma-203	94	15	,	,	PUNCT
ma-203	94	16	2	2	NUM
ma-203	94	17	)	)	PUNCT
ma-203	94	18	which	which	PRON
ma-203	94	19	can	can	AUX
ma-203	94	20	be	be	AUX
ma-203	94	21	expanded	expand	VERB
ma-203	94	22	in	in	ADP
ma-203	94	23	the	the	DET
ma-203	94	24	series	series	NOUN
ma-203	94	25	z(t	z(t	NOUN
ma-203	94	26	)	)	PUNCT
ma-203	94	27	=	=	PUNCT
ma-203	95	1	∞∑	∞∑	NOUN
ma-203	95	2	i=1	i=1	PRON
ma-203	95	3	γizi(t)hi	γizi(t)hi	X
ma-203	95	4	,	,	PUNCT
ma-203	95	5	t	t	PROPN
ma-203	95	6	≥	≥	NOUN
ma-203	95	7	0	0	NUM
ma-203	95	8	where	where	SCONJ
ma-203	95	9	{	{	PUNCT
ma-203	95	10	zi(t)}∞i=1	zi(t)}∞i=1	NOUN
ma-203	95	11	are	be	AUX
ma-203	95	12	independent	independent	ADJ
ma-203	95	13	,	,	PUNCT
ma-203	95	14	real	real	ADV
ma-203	95	15	valued	value	VERB
ma-203	95	16	,	,	PUNCT
ma-203	95	17	one	one	NUM
ma-203	95	18	dimensional	dimensional	ADJ
ma-203	95	19	,	,	PUNCT
ma-203	95	20	normalized	normalize	VERB
ma-203	95	21	,	,	PUNCT
ma-203	95	22	symmetric	symmetric	ADJ
ma-203	95	23	,	,	PUNCT
ma-203	95	24	α	α	NOUN
ma-203	95	25	-	-	PUNCT
ma-203	95	26	stableprocesses	stableprocesse	NOUN
ma-203	95	27	and	and	CCONJ
ma-203	95	28	(	(	PUNCT
ma-203	95	29	γi	γi	INTJ
ma-203	95	30	)	)	PUNCT
ma-203	95	31	∞	∞	PROPN
ma-203	95	32	i=1	i=1	PROPN
ma-203	95	33	is	be	AUX
ma-203	95	34	a	a	DET
ma-203	95	35	given	give	VERB
ma-203	95	36	sequence	sequence	NOUN
ma-203	95	37	of	of	ADP
ma-203	95	38	,	,	PUNCT
ma-203	95	39	possibly	possibly	ADV
ma-203	95	40	unbounded	unbounded	ADJ
ma-203	95	41	,	,	PUNCT
ma-203	95	42	positive	positive	ADJ
ma-203	95	43	numbers	number	NOUN
ma-203	95	44	,	,	PUNCT
ma-203	95	45	and	and	CCONJ
ma-203	95	46	hi	hi	INTJ
ma-203	95	47	is	be	AUX
ma-203	95	48	afixed	afixe	VERB
ma-203	95	49	orthonormal	orthonormal	ADJ
ma-203	95	50	basis	basis	NOUN
ma-203	95	51	in	in	ADP
ma-203	95	52	h.	h.	PROPN
ma-203	95	53	the	the	DET
ma-203	95	54	latter	latter	ADJ
ma-203	95	55	series	series	NOUN
ma-203	95	56	converges	converge	VERB
ma-203	95	57	p	p	NOUN
ma-203	95	58	-a.s	-a.s	PUNCT
ma-203	95	59	.	.	PUNCT
ma-203	96	1	in	in	ADP
ma-203	96	2	h−α	h−α	NOUN
ma-203	96	3	for	for	ADP
ma-203	96	4	α	α	PROPN
ma-203	96	5	>	>	X
ma-203	96	6	d/2	d/2	PROPN
ma-203	96	7	.	.	PUNCT
ma-203	97	1	indeed	indeed	ADV
ma-203	97	2	‖z(t)‖2	‖z(t)‖2	VERB
ma-203	97	3	−α	−α	NOUN
ma-203	97	4	=	=	PUNCT
ma-203	98	1	∞∑	∞∑	NUM
ma-203	98	2	i=1	i=1	NOUN
ma-203	98	3	γ2	γ2	NOUN
ma-203	99	1	i	i	PRON
ma-203	99	2	z	z	PROPN
ma-203	99	3	2	2	NUM
ma-203	99	4	i	i	NOUN
ma-203	99	5	(	(	PUNCT
ma-203	99	6	t)‖hi‖2	t)‖hi‖2	PROPN
ma-203	99	7	−α	−α	NOUN
ma-203	99	8	=	=	PUNCT
ma-203	100	1	∞∑	∞∑	NUM
ma-203	100	2	i=1	i=1	PROPN
ma-203	100	3	z2	z2	NOUN
ma-203	100	4	i	i	PRON
ma-203	100	5	(	(	PUNCT
ma-203	100	6	t)β−2α	t)β−2α	PROPN
ma-203	100	7	i	i	PRON
ma-203	100	8	and	and	CCONJ
ma-203	100	9	the	the	DET
ma-203	100	10	later	later	ADJ
ma-203	100	11	series	series	NOUN
ma-203	100	12	converges	converge	VERB
ma-203	100	13	p	p	PRON
ma-203	100	14	-a.s.for	-a.s.for	ADP
ma-203	100	15	any	any	DET
ma-203	100	16	j	j	PROPN
ma-203	100	17	∈	∈	PROPN
ma-203	100	18	n	n	CCONJ
ma-203	100	19	,	,	PUNCT
ma-203	100	20	t	t	PROPN
ma-203	100	21	≥	≥	NUM
ma-203	100	22	0	0	NUM
ma-203	100	23	,	,	PUNCT
ma-203	100	24	e[e	e[e	ADJ
ma-203	100	25	izj	izj	ADJ
ma-203	100	26	(	(	PUNCT
ma-203	100	27	t)h	t)h	NOUN
ma-203	100	28	]	]	X
ma-203	100	29	=	=	SYM
ma-203	100	30	e−t|h|	e−t|h|	NOUN
ma-203	100	31	α	α	NOUN
ma-203	100	32	.	.	PUNCT
ma-203	101	1	stable	stable	ADJ
ma-203	101	2	one	one	NUM
ma-203	101	3	-	-	PUNCT
ma-203	101	4	dimensional	dimensional	ADJ
ma-203	101	5	density	density	NOUN
ma-203	101	6	:	:	PUNCT
ma-203	101	7	a	a	DET
ma-203	101	8	one	one	NUM
ma-203	101	9	-	-	PUNCT
ma-203	101	10	dimensional	dimensional	ADJ
ma-203	101	11	,	,	PUNCT
ma-203	101	12	normalized	normalize	VERB
ma-203	101	13	,	,	PUNCT
ma-203	101	14	symmetric	symmetric	ADJ
ma-203	101	15	α	α	VERB
ma-203	101	16	-	-	ADJ
ma-203	101	17	stable	stable	ADJ
ma-203	101	18	distribution	distribution	NOUN
ma-203	101	19	µα	µα	ADP
ma-203	101	20	,	,	PUNCT
ma-203	101	21	α	α	PROPN
ma-203	101	22	∈	∈	PROPN
ma-203	101	23	(	(	PUNCT
ma-203	101	24	0	0	NUM
ma-203	101	25	,	,	PUNCT
ma-203	101	26	2	2	NUM
ma-203	101	27	]	]	PUNCT
ma-203	101	28	has	have	VERB
ma-203	101	29	characteristic	characteristic	ADJ
ma-203	101	30	function	function	NOUN
ma-203	101	31	µ̂α(s	µ̂α(s	NUM
ma-203	101	32	)	)	PUNCT
ma-203	102	1	=	=	PUNCT
ma-203	102	2	e−|s|	e−|s|	NUM
ma-203	102	3	α	α	PROPN
ma-203	102	4	,	,	PUNCT
ma-203	102	5	s	s	PROPN
ma-203	102	6	∈	∈	PROPN
ma-203	102	7	r.	r.	NOUN
ma-203	102	8	the	the	DET
ma-203	102	9	density	density	NOUN
ma-203	102	10	of	of	ADP
ma-203	102	11	µα	µα	ADP
ma-203	102	12	with	with	ADP
ma-203	102	13	respect	respect	NOUN
ma-203	102	14	to	to	ADP
ma-203	102	15	lebesgue	lebesgue	NOUN
ma-203	102	16	measure	measure	NOUN
ma-203	102	17	will	will	AUX
ma-203	102	18	be	be	AUX
ma-203	102	19	denoted	denote	VERB
ma-203	102	20	by	by	ADP
ma-203	102	21	pα	pα	PROPN
ma-203	102	22	.	.	PUNCT
ma-203	103	1	this	this	DET
ma-203	103	2	even	even	ADV
ma-203	103	3	functionis	functionis	PROPN
ma-203	103	4	known	know	VERB
ma-203	103	5	in	in	ADP
ma-203	103	6	closed	closed	ADJ
ma-203	103	7	form	form	NOUN
ma-203	103	8	only	only	ADV
ma-203	103	9	if	if	SCONJ
ma-203	103	10	α	α	NOUN
ma-203	103	11	=	=	SYM
ma-203	103	12	1	1	NUM
ma-203	103	13	or	or	CCONJ
ma-203	103	14	2	2	NUM
ma-203	103	15	.	.	PUNCT
ma-203	104	1	the	the	DET
ma-203	104	2	precise	precise	ADJ
ma-203	104	3	asymptotic	asymptotic	ADJ
ma-203	104	4	behavior	behavior	NOUN
ma-203	104	5	of	of	ADP
ma-203	104	6	the	the	DET
ma-203	104	7	density	density	NOUN
ma-203	104	8	pα	pα	PROPN
ma-203	104	9	,	,	PUNCT
ma-203	104	10	α	α	PROPN
ma-203	104	11	∈	∈	PROPN
ma-203	104	12	(	(	PUNCT
ma-203	104	13	0	0	NUM
ma-203	104	14	,	,	PUNCT
ma-203	104	15	2	2	NUM
ma-203	104	16	)	)	PUNCT
ma-203	104	17	is	be	AUX
ma-203	104	18	as	as	SCONJ
ma-203	104	19	follows	follow	VERB
ma-203	104	20	:	:	PUNCT
ma-203	104	21	for	for	ADP
ma-203	104	22	any	any	DET
ma-203	104	23	α	α	NOUN
ma-203	104	24	∈	∈	PROPN
ma-203	104	25	(	(	PUNCT
ma-203	104	26	0	0	NUM
ma-203	104	27	,	,	PUNCT
ma-203	104	28	2	2	NUM
ma-203	104	29	)	)	PUNCT
ma-203	104	30	,	,	PUNCT
ma-203	104	31	there	there	PRON
ma-203	104	32	exists	exist	VERB
ma-203	104	33	cα	cα	ADP
ma-203	104	34	such	such	ADJ
ma-203	104	35	that	that	PRON
ma-203	104	36	pα(x	pα(x	PUNCT
ma-203	104	37	)	)	PUNCT
ma-203	104	38	∼	∼	NOUN
ma-203	104	39	cα	cα	ADP
ma-203	104	40	xα+1	xα+1	PRON
ma-203	104	41	as	as	ADP
ma-203	104	42	x	x	PROPN
ma-203	104	43	→∞.	→∞.	PROPN
ma-203	104	44	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	104	45	eur	eur	PROPN
ma-203	104	46	.	.	PUNCT
ma-203	105	1	j.	j.	PROPN
ma-203	105	2	math	math	PROPN
ma-203	105	3	.	.	PUNCT
ma-203	106	1	anal	anal	PROPN
ma-203	106	2	.	.	PUNCT
ma-203	107	1	10.28924	10.28924	NUM
ma-203	107	2	/	/	SYM
ma-203	107	3	ada	ada	PROPN
ma-203	107	4	/	/	SYM
ma-203	107	5	ma.4.12	ma.4.12	NOUN
ma-203	107	6	5	5	NUM
ma-203	107	7	stable	stable	ADJ
ma-203	107	8	measures	measure	NOUN
ma-203	107	9	on	on	ADP
ma-203	107	10	hilbert	hilbert	NOUN
ma-203	107	11	space	space	NOUN
ma-203	107	12	:	:	PUNCT
ma-203	107	13	a	a	DET
ma-203	107	14	random	random	ADJ
ma-203	107	15	variable	variable	NOUN
ma-203	107	16	ξ	ξ	PROPN
ma-203	107	17	on	on	ADP
ma-203	107	18	h	h	NOUN
ma-203	107	19	is	be	AUX
ma-203	107	20	called	call	VERB
ma-203	107	21	α	α	PRON
ma-203	107	22	-	-	ADJ
ma-203	107	23	stable	stable	ADJ
ma-203	107	24	(	(	PUNCT
ma-203	107	25	α	α	NOUN
ma-203	107	26	∈	∈	PROPN
ma-203	107	27	(	(	PUNCT
ma-203	107	28	0	0	NUM
ma-203	107	29	,	,	PUNCT
ma-203	107	30	2	2	NUM
ma-203	107	31	]	]	PUNCT
ma-203	107	32	)	)	PUNCT
ma-203	107	33	if	if	SCONJ
ma-203	107	34	forany	forany	NOUN
ma-203	107	35	n	n	CCONJ
ma-203	107	36	there	there	ADV
ma-203	107	37	exists	exist	VERB
ma-203	107	38	a	a	DET
ma-203	107	39	vector	vector	NOUN
ma-203	107	40	an	an	DET
ma-203	107	41	∈	∈	ADJ
ma-203	107	42	h	h	NOUN
ma-203	107	43	such	such	ADJ
ma-203	107	44	that	that	PRON
ma-203	107	45	for	for	ADP
ma-203	107	46	any	any	DET
ma-203	107	47	independent	independent	ADJ
ma-203	107	48	copies	copy	NOUN
ma-203	107	49	ξ1	ξ1	NOUN
ma-203	107	50	,	,	PUNCT
ma-203	107	51	ξ2	ξ2	NOUN
ma-203	107	52	,	,	PUNCT
ma-203	107	53	.	.	PUNCT
ma-203	107	54	.	.	PUNCT
ma-203	107	55	.	.	PUNCT
ma-203	108	1	,	,	PUNCT
ma-203	108	2	ξn	ξn	PROPN
ma-203	108	3	of	of	ADP
ma-203	108	4	ξ	ξ	PROPN
ma-203	108	5	,	,	PUNCT
ma-203	108	6	therandom	therandom	X
ma-203	108	7	variable	variable	ADJ
ma-203	108	8	n−1	n−1	PROPN
ma-203	108	9	/	/	SYM
ma-203	108	10	α(ξ1	α(ξ1	NOUN
ma-203	108	11	+	+	X
ma-203	108	12	ξ2	ξ2	ADJ
ma-203	108	13	,	,	PUNCT
ma-203	108	14	.	.	PUNCT
ma-203	108	15	.	.	PUNCT
ma-203	109	1	.+	.+	NOUN
ma-203	109	2	ξn)−	ξn)−	NOUN
ma-203	109	3	an	an	PRON
ma-203	109	4	has	have	VERB
ma-203	109	5	the	the	DET
ma-203	109	6	same	same	ADJ
ma-203	109	7	distribution	distribution	NOUN
ma-203	109	8	as	as	ADP
ma-203	109	9	ξ	ξ	X
ma-203	109	10	.	.	PUNCT
ma-203	110	1	a	a	DET
ma-203	110	2	borel	borel	PROPN
ma-203	110	3	probabilitymeasure	probabilitymeasure	PROPN
ma-203	110	4	µ	µ	PROPN
ma-203	110	5	on	on	ADP
ma-203	110	6	h	h	NOUN
ma-203	110	7	is	be	AUX
ma-203	110	8	said	say	VERB
ma-203	110	9	to	to	PART
ma-203	110	10	be	be	AUX
ma-203	110	11	α	α	NOUN
ma-203	110	12	-	-	ADJ
ma-203	110	13	stable	stable	ADJ
ma-203	110	14	if	if	SCONJ
ma-203	110	15	it	it	PRON
ma-203	110	16	is	be	AUX
ma-203	110	17	the	the	DET
ma-203	110	18	distribution	distribution	NOUN
ma-203	110	19	of	of	ADP
ma-203	110	20	a	a	DET
ma-203	110	21	stable	stable	ADJ
ma-203	110	22	random	random	ADJ
ma-203	110	23	variable	variable	ADJ
ma-203	110	24	withvales	withvale	NOUN
ma-203	110	25	in	in	ADP
ma-203	110	26	h.consider	h.consider	NOUN
ma-203	110	27	the	the	DET
ma-203	110	28	spde	spde	NOUN
ma-203	110	29	with	with	ADP
ma-203	110	30	multiplicative	multiplicative	ADJ
ma-203	110	31	noise	noise	NOUN
ma-203	110	32	:	:	PUNCT
ma-203	110	33	duθ(t	duθ(t	PROPN
ma-203	110	34	,	,	PUNCT
ma-203	110	35	x	x	NOUN
ma-203	110	36	)	)	PUNCT
ma-203	110	37	=	=	SYM
ma-203	110	38	(	(	PUNCT
ma-203	110	39	a0	a0	PROPN
ma-203	110	40	+	+	CCONJ
ma-203	110	41	θa1)uθ(t	θa1)uθ(t	PROPN
ma-203	110	42	,	,	PUNCT
ma-203	110	43	x)dt	x)dt	PROPN
ma-203	110	44	+	+	PROPN
ma-203	110	45	muθ(t	muθ(t	PROPN
ma-203	110	46	,	,	PUNCT
ma-203	110	47	x)dz(t	x)dz(t	PROPN
ma-203	110	48	,	,	PUNCT
ma-203	110	49	x	x	X
ma-203	110	50	)	)	PUNCT
ma-203	110	51	,	,	PUNCT
ma-203	110	52	t	t	PROPN
ma-203	110	53	≥	≥	NUM
ma-203	110	54	0	0	NUM
ma-203	110	55	,	,	PUNCT
ma-203	110	56	x	x	SYM
ma-203	110	57	∈	∈	PROPN
ma-203	111	1	[	[	X
ma-203	111	2	0	0	NUM
ma-203	111	3	,	,	PUNCT
ma-203	111	4	1	1	NUM
ma-203	111	5	]	]	PUNCT
ma-203	111	6	(	(	PUNCT
ma-203	111	7	2.1	2.1	NUM
ma-203	111	8	)	)	PUNCT
ma-203	111	9	where	where	SCONJ
ma-203	111	10	m	m	NOUN
ma-203	111	11	is	be	AUX
ma-203	111	12	a	a	DET
ma-203	111	13	known	know	VERB
ma-203	111	14	nonlinear	nonlinear	ADJ
ma-203	111	15	operator	operator	NOUN
ma-203	111	16	and	and	CCONJ
ma-203	111	17	z(t	z(t	NOUN
ma-203	111	18	,	,	PUNCT
ma-203	111	19	x	x	PRON
ma-203	111	20	)	)	PUNCT
ma-203	111	21	is	be	AUX
ma-203	111	22	a	a	DET
ma-203	111	23	cylindrical	cylindrical	ADJ
ma-203	111	24	subfractional	subfractional	ADJ
ma-203	111	25	levy	levy	NOUN
ma-203	111	26	process.equation	process.equation	NOUN
ma-203	111	27	(	(	PUNCT
ma-203	111	28	2.1	2.1	NUM
ma-203	111	29	)	)	PUNCT
ma-203	111	30	is	be	AUX
ma-203	111	31	called	call	VERB
ma-203	111	32	diagonalizable	diagonalizable	ADJ
ma-203	111	33	if	if	SCONJ
ma-203	111	34	a0	a0	PROPN
ma-203	111	35	,	,	PUNCT
ma-203	111	36	a1	a1	NOUN
ma-203	111	37	and	and	CCONJ
ma-203	111	38	m	m	VERB
ma-203	111	39	have	have	AUX
ma-203	111	40	point	point	NOUN
ma-203	111	41	spectrum	spectrum	NOUN
ma-203	111	42	and	and	CCONJ
ma-203	111	43	a	a	DET
ma-203	111	44	commonsystem	commonsystem	NOUN
ma-203	111	45	of	of	ADP
ma-203	111	46	eigenfunction	eigenfunction	NOUN
ma-203	111	47	{	{	PUNCT
ma-203	111	48	hj	hj	PROPN
ma-203	111	49	,	,	PUNCT
ma-203	111	50	j	j	PROPN
ma-203	111	51	≥	≥	PROPN
ma-203	111	52	1	1	NUM
ma-203	111	53	}	}	PUNCT
ma-203	111	54	.	.	PUNCT
ma-203	112	1	denote	denote	VERB
ma-203	112	2	by	by	ADP
ma-203	112	3	ρk	ρk	PRON
ma-203	112	4	,	,	PUNCT
ma-203	112	5	νk	νk	NOUN
ma-203	112	6	and	and	CCONJ
ma-203	112	7	µk	µk	INTJ
ma-203	112	8	,	,	PUNCT
ma-203	112	9	the	the	DET
ma-203	112	10	eigenvalues	eigenvalue	NOUN
ma-203	112	11	of	of	ADP
ma-203	112	12	the	the	DET
ma-203	112	13	operators	operator	NOUN
ma-203	112	14	a0	a0	PROPN
ma-203	112	15	,	,	PUNCT
ma-203	112	16	a1	a1	NOUN
ma-203	112	17	and	and	CCONJ
ma-203	112	18	m	m	NOUN
ma-203	112	19	respectively	respectively	ADV
ma-203	112	20	.	.	PUNCT
ma-203	113	1	then	then	ADV
ma-203	113	2	uθ(t	uθ(t	VERB
ma-203	113	3	,	,	PUNCT
ma-203	113	4	x	x	NOUN
ma-203	113	5	)	)	PUNCT
ma-203	113	6	=	=	NOUN
ma-203	114	1	∑∞	∑∞	NOUN
ma-203	114	2	j=1	j=1	PROPN
ma-203	114	3	uj	uj	PROPN
ma-203	114	4	,	,	PUNCT
ma-203	114	5	thj	thj	PROPN
ma-203	114	6	.consider	.consider	X
ma-203	114	7	spde	spde	ADJ
ma-203	114	8	model	model	NOUN
ma-203	114	9	with	with	ADP
ma-203	114	10	multiplicative	multiplicative	ADJ
ma-203	114	11	noise	noise	NOUN
ma-203	114	12	and	and	CCONJ
ma-203	114	13	mean	mean	ADJ
ma-203	114	14	reversion	reversion	NOUN
ma-203	114	15	,	,	PUNCT
ma-203	114	16	where	where	SCONJ
ma-203	114	17	the	the	DET
ma-203	114	18	j	j	PROPN
ma-203	114	19	-	-	PUNCT
ma-203	114	20	th	th	PROPN
ma-203	114	21	fouriercoefficient	fouriercoefficient	NOUN
ma-203	114	22	is	be	AUX
ma-203	114	23	the	the	DET
ma-203	114	24	stable	stable	ADJ
ma-203	114	25	cox	cox	PROPN
ma-203	114	26	-	-	PUNCT
ma-203	114	27	ingersoll	ingersoll	PROPN
ma-203	114	28	-	-	PUNCT
ma-203	114	29	ross	ross	PROPN
ma-203	114	30	(	(	PUNCT
ma-203	114	31	scir	scir	PROPN
ma-203	114	32	)	)	PUNCT
ma-203	114	33	model	model	NOUN
ma-203	114	34	:	:	PUNCT
ma-203	114	35	duj	duj	PROPN
ma-203	114	36	,	,	PUNCT
ma-203	114	37	t	t	NOUN
ma-203	114	38	=	=	SYM
ma-203	114	39	(	(	PUNCT
ma-203	114	40	a	a	DET
ma-203	114	41	−	−	NOUN
ma-203	114	42	θuj	θuj	NOUN
ma-203	114	43	,	,	PUNCT
ma-203	115	1	t)dt	t)dt	PROPN
ma-203	115	2	+	+	PROPN
ma-203	115	3	σu	σu	PROPN
ma-203	115	4	1	1	NUM
ma-203	115	5	/	/	SYM
ma-203	115	6	α	α	PRON
ma-203	115	7	j	j	PROPN
ma-203	115	8	,	,	PUNCT
ma-203	115	9	t−dzj	t−dzj	ADJ
ma-203	115	10	,	,	PUNCT
ma-203	115	11	t	t	PROPN
ma-203	115	12	,	,	PUNCT
ma-203	115	13	j	j	PROPN
ma-203	115	14	≥	≥	NUM
ma-203	115	15	1	1	NUM
ma-203	115	16	(	(	PUNCT
ma-203	115	17	2.2	2.2	NUM
ma-203	115	18	)	)	PUNCT
ma-203	115	19	where	where	SCONJ
ma-203	115	20	a	a	PRON
ma-203	115	21	is	be	AUX
ma-203	115	22	the	the	DET
ma-203	115	23	mean	mean	ADJ
ma-203	115	24	reverting	revert	VERB
ma-203	115	25	level	level	NOUN
ma-203	115	26	and	and	CCONJ
ma-203	115	27	θ	θ	NOUN
ma-203	115	28	is	be	AUX
ma-203	115	29	mean	mean	VERB
ma-203	115	30	reverting	revert	VERB
ma-203	115	31	speed	speed	NOUN
ma-203	115	32	.	.	PUNCT
ma-203	116	1	recall	recall	VERB
ma-203	116	2	that	that	PRON
ma-203	116	3	for	for	ADP
ma-203	116	4	α	α	NOUN
ma-203	116	5	=	=	SYM
ma-203	116	6	2	2	NUM
ma-203	116	7	,	,	PUNCT
ma-203	116	8	for	for	ADP
ma-203	116	9	every	every	DET
ma-203	116	10	j	j	PROPN
ma-203	116	11	≥	≥	NUM
ma-203	116	12	1	1	NUM
ma-203	116	13	,	,	PUNCT
ma-203	116	14	the	the	DET
ma-203	116	15	process	process	NOUN
ma-203	116	16	zj	zj	PROPN
ma-203	116	17	,	,	PUNCT
ma-203	116	18	t	t	PROPN
ma-203	116	19	is	be	AUX
ma-203	116	20	a	a	DET
ma-203	116	21	standard	standard	ADJ
ma-203	116	22	brownian	brownian	ADJ
ma-203	116	23	motion	motion	NOUN
ma-203	116	24	,	,	PUNCT
ma-203	116	25	this	this	PRON
ma-203	116	26	is	be	AUX
ma-203	116	27	the	the	DET
ma-203	116	28	famous	famous	ADJ
ma-203	116	29	cox	cox	PROPN
ma-203	116	30	-	-	PUNCT
ma-203	116	31	ingersoll	ingersoll	PROPN
ma-203	116	32	-	-	PUNCT
ma-203	116	33	ross	ross	PROPN
ma-203	116	34	(	(	PUNCT
ma-203	116	35	cir)model	cir)model	PROPN
ma-203	116	36	used	use	VERB
ma-203	116	37	for	for	ADP
ma-203	116	38	modeling	model	VERB
ma-203	116	39	interest	interest	NOUN
ma-203	116	40	rate	rate	NOUN
ma-203	116	41	,	,	PUNCT
ma-203	116	42	which	which	PRON
ma-203	116	43	is	be	AUX
ma-203	116	44	also	also	ADV
ma-203	116	45	used	use	VERB
ma-203	116	46	a	a	DET
ma-203	116	47	stochastic	stochastic	ADJ
ma-203	116	48	volatility	volatility	NOUN
ma-203	116	49	process	process	NOUN
ma-203	116	50	in	in	ADP
ma-203	116	51	hestonmodel	hestonmodel	PROPN
ma-203	116	52	.	.	PUNCT
ma-203	117	1	note	note	VERB
ma-203	117	2	that	that	SCONJ
ma-203	117	3	there	there	PRON
ma-203	117	4	are	be	VERB
ma-203	117	5	brownian	brownian	ADJ
ma-203	117	6	cir	cir	NOUN
ma-203	117	7	models	model	NOUN
ma-203	117	8	with	with	ADP
ma-203	117	9	additive	additive	ADJ
ma-203	117	10	compound	compound	NOUN
ma-203	117	11	poisson	poisson	NOUN
ma-203	117	12	type	type	NOUN
ma-203	117	13	jumps.when	jumps.when	ADV
ma-203	117	14	1	1	NUM
ma-203	117	15	<	<	X
ma-203	117	16	α	α	X
ma-203	117	17	<	<	X
ma-203	117	18	2	2	NUM
ma-203	117	19	,	,	PUNCT
ma-203	117	20	zj	zj	PROPN
ma-203	117	21	,	,	PUNCT
ma-203	117	22	t	t	PROPN
ma-203	117	23	is	be	AUX
ma-203	117	24	stable	stable	ADJ
ma-203	117	25	process	process	NOUN
ma-203	117	26	with	with	ADP
ma-203	117	27	levy	levy	NOUN
ma-203	117	28	measure	measure	NOUN
ma-203	117	29	να(dz	να(dz	NOUN
ma-203	117	30	)	)	PUNCT
ma-203	117	31	=	=	SYM
ma-203	117	32	1{z>0}dz	1{z>0}dz	NUM
ma-203	117	33	αγ(−α)zα+1	αγ(−α)zα+1	NOUN
ma-203	117	34	.	.	PUNCT
ma-203	118	1	(	(	PUNCT
ma-203	118	2	2.3	2.3	NUM
ma-203	118	3	)	)	PUNCT
ma-203	118	4	the	the	DET
ma-203	118	5	discontinuous	discontinuous	ADJ
ma-203	118	6	scir	scir	PROPN
ma-203	118	7	model	model	PROPN
ma-203	118	8	captures	capture	VERB
ma-203	118	9	the	the	DET
ma-203	118	10	heavy	heavy	ADJ
ma-203	118	11	tailed	tail	VERB
ma-203	118	12	property	property	NOUN
ma-203	118	13	in	in	ADP
ma-203	118	14	the	the	DET
ma-203	118	15	sense	sense	NOUN
ma-203	118	16	of	of	ADP
ma-203	118	17	infinite	infinite	NOUN
ma-203	118	18	variance.there	variance.there	ADV
ma-203	118	19	is	be	VERB
ma-203	118	20	empirical	empirical	ADJ
ma-203	118	21	evidence	evidence	NOUN
ma-203	118	22	from	from	ADP
ma-203	118	23	high	high	ADJ
ma-203	118	24	frequency	frequency	NOUN
ma-203	118	25	data	datum	NOUN
ma-203	118	26	available	available	ADJ
ma-203	118	27	in	in	ADP
ma-203	118	28	support	support	NOUN
ma-203	118	29	of	of	ADP
ma-203	118	30	application	application	NOUN
ma-203	118	31	of	of	ADP
ma-203	118	32	purejump	purejump	NOUN
ma-203	118	33	models	model	NOUN
ma-203	118	34	in	in	ADP
ma-203	118	35	financial	financial	ADJ
ma-203	118	36	modeling.the	modeling.the	DET
ma-203	118	37	scir	scir	PROPN
ma-203	118	38	model	model	NOUN
ma-203	118	39	has	have	VERB
ma-203	118	40	the	the	DET
ma-203	118	41	unique	unique	ADJ
ma-203	118	42	stationary	stationary	ADJ
ma-203	118	43	distribution	distribution	NOUN
ma-203	118	44	µ	µ	NOUN
ma-203	118	45	with	with	ADP
ma-203	118	46	laplace	laplace	NOUN
ma-203	118	47	transform	transform	NOUN
ma-203	118	48	given	give	VERB
ma-203	118	49	by	by	ADP
ma-203	118	50	lµ(λ	lµ(λ	NOUN
ma-203	118	51	)	)	PUNCT
ma-203	118	52	=	=	SYM
ma-203	119	1	∫	∫	PROPN
ma-203	119	2	∞	∞	NOUN
ma-203	119	3	0	0	NUM
ma-203	120	1	e−λxµ(dx	e−λxµ(dx	ADJ
ma-203	120	2	)	)	PUNCT
ma-203	120	3	=	=	SYM
ma-203	120	4	exp	exp	NOUN
ma-203	120	5	{	{	PUNCT
ma-203	120	6	−	−	PROPN
ma-203	120	7	∫	∫	PROPN
ma-203	120	8	λ	λ	X
ma-203	120	9	0	0	PROPN
ma-203	120	10	αa	αa	PROPN
ma-203	120	11	αθ	αθ	NUM
ma-203	120	12	+	+	CCONJ
ma-203	120	13	σαzα−1	σαzα−1	NOUN
ma-203	120	14	dz	dz	X
ma-203	120	15	}	}	PUNCT
ma-203	120	16	,	,	PUNCT
ma-203	120	17	λ	λ	X
ma-203	120	18	≥	≥	NOUN
ma-203	120	19	0	0	NUM
ma-203	120	20	.	.	PUNCT
ma-203	121	1	(	(	PUNCT
ma-203	121	2	2.4	2.4	NUM
ma-203	121	3	)	)	PUNCT
ma-203	121	4	now	now	ADV
ma-203	121	5	we	we	PRON
ma-203	121	6	focus	focus	VERB
ma-203	121	7	on	on	ADP
ma-203	121	8	the	the	DET
ma-203	121	9	fundamental	fundamental	ADJ
ma-203	121	10	semimartingale	semimartingale	NOUN
ma-203	121	11	behind	behind	ADP
ma-203	121	12	the	the	DET
ma-203	121	13	cir	cir	PROPN
ma-203	121	14	model	model	NOUN
ma-203	121	15	.	.	PUNCT
ma-203	122	1	define	define	VERB
ma-203	122	2	κh	κh	INTJ
ma-203	122	3	:	:	PUNCT
ma-203	122	4	=	=	SYM
ma-203	122	5	2hγ(3/2−h)γ(h	2hγ(3/2−h)γ(h	NUM
ma-203	122	6	+	+	NUM
ma-203	122	7	1/2	1/2	NUM
ma-203	122	8	)	)	PUNCT
ma-203	122	9	,	,	PUNCT
ma-203	122	10	kh(t	kh(t	X
ma-203	122	11	,	,	PUNCT
ma-203	122	12	s	s	X
ma-203	122	13	)	)	PUNCT
ma-203	122	14	:	:	PUNCT
ma-203	122	15	=	=	PUNCT
ma-203	122	16	κ−1	κ−1	PROPN
ma-203	122	17	h	h	NOUN
ma-203	122	18	(	(	PUNCT
ma-203	122	19	s(t	s(t	PROPN
ma-203	122	20	−	−	PROPN
ma-203	122	21	s	s	PART
ma-203	122	22	)	)	PUNCT
ma-203	122	23	)	)	PUNCT
ma-203	122	24	1	1	NUM
ma-203	122	25	2	2	NUM
ma-203	122	26	−h	−h	VERB
ma-203	122	27	,	,	PUNCT
ma-203	122	28	ηh	ηh	ADP
ma-203	122	29	:	:	PUNCT
ma-203	122	30	=	=	SYM
ma-203	122	31	2hγ(3−	2hγ(3−	NUM
ma-203	122	32	2h)γ(h	2h)γ(h	NUM
ma-203	122	33	+	+	CCONJ
ma-203	122	34	1	1	NUM
ma-203	122	35	2	2	NUM
ma-203	122	36	)	)	PUNCT
ma-203	122	37	γ(3/2−h	γ(3/2−h	NOUN
ma-203	122	38	)	)	PUNCT
ma-203	122	39	,	,	PUNCT
ma-203	122	40	vt	vt	PROPN
ma-203	122	41	≡	≡	PROPN
ma-203	122	42	vht	vht	NOUN
ma-203	122	43	:	:	PUNCT
ma-203	122	44	=	=	SYM
ma-203	122	45	η−1	η−1	PROPN
ma-203	122	46	h	h	NOUN
ma-203	122	47	t2−2h	t2−2h	PROPN
ma-203	122	48	,	,	PUNCT
ma-203	122	49	mh	mh	PROPN
ma-203	122	50	t	t	PROPN
ma-203	122	51	:	:	PUNCT
ma-203	123	1	=	=	SYM
ma-203	123	2	∫	∫	PROPN
ma-203	123	3	t	t	PROPN
ma-203	123	4	0	0	NUM
ma-203	123	5	kh(t	kh(t	NUM
ma-203	123	6	,	,	PUNCT
ma-203	123	7	s)dmh	s)dmh	PROPN
ma-203	123	8	s	s	PART
ma-203	123	9	.for	.for	PUNCT
ma-203	123	10	using	use	VERB
ma-203	123	11	girsanov	girsanov	PROPN
ma-203	123	12	theorem	theorem	NOUN
ma-203	123	13	for	for	ADP
ma-203	123	14	brownian	brownian	ADJ
ma-203	123	15	motion	motion	NOUN
ma-203	123	16	,	,	PUNCT
ma-203	123	17	since	since	SCONJ
ma-203	123	18	a	a	DET
ma-203	123	19	radon	radon	PROPN
ma-203	123	20	-	-	PUNCT
ma-203	123	21	nikodym	nikodym	ADJ
ma-203	123	22	derivative	derivative	ADJ
ma-203	123	23	process	process	NOUN
ma-203	123	24	is	be	AUX
ma-203	123	25	al	al	PROPN
ma-203	123	26	-	-	PUNCT
ma-203	123	27	ways	way	NOUN
ma-203	123	28	a	a	DET
ma-203	123	29	martingale	martingale	NOUN
ma-203	123	30	,	,	PUNCT
ma-203	123	31	a	a	DET
ma-203	123	32	central	central	ADJ
ma-203	123	33	problem	problem	NOUN
ma-203	123	34	is	be	AUX
ma-203	123	35	how	how	SCONJ
ma-203	123	36	to	to	PART
ma-203	123	37	construct	construct	VERB
ma-203	123	38	an	an	DET
ma-203	123	39	appropriate	appropriate	ADJ
ma-203	123	40	martingale	martingale	NOUN
ma-203	123	41	which	which	DET
ma-203	123	42	generatesthe	generatesthe	PRON
ma-203	123	43	same	same	ADJ
ma-203	123	44	filtration	filtration	NOUN
ma-203	123	45	,	,	PUNCT
ma-203	123	46	up	up	ADP
ma-203	123	47	to	to	ADP
ma-203	123	48	sets	set	NOUN
ma-203	123	49	of	of	ADP
ma-203	123	50	measure	measure	NOUN
ma-203	123	51	zero	zero	NUM
ma-203	123	52	,	,	PUNCT
ma-203	123	53	as	as	SCONJ
ma-203	123	54	the	the	DET
ma-203	123	55	non	non	ADJ
ma-203	123	56	-	-	NOUN
ma-203	123	57	semimartingale	semimartingale	NOUN
ma-203	123	58	called	call	VERB
ma-203	123	59	the	the	DET
ma-203	123	60	fundamental	fundamental	ADJ
ma-203	123	61	martingale.extending	martingale.extende	VERB
ma-203	123	62	norros	norro	NOUN
ma-203	123	63	et	et	PROPN
ma-203	123	64	al	al	PROPN
ma-203	123	65	.	.	PUNCT
ma-203	124	1	(	(	PUNCT
ma-203	124	2	1999	1999	NUM
ma-203	124	3	)	)	PUNCT
ma-203	124	4	it	it	PRON
ma-203	124	5	can	can	AUX
ma-203	124	6	be	be	AUX
ma-203	124	7	shown	show	VERB
ma-203	124	8	that	that	SCONJ
ma-203	124	9	mh	mh	PROPN
ma-203	124	10	t	t	PROPN
ma-203	124	11	is	be	AUX
ma-203	124	12	a	a	DET
ma-203	124	13	martingale	martingale	NOUN
ma-203	124	14	,	,	PUNCT
ma-203	124	15	called	call	VERB
ma-203	124	16	the	the	DET
ma-203	124	17	funda	funda	PROPN
ma-203	124	18	-	-	PUNCT
ma-203	124	19	mental	mental	ADJ
ma-203	124	20	martingale	martingale	NOUN
ma-203	124	21	whose	whose	DET
ma-203	124	22	quadratic	quadratic	ADJ
ma-203	124	23	variation	variation	NOUN
ma-203	124	24	〈	〈	PROPN
ma-203	124	25	mh〉t	mh〉t	PROPN
ma-203	124	26	is	be	AUX
ma-203	124	27	vht	vht	ADJ
ma-203	124	28	.	.	PUNCT
ma-203	125	1	moreover	moreover	ADV
ma-203	125	2	,	,	PUNCT
ma-203	125	3	the	the	DET
ma-203	125	4	natural	natural	ADJ
ma-203	125	5	filtration	filtration	NOUN
ma-203	125	6	of	of	ADP
ma-203	125	7	the	the	DET
ma-203	125	8	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	NOUN
ma-203	125	9	eur	eur	PROPN
ma-203	125	10	.	.	PUNCT
ma-203	126	1	j.	j.	PROPN
ma-203	126	2	math	math	PROPN
ma-203	126	3	.	.	PUNCT
ma-203	127	1	anal	anal	PROPN
ma-203	127	2	.	.	PUNCT
ma-203	128	1	10.28924	10.28924	NUM
ma-203	128	2	/	/	SYM
ma-203	128	3	ada	ada	PROPN
ma-203	128	4	/	/	SYM
ma-203	128	5	ma.4.12	ma.4.12	NOUN
ma-203	128	6	6	6	NUM
ma-203	128	7	martingale	martingale	NOUN
ma-203	128	8	mh	mh	PROPN
ma-203	128	9	coincides	coincide	VERB
ma-203	128	10	with	with	ADP
ma-203	128	11	the	the	DET
ma-203	128	12	natural	natural	ADJ
ma-203	128	13	filtration	filtration	NOUN
ma-203	128	14	of	of	ADP
ma-203	128	15	the	the	DET
ma-203	128	16	flp	flp	PROPN
ma-203	128	17	mh	mh	PROPN
ma-203	128	18	since	since	SCONJ
ma-203	128	19	mh	mh	PROPN
ma-203	128	20	t	t	PROPN
ma-203	128	21	:	:	PUNCT
ma-203	129	1	=	=	SYM
ma-203	129	2	∫	∫	PROPN
ma-203	129	3	t	t	PROPN
ma-203	129	4	0	0	NUM
ma-203	129	5	k(t	k(t	NOUN
ma-203	129	6	,	,	PUNCT
ma-203	129	7	s)dmh	s)dmh	VERB
ma-203	129	8	sholds	shold	NOUN
ma-203	129	9	for	for	ADP
ma-203	129	10	h	h	NOUN
ma-203	129	11	∈	∈	PROPN
ma-203	129	12	(	(	PUNCT
ma-203	129	13	1/2	1/2	NUM
ma-203	129	14	,	,	PUNCT
ma-203	129	15	1	1	NUM
ma-203	129	16	)	)	PUNCT
ma-203	129	17	where	where	SCONJ
ma-203	129	18	kh(t	kh(t	X
ma-203	129	19	,	,	PUNCT
ma-203	129	20	s	s	NOUN
ma-203	129	21	)	)	PUNCT
ma-203	129	22	:	:	PUNCT
ma-203	129	23	=	=	SYM
ma-203	129	24	h(2h	h(2h	PUNCT
ma-203	129	25	−	−	NOUN
ma-203	129	26	1	1	NUM
ma-203	129	27	)	)	PUNCT
ma-203	129	28	∫	∫	PROPN
ma-203	130	1	t	t	PROPN
ma-203	130	2	s	s	PART
ma-203	130	3	r	r	NOUN
ma-203	130	4	h−	h−	PROPN
ma-203	130	5	1	1	NUM
ma-203	130	6	2	2	NUM
ma-203	130	7	(	(	PUNCT
ma-203	130	8	r	r	NOUN
ma-203	130	9	−	−	PROPN
ma-203	130	10	s)h−	s)h−	NOUN
ma-203	130	11	3	3	NUM
ma-203	130	12	2	2	NUM
ma-203	130	13	dr	dr	PROPN
ma-203	130	14	,	,	PUNCT
ma-203	130	15	0	0	NUM
ma-203	130	16	≤	≤	NUM
ma-203	130	17	s	s	PART
ma-203	130	18	≤	≤	NOUN
ma-203	130	19	t	t	NOUN
ma-203	130	20	and	and	CCONJ
ma-203	130	21	for	for	ADP
ma-203	130	22	h	h	NOUN
ma-203	130	23	=	=	SYM
ma-203	130	24	1/2	1/2	NUM
ma-203	130	25	,	,	PUNCT
ma-203	130	26	the	the	DET
ma-203	130	27	convention	convention	NOUN
ma-203	130	28	k1/2	k1/2	NOUN
ma-203	130	29	≡	≡	PROPN
ma-203	130	30	1	1	NUM
ma-203	130	31	is	be	AUX
ma-203	130	32	used.define	used.define	NUM
ma-203	130	33	qi(t	qi(t	NOUN
ma-203	130	34	)	)	PUNCT
ma-203	130	35	:	:	PUNCT
ma-203	131	1	=	=	SYM
ma-203	131	2	d	d	X
ma-203	131	3	dvt	dvt	PROPN
ma-203	131	4	∫	∫	PROPN
ma-203	131	5	t	t	PROPN
ma-203	131	6	0	0	NUM
ma-203	131	7	kh(t	kh(t	NUM
ma-203	131	8	,	,	PUNCT
ma-203	131	9	s)ui(s)ds	s)ui(s)ds	PROPN
ma-203	131	10	.	.	PUNCT
ma-203	132	1	it	it	PRON
ma-203	132	2	is	be	AUX
ma-203	132	3	easy	easy	ADJ
ma-203	132	4	to	to	PART
ma-203	132	5	see	see	VERB
ma-203	132	6	that	that	DET
ma-203	132	7	qi(t	qi(t	NOUN
ma-203	132	8	)	)	PUNCT
ma-203	133	1	=	=	PUNCT
ma-203	133	2	ηh	ηh	VERB
ma-203	133	3	2(2−2h	2(2−2h	NUM
ma-203	133	4	)	)	PUNCT
ma-203	133	5	{	{	PUNCT
ma-203	133	6	t2h−1zi(t	t2h−1zi(t	NOUN
ma-203	133	7	)	)	PUNCT
ma-203	133	8	+	+	CCONJ
ma-203	133	9	∫	∫	PROPN
ma-203	133	10	t	t	NOUN
ma-203	133	11	0	0	NUM
ma-203	133	12	r	r	NOUN
ma-203	133	13	2h−1dzi(s	2h−1dzi(s	NOUN
ma-203	133	14	)	)	PUNCT
ma-203	133	15	}	}	PUNCT
ma-203	133	16	.	.	PUNCT
ma-203	134	1	define	define	VERB
ma-203	134	2	the	the	DET
ma-203	134	3	process	process	NOUN
ma-203	134	4	zi	zi	NOUN
ma-203	134	5	=	=	PUNCT
ma-203	134	6	(	(	PUNCT
ma-203	134	7	zi(t	zi(t	NOUN
ma-203	134	8	)	)	PUNCT
ma-203	134	9	,	,	PUNCT
ma-203	134	10	t	t	PROPN
ma-203	134	11	∈	∈	PROPN
ma-203	135	1	[	[	X
ma-203	135	2	0	0	NUM
ma-203	135	3	,	,	PUNCT
ma-203	135	4	t	t	X
ma-203	135	5	]	]	PUNCT
ma-203	135	6	)	)	PUNCT
ma-203	135	7	by	by	ADP
ma-203	135	8	zi(t	zi(t	NOUN
ma-203	135	9	)	)	PUNCT
ma-203	135	10	:	:	PUNCT
ma-203	136	1	=	=	SYM
ma-203	136	2	∫	∫	PROPN
ma-203	136	3	t	t	PROPN
ma-203	136	4	0	0	NUM
ma-203	136	5	kh(t	kh(t	PROPN
ma-203	136	6	,	,	PUNCT
ma-203	136	7	s)dui(s).extending	s)dui(s).extende	VERB
ma-203	136	8	kleptsyna	kleptsyna	NOUN
ma-203	136	9	and	and	CCONJ
ma-203	136	10	le	le	X
ma-203	136	11	breton	breton	PROPN
ma-203	136	12	(	(	PUNCT
ma-203	136	13	2002	2002	NUM
ma-203	136	14	)	)	PUNCT
ma-203	136	15	,	,	PUNCT
ma-203	136	16	we	we	PRON
ma-203	136	17	have:(i	have:(i	NOUN
ma-203	136	18	)	)	PUNCT
ma-203	136	19	zi	zi	PROPN
ma-203	136	20	is	be	AUX
ma-203	136	21	the	the	DET
ma-203	136	22	fundamental	fundamental	ADJ
ma-203	136	23	semimartingale	semimartingale	NOUN
ma-203	136	24	associated	associate	VERB
ma-203	136	25	with	with	ADP
ma-203	136	26	the	the	DET
ma-203	136	27	process	process	NOUN
ma-203	136	28	ui	ui	PROPN
ma-203	136	29	.(ii	.(ii	PROPN
ma-203	136	30	)	)	PUNCT
ma-203	136	31	zi	zi	PROPN
ma-203	136	32	is	be	AUX
ma-203	136	33	a	a	DET
ma-203	136	34	(	(	PUNCT
ma-203	136	35	ft	ft	NOUN
ma-203	136	36	)	)	PUNCT
ma-203	136	37	-semimartingale	-semimartingale	NOUN
ma-203	136	38	with	with	ADP
ma-203	136	39	the	the	DET
ma-203	136	40	decomposition	decomposition	NOUN
ma-203	136	41	zi(t	zi(t	NOUN
ma-203	136	42	)	)	PUNCT
ma-203	136	43	=	=	SYM
ma-203	136	44	µi(θ	µi(θ	NOUN
ma-203	136	45	)	)	PUNCT
ma-203	136	46	∫	∫	PROPN
ma-203	136	47	t	t	PROPN
ma-203	136	48	0	0	NUM
ma-203	136	49	qi(s)dvs	qi(s)dvs	PROPN
ma-203	136	50	+	+	CCONJ
ma-203	136	51	β−νi	β−νi	NOUN
ma-203	137	1	m	m	PROPN
ma-203	137	2	h	h	PROPN
ma-203	137	3	t	t	PROPN
ma-203	137	4	.(iii	.(iii	PROPN
ma-203	137	5	)	)	PUNCT
ma-203	137	6	ui	ui	PROPN
ma-203	137	7	admits	admit	VERB
ma-203	137	8	the	the	DET
ma-203	137	9	representation	representation	NOUN
ma-203	137	10	ui(t	ui(t	NOUN
ma-203	137	11	)	)	PUNCT
ma-203	138	1	=	=	SYM
ma-203	138	2	∫	∫	PROPN
ma-203	138	3	t	t	PROPN
ma-203	138	4	0	0	NUM
ma-203	138	5	kh(t	kh(t	PROPN
ma-203	138	6	,	,	PUNCT
ma-203	138	7	s)dzi(s	s)dzi(s	NOUN
ma-203	138	8	)	)	PUNCT
ma-203	138	9	.	.	PUNCT
ma-203	139	1	(	(	PUNCT
ma-203	139	2	iv	iv	X
ma-203	139	3	)	)	PUNCT
ma-203	139	4	the	the	DET
ma-203	139	5	natural	natural	ADJ
ma-203	139	6	filtration	filtration	NOUN
ma-203	139	7	(	(	PUNCT
ma-203	139	8	zi(t	zi(t	NOUN
ma-203	139	9	)	)	PUNCT
ma-203	139	10	)	)	PUNCT
ma-203	139	11	of	of	ADP
ma-203	139	12	zi	zi	PROPN
ma-203	139	13	and	and	CCONJ
ma-203	139	14	(	(	PUNCT
ma-203	139	15	ui(t	ui(t	NOUN
ma-203	139	16	)	)	PUNCT
ma-203	139	17	)	)	PUNCT
ma-203	139	18	of	of	ADP
ma-203	139	19	ui	ui	NOUN
ma-203	139	20	coincide.we	coincide.we	NOUN
ma-203	139	21	describe	describe	VERB
ma-203	139	22	our	our	PRON
ma-203	139	23	observations	observation	NOUN
ma-203	139	24	now	now	ADV
ma-203	139	25	.	.	PUNCT
ma-203	140	1	note	note	VERB
ma-203	140	2	that	that	SCONJ
ma-203	140	3	for	for	ADP
ma-203	140	4	equally	equally	ADV
ma-203	140	5	spaced	space	VERB
ma-203	140	6	data	datum	NOUN
ma-203	140	7	(	(	PUNCT
ma-203	140	8	homoscedastic	homoscedastic	ADJ
ma-203	140	9	case	case	NOUN
ma-203	140	10	)	)	PUNCT
ma-203	140	11	vtk	vtk	NOUN
ma-203	140	12	−	−	PROPN
ma-203	140	13	vtk−1	vtk−1	PROPN
ma-203	140	14	=	=	SYM
ma-203	140	15	η−1	η−1	PROPN
ma-203	140	16	h	h	NOUN
ma-203	140	17	(	(	PUNCT
ma-203	140	18	t	t	PROPN
ma-203	140	19	n	n	CCONJ
ma-203	140	20	)	)	PUNCT
ma-203	140	21	2−2h	2−2h	NUM
ma-203	141	1	[	[	X
ma-203	141	2	k2−2h	k2−2h	INTJ
ma-203	141	3	−	−	PROPN
ma-203	141	4	(	(	PUNCT
ma-203	141	5	k	k	PROPN
ma-203	141	6	−	−	PROPN
ma-203	141	7	1)2−2h	1)2−2h	NUM
ma-203	141	8	]	]	PUNCT
ma-203	141	9	,	,	PUNCT
ma-203	141	10	k	k	X
ma-203	141	11	=	=	SYM
ma-203	141	12	1	1	NUM
ma-203	141	13	,	,	PUNCT
ma-203	141	14	2	2	NUM
ma-203	141	15	,	,	PUNCT
ma-203	141	16	·	·	PUNCT
ma-203	141	17	·	·	PUNCT
ma-203	141	18	·	·	PUNCT
ma-203	141	19	,	,	PUNCT
ma-203	141	20	n.for	n.for	NUM
ma-203	141	21	h	h	NOUN
ma-203	141	22	=	=	SYM
ma-203	141	23	0.5	0.5	NUM
ma-203	141	24	,	,	PUNCT
ma-203	141	25	vtk	vtk	NOUN
ma-203	141	26	−	−	PROPN
ma-203	141	27	vtk−1	vtk−1	PROPN
ma-203	141	28	=	=	SYM
ma-203	141	29	η−1	η−1	PROPN
ma-203	141	30	h	h	NOUN
ma-203	141	31	(	(	PUNCT
ma-203	141	32	t	t	PROPN
ma-203	141	33	n	n	CCONJ
ma-203	141	34	)	)	PUNCT
ma-203	141	35	2−2h	2−2h	NUM
ma-203	142	1	[	[	X
ma-203	142	2	k2−2h	k2−2h	INTJ
ma-203	142	3	−	−	PROPN
ma-203	142	4	(	(	PUNCT
ma-203	142	5	k	k	PROPN
ma-203	142	6	−	−	PROPN
ma-203	142	7	1)2−2h	1)2−2h	NUM
ma-203	142	8	]	]	X
ma-203	142	9	=	=	SYM
ma-203	143	1	t	t	PROPN
ma-203	143	2	n	n	NOUN
ma-203	143	3	,	,	PUNCT
ma-203	143	4	k	k	PROPN
ma-203	143	5	=	=	SYM
ma-203	143	6	1	1	NUM
ma-203	143	7	,	,	PUNCT
ma-203	143	8	2	2	NUM
ma-203	143	9	,	,	PUNCT
ma-203	143	10	.	.	PUNCT
ma-203	143	11	.	.	PUNCT
ma-203	143	12	.	.	PUNCT
ma-203	144	1	,	,	PUNCT
ma-203	144	2	n.	n.	NOUN
ma-203	144	3	we	we	PRON
ma-203	144	4	have	have	VERB
ma-203	144	5	qi(t	qi(t	NOUN
ma-203	144	6	)	)	PUNCT
ma-203	145	1	=	=	SYM
ma-203	146	1	d	d	X
ma-203	146	2	dvt	dvt	PROPN
ma-203	146	3	∫	∫	PROPN
ma-203	146	4	t	t	PROPN
ma-203	146	5	0	0	NUM
ma-203	146	6	kh(t	kh(t	NUM
ma-203	146	7	,	,	PUNCT
ma-203	146	8	s)ui(s)ds	s)ui(s)ds	PROPN
ma-203	147	1	=	=	SYM
ma-203	147	2	κ−1	κ−1	PROPN
ma-203	147	3	h	h	NOUN
ma-203	148	1	d	d	NOUN
ma-203	148	2	dvt	dvt	PROPN
ma-203	148	3	∫	∫	PROPN
ma-203	148	4	t	t	PROPN
ma-203	148	5	0	0	NUM
ma-203	148	6	s1/2−h(t	s1/2−h(t	PROPN
ma-203	148	7	−	−	PROPN
ma-203	148	8	s)1/2−hui(s)ds	s)1/2−hui(s)ds	NOUN
ma-203	148	9	=	=	PUNCT
ma-203	148	10	κ−1	κ−1	PROPN
ma-203	148	11	h	h	NOUN
ma-203	148	12	ηht	ηht	VERB
ma-203	148	13	2h−1	2h−1	NUM
ma-203	149	1	d	d	NOUN
ma-203	149	2	dt	dt	X
ma-203	149	3	∫	∫	PROPN
ma-203	149	4	t	t	PROPN
ma-203	149	5	0	0	NUM
ma-203	149	6	s1/2−h(t	s1/2−h(t	PROPN
ma-203	149	7	−	−	PROPN
ma-203	149	8	s)1/2−hui(s)ds	s)1/2−hui(s)ds	NOUN
ma-203	149	9	=	=	PUNCT
ma-203	149	10	κ−1	κ−1	PROPN
ma-203	149	11	h	h	NOUN
ma-203	149	12	ηht	ηht	VERB
ma-203	149	13	2h−1	2h−1	NUM
ma-203	149	14	∫	∫	NOUN
ma-203	149	15	t	t	NOUN
ma-203	149	16	0	0	NUM
ma-203	150	1	d	d	NOUN
ma-203	150	2	dt	dt	X
ma-203	150	3	s1/2−h(t	s1/2−h(t	PROPN
ma-203	150	4	−	−	PROPN
ma-203	150	5	s)1/2−hui(s)ds	s)1/2−hui(s)ds	NOUN
ma-203	150	6	=	=	PUNCT
ma-203	150	7	κ−1	κ−1	PROPN
ma-203	150	8	h	h	NOUN
ma-203	150	9	ηht	ηht	VERB
ma-203	150	10	2h−1	2h−1	NUM
ma-203	150	11	∫	∫	NOUN
ma-203	150	12	t	t	PROPN
ma-203	150	13	0	0	PUNCT
ma-203	150	14	s1/2−h(t	s1/2−h(t	PROPN
ma-203	150	15	−	−	PROPN
ma-203	150	16	s)−1/2−hui(s)ds	s)−1/2−hui(s)ds	PROPN
ma-203	150	17	.	.	PUNCT
ma-203	151	1	the	the	DET
ma-203	151	2	process	process	NOUN
ma-203	151	3	qi	qi	NOUN
ma-203	151	4	depends	depend	VERB
ma-203	151	5	continuously	continuously	ADV
ma-203	151	6	on	on	ADP
ma-203	151	7	ui	ui	PROPN
ma-203	151	8	and	and	CCONJ
ma-203	151	9	therefore	therefore	ADV
ma-203	151	10	,	,	PUNCT
ma-203	151	11	the	the	DET
ma-203	151	12	discrete	discrete	ADJ
ma-203	151	13	observations	observation	NOUN
ma-203	151	14	of	of	ADP
ma-203	151	15	ui	ui	PROPN
ma-203	151	16	does	do	AUX
ma-203	151	17	notallow	notallow	VERB
ma-203	151	18	one	one	NUM
ma-203	151	19	to	to	PART
ma-203	151	20	obtain	obtain	VERB
ma-203	151	21	the	the	DET
ma-203	151	22	discrete	discrete	ADJ
ma-203	151	23	observations	observation	NOUN
ma-203	151	24	of	of	ADP
ma-203	151	25	qi	qi	PROPN
ma-203	151	26	.	.	PUNCT
ma-203	152	1	the	the	DET
ma-203	152	2	process	process	NOUN
ma-203	152	3	qi	qi	PROPN
ma-203	152	4	can	can	AUX
ma-203	152	5	be	be	AUX
ma-203	152	6	approximated	approximate	VERB
ma-203	152	7	by	by	ADP
ma-203	152	8	qi(n	qi(n	NOUN
ma-203	152	9	)	)	PUNCT
ma-203	152	10	=	=	SYM
ma-203	153	1	κ−1	κ−1	PROPN
ma-203	153	2	h	h	NOUN
ma-203	153	3	ηhn	ηhn	NOUN
ma-203	153	4	2h−1	2h−1	NUM
ma-203	153	5	n−1∑	n−1∑	NUM
ma-203	153	6	j=0	j=0	PROPN
ma-203	153	7	j1/2−h(n	j1/2−h(n	PROPN
ma-203	153	8	−	−	PROPN
ma-203	153	9	j)−1/2−hui(j	j)−1/2−hui(j	ADJ
ma-203	153	10	)	)	PUNCT
ma-203	153	11	.	.	PUNCT
ma-203	154	1	it	it	PRON
ma-203	154	2	is	be	AUX
ma-203	154	3	easy	easy	ADJ
ma-203	154	4	to	to	PART
ma-203	154	5	show	show	VERB
ma-203	154	6	that	that	SCONJ
ma-203	154	7	qi(n)→	qi(n)→	PROPN
ma-203	154	8	qi(t	qi(t	NOUN
ma-203	154	9	)	)	PUNCT
ma-203	154	10	almost	almost	ADV
ma-203	154	11	surely	surely	ADV
ma-203	154	12	as	as	ADP
ma-203	154	13	n	n	X
ma-203	154	14	→∞	→∞	NOUN
ma-203	154	15	,	,	PUNCT
ma-203	154	16	see	see	VERB
ma-203	154	17	tudor	tudor	PROPN
ma-203	154	18	and	and	CCONJ
ma-203	154	19	viens	vien	NOUN
ma-203	154	20	(	(	PUNCT
ma-203	154	21	2007).define	2007).define	NUM
ma-203	154	22	a	a	DET
ma-203	154	23	new	new	ADJ
ma-203	154	24	partition	partition	NOUN
ma-203	154	25	0	0	NUM
ma-203	154	26	≤	≤	PROPN
ma-203	154	27	r1	r1	PROPN
ma-203	154	28	<	<	X
ma-203	154	29	r2	r2	PROPN
ma-203	154	30	<	<	X
ma-203	154	31	r3	r3	PROPN
ma-203	154	32	<	<	X
ma-203	154	33	·	·	PUNCT
ma-203	154	34	·	·	PUNCT
ma-203	154	35	·	·	PUNCT
ma-203	155	1	<	<	X
ma-203	155	2	rmk	rmk	PROPN
ma-203	155	3	=	=	SYM
ma-203	155	4	tk	tk	PROPN
ma-203	155	5	,	,	PUNCT
ma-203	155	6	k	k	PROPN
ma-203	155	7	=	=	SYM
ma-203	155	8	1	1	NUM
ma-203	155	9	,	,	PUNCT
ma-203	155	10	2	2	NUM
ma-203	155	11	,	,	PUNCT
ma-203	155	12	·	·	PUNCT
ma-203	155	13	·	·	PUNCT
ma-203	155	14	·	·	PUNCT
ma-203	155	15	,	,	PUNCT
ma-203	155	16	n.	n.	NOUN
ma-203	155	17	define	define	VERB
ma-203	155	18	qi(tk	qi(tk	NOUN
ma-203	155	19	)	)	PUNCT
ma-203	156	1	=	=	SYM
ma-203	156	2	κ−1	κ−1	PROPN
ma-203	156	3	h	h	NOUN
ma-203	156	4	ηht	ηht	VERB
ma-203	156	5	2h−1	2h−1	NUM
ma-203	156	6	k	k	PROPN
ma-203	156	7	mk∑	mk∑	NOUN
ma-203	156	8	j=1	j=1	NOUN
ma-203	157	1	r	r	NOUN
ma-203	157	2	1/2−h	1/2−h	NUM
ma-203	157	3	j	j	PROPN
ma-203	157	4	(	(	PUNCT
ma-203	157	5	rmk	rmk	PROPN
ma-203	157	6	−	−	PROPN
ma-203	157	7	rj	rj	PROPN
ma-203	157	8	)	)	PUNCT
ma-203	157	9	−1/2−hui(rj)(rj	−1/2−hui(rj)(rj	NOUN
ma-203	157	10	−	−	PROPN
ma-203	157	11	rj−1	rj−1	NOUN
ma-203	157	12	)	)	PUNCT
ma-203	157	13	,	,	PUNCT
ma-203	157	14	k	k	PROPN
ma-203	157	15	=	=	SYM
ma-203	157	16	1	1	NUM
ma-203	157	17	,	,	PUNCT
ma-203	157	18	2	2	NUM
ma-203	157	19	,	,	PUNCT
ma-203	157	20	·	·	PUNCT
ma-203	157	21	·	·	PUNCT
ma-203	157	22	·	·	PUNCT
ma-203	157	23	,	,	PUNCT
ma-203	157	24	n.	n.	INTJ
ma-203	157	25	it	it	PRON
ma-203	157	26	is	be	AUX
ma-203	157	27	easy	easy	ADJ
ma-203	157	28	to	to	PART
ma-203	157	29	show	show	VERB
ma-203	157	30	that	that	SCONJ
ma-203	157	31	qi(tk)→	qi(tk)→	PROPN
ma-203	157	32	qi(t	qi(t	NOUN
ma-203	157	33	)	)	PUNCT
ma-203	157	34	almost	almost	ADV
ma-203	157	35	surely	surely	ADV
ma-203	157	36	as	as	SCONJ
ma-203	157	37	mk	mk	X
ma-203	157	38	→∞	→∞	PROPN
ma-203	157	39	for	for	ADP
ma-203	157	40	each	each	PRON
ma-203	157	41	k	k	NOUN
ma-203	158	1	=	=	SYM
ma-203	158	2	1	1	NUM
ma-203	158	3	,	,	PUNCT
ma-203	158	4	2	2	NUM
ma-203	158	5	,	,	PUNCT
ma-203	158	6	·	·	PUNCT
ma-203	158	7	·	·	PUNCT
ma-203	158	8	·	·	PUNCT
ma-203	158	9	,	,	PUNCT
ma-203	158	10	n.	n.	INTJ
ma-203	158	11	we	we	PRON
ma-203	158	12	usethis	usethi	VERB
ma-203	158	13	approximate	approximate	ADJ
ma-203	158	14	observation	observation	NOUN
ma-203	158	15	in	in	ADP
ma-203	158	16	the	the	DET
ma-203	158	17	calculation	calculation	NOUN
ma-203	158	18	of	of	ADP
ma-203	158	19	our	our	PRON
ma-203	158	20	estimators.applying	estimators.applying	PROPN
ma-203	158	21	itô	itô	PROPN
ma-203	158	22	’s	’s	PART
ma-203	158	23	formula	formula	NOUN
ma-203	158	24	,	,	PUNCT
ma-203	158	25	for	for	ADP
ma-203	158	26	t	t	PROPN
ma-203	158	27	≥	≥	PROPN
ma-203	158	28	r	r	NOUN
ma-203	158	29	≥	≥	NOUN
ma-203	158	30	0	0	NUM
ma-203	158	31	,	,	PUNCT
ma-203	158	32	we	we	PRON
ma-203	158	33	obtain	obtain	VERB
ma-203	158	34	qj	qj	PROPN
ma-203	158	35	,	,	PUNCT
ma-203	158	36	t	t	PROPN
ma-203	158	37	=	=	SYM
ma-203	158	38	e−θ(t−r)qj	e−θ(t−r)qj	PROPN
ma-203	158	39	,	,	PUNCT
ma-203	158	40	r	r	NOUN
ma-203	158	41	+	+	CCONJ
ma-203	158	42	a	a	DET
ma-203	158	43	∫	∫	PROPN
ma-203	158	44	t	t	PROPN
ma-203	158	45	r	r	NOUN
ma-203	158	46	e−θ(t−s)ds	e−θ(t−s)ds	PROPN
ma-203	158	47	+	+	CCONJ
ma-203	158	48	σ	σ	NUM
ma-203	158	49	∫	∫	PROPN
ma-203	158	50	t	t	PROPN
ma-203	158	51	r	r	NOUN
ma-203	158	52	e−θ(t−s)q	e−θ(t−s)q	ADP
ma-203	158	53	1	1	NUM
ma-203	158	54	/	/	SYM
ma-203	158	55	α	α	PRON
ma-203	158	56	j	j	PROPN
ma-203	158	57	,	,	PUNCT
ma-203	158	58	s−dzj	s−dzj	ADJ
ma-203	158	59	,	,	PUNCT
ma-203	158	60	s	s	PART
ma-203	158	61	,	,	PUNCT
ma-203	158	62	j	j	PROPN
ma-203	158	63	≥	≥	PROPN
ma-203	158	64	1	1	NUM
ma-203	158	65	.	.	PUNCT
ma-203	159	1	(	(	PUNCT
ma-203	159	2	2.5	2.5	NUM
ma-203	159	3	)	)	PUNCT
ma-203	159	4	let	let	VERB
ma-203	159	5	the	the	DET
ma-203	159	6	process	process	NOUN
ma-203	159	7	be	be	AUX
ma-203	159	8	observed	observe	VERB
ma-203	159	9	at	at	ADP
ma-203	159	10	{	{	PUNCT
ma-203	159	11	kh	kh	PROPN
ma-203	159	12	,	,	PUNCT
ma-203	159	13	k	k	PROPN
ma-203	159	14	=	=	SYM
ma-203	159	15	0	0	NUM
ma-203	159	16	,	,	PUNCT
ma-203	159	17	1	1	NUM
ma-203	159	18	,	,	PUNCT
ma-203	159	19	.	.	PUNCT
ma-203	159	20	.	.	PUNCT
ma-203	160	1	.	.	PUNCT
ma-203	161	1	,	,	PUNCT
ma-203	161	2	n	n	CCONJ
ma-203	161	3	}	}	PUNCT
ma-203	161	4	from	from	ADP
ma-203	161	5	a	a	DET
ma-203	161	6	single	single	ADJ
ma-203	161	7	realization	realization	NOUN
ma-203	161	8	{	{	PUNCT
ma-203	161	9	qj	qj	PROPN
ma-203	161	10	,	,	PUNCT
ma-203	161	11	t	t	PROPN
ma-203	161	12	,	,	PUNCT
ma-203	161	13	t	t	PROPN
ma-203	161	14	≥	≥	NUM
ma-203	161	15	0	0	NUM
ma-203	161	16	}	}	PUNCT
ma-203	161	17	for	for	ADP
ma-203	161	18	fixed	fix	VERB
ma-203	161	19	h.	h.	PROPN
ma-203	161	20	for	for	ADP
ma-203	161	21	simplicity	simplicity	NOUN
ma-203	161	22	,	,	PUNCT
ma-203	161	23	we	we	PRON
ma-203	161	24	take	take	VERB
ma-203	161	25	h	h	NOUN
ma-203	161	26	=	=	NOUN
ma-203	161	27	1	1	X
ma-203	161	28	.	.	PUNCT
ma-203	162	1	this	this	DET
ma-203	162	2	equation	equation	NOUN
ma-203	162	3	can	can	AUX
ma-203	162	4	be	be	AUX
ma-203	162	5	considered	consider	VERB
ma-203	162	6	as	as	ADP
ma-203	162	7	a	a	DET
ma-203	162	8	first	first	ADJ
ma-203	162	9	order	order	NOUN
ma-203	162	10	autoregressive	autoregressive	ADJ
ma-203	162	11	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	NOUN
ma-203	162	12	eur	eur	NOUN
ma-203	162	13	.	.	PUNCT
ma-203	163	1	j.	j.	PROPN
ma-203	163	2	math	math	PROPN
ma-203	163	3	.	.	PUNCT
ma-203	164	1	anal	anal	PROPN
ma-203	164	2	.	.	PUNCT
ma-203	165	1	10.28924	10.28924	NUM
ma-203	165	2	/	/	SYM
ma-203	165	3	ada	ada	PROPN
ma-203	165	4	/	/	SYM
ma-203	165	5	ma.4.12	ma.4.12	NOUN
ma-203	165	6	7(ar(1	7(ar(1	NUM
ma-203	165	7	)	)	PUNCT
ma-203	165	8	)	)	PUNCT
ma-203	166	1	equation	equation	NOUN
ma-203	166	2	qj	qj	PROPN
ma-203	166	3	,	,	PUNCT
ma-203	166	4	k	k	PROPN
ma-203	166	5	=	=	X
ma-203	166	6	ρ+	ρ+	NUM
ma-203	166	7	γqj	γqj	ADJ
ma-203	166	8	,	,	PUNCT
ma-203	166	9	k−1	k−1	PROPN
ma-203	166	10	+	+	CCONJ
ma-203	166	11	εj	εj	PROPN
ma-203	166	12	,	,	PUNCT
ma-203	166	13	k	k	PROPN
ma-203	166	14	,	,	PUNCT
ma-203	166	15	j	j	PROPN
ma-203	166	16	≥	≥	NUM
ma-203	166	17	1	1	NUM
ma-203	166	18	(	(	PUNCT
ma-203	166	19	2.6)where	2.6)where	NUM
ma-203	166	20	γ	γ	X
ma-203	166	21	=	=	PUNCT
ma-203	166	22	e−θ	e−θ	PROPN
ma-203	166	23	,	,	PUNCT
ma-203	166	24	ρ	ρ	X
ma-203	166	25	=	=	PUNCT
ma-203	166	26	aθ−1(1−	aθ−1(1−	PROPN
ma-203	166	27	γ	γ	PROPN
ma-203	166	28	)	)	PUNCT
ma-203	166	29	and	and	CCONJ
ma-203	166	30	εj	εj	NOUN
ma-203	166	31	,	,	PUNCT
ma-203	166	32	k	k	PROPN
ma-203	167	1	=	=	PROPN
ma-203	167	2	σ	σ	PROPN
ma-203	167	3	∫	∫	PROPN
ma-203	167	4	k	k	PROPN
ma-203	167	5	k−1	k−1	PROPN
ma-203	167	6	e−θ(k−s)q	e−θ(k−s)q	PROPN
ma-203	167	7	1	1	NUM
ma-203	167	8	/	/	SYM
ma-203	167	9	α	α	PRON
ma-203	167	10	j	j	PROPN
ma-203	167	11	,	,	PUNCT
ma-203	167	12	s−dzj	s−dzj	ADJ
ma-203	167	13	,	,	PUNCT
ma-203	167	14	s	s	PART
ma-203	167	15	,	,	PUNCT
ma-203	167	16	k	k	PROPN
ma-203	167	17	≥	≥	NUM
ma-203	167	18	1	1	NUM
ma-203	167	19	,	,	PUNCT
ma-203	167	20	j	j	PROPN
ma-203	167	21	≥	≥	PROPN
ma-203	167	22	1	1	NUM
ma-203	167	23	.	.	PUNCT
ma-203	168	1	(	(	PUNCT
ma-203	168	2	2.7	2.7	NUM
ma-203	168	3	)	)	PUNCT
ma-203	168	4	for	for	ADP
ma-203	168	5	b	b	PROPN
ma-203	168	6	∈	∈	PROPN
ma-203	168	7	b(r+	b(r+	NOUN
ma-203	168	8	)	)	PUNCT
ma-203	168	9	,	,	PUNCT
ma-203	168	10	let	let	VERB
ma-203	168	11	s2,j	s2,j	PROPN
ma-203	168	12	,	,	PUNCT
ma-203	168	13	n(b	n(b	PROPN
ma-203	168	14	)	)	PUNCT
ma-203	169	1	=	=	PUNCT
ma-203	169	2	n∑	n∑	NOUN
ma-203	169	3	k=1	k=1	PROPN
ma-203	170	1	qj	qj	PROPN
ma-203	170	2	,	,	PUNCT
ma-203	170	3	k−1εk	k−1εk	PROPN
ma-203	170	4	ib(|qj	ib(|qj	NOUN
ma-203	170	5	,	,	PUNCT
ma-203	170	6	k−1εj	k−1εj	PROPN
ma-203	170	7	,	,	PUNCT
ma-203	170	8	k	k	PROPN
ma-203	170	9	|	|	NOUN
ma-203	170	10	)	)	PUNCT
ma-203	170	11	,	,	PUNCT
ma-203	170	12	s1,j	s1,j	PROPN
ma-203	170	13	,	,	PUNCT
ma-203	170	14	n(b	n(b	PROPN
ma-203	170	15	)	)	PUNCT
ma-203	170	16	=	=	SYM
ma-203	170	17	n∑	n∑	NOUN
ma-203	170	18	k=1	k=1	PROPN
ma-203	170	19	q2	q2	PROPN
ma-203	170	20	j	j	PROPN
ma-203	170	21	,	,	PUNCT
ma-203	170	22	k−1ib(qj	k−1ib(qj	NOUN
ma-203	170	23	,	,	PUNCT
ma-203	170	24	k−1	k−1	PROPN
ma-203	170	25	)	)	PUNCT
ma-203	170	26	,	,	PUNCT
ma-203	170	27	j	j	PROPN
ma-203	170	28	≥	≥	PROPN
ma-203	170	29	1	1	NUM
ma-203	170	30	.	.	PUNCT
ma-203	171	1	(	(	PUNCT
ma-203	171	2	2.8	2.8	NUM
ma-203	171	3	)	)	PUNCT
ma-203	171	4	it	it	PRON
ma-203	171	5	is	be	AUX
ma-203	171	6	easy	easy	ADJ
ma-203	171	7	to	to	PART
ma-203	171	8	see	see	VERB
ma-203	171	9	that	that	DET
ma-203	171	10	εj	εj	NOUN
ma-203	171	11	,	,	PUNCT
ma-203	171	12	k	k	PROPN
ma-203	171	13	=	=	SYM
ma-203	171	14	qj	qj	PROPN
ma-203	171	15	,	,	PUNCT
ma-203	171	16	k	k	PROPN
ma-203	172	1	−	−	PROPN
ma-203	172	2	e(qj	e(qj	PROPN
ma-203	172	3	,	,	PUNCT
ma-203	172	4	k	k	PROPN
ma-203	172	5	|fk−1	|fk−1	NOUN
ma-203	172	6	)	)	PUNCT
ma-203	172	7	,	,	PUNCT
ma-203	172	8	k	k	PROPN
ma-203	172	9	≥	≥	NUM
ma-203	172	10	1	1	NUM
ma-203	172	11	,	,	PUNCT
ma-203	172	12	j	j	PROPN
ma-203	172	13	≥	≥	PROPN
ma-203	172	14	1	1	NUM
ma-203	172	15	.	.	PUNCT
ma-203	172	16	(	(	PUNCT
ma-203	172	17	2.9)is	2.9)is	NUM
ma-203	172	18	a	a	DET
ma-203	172	19	sequence	sequence	NOUN
ma-203	172	20	of	of	ADP
ma-203	172	21	martingale	martingale	ADJ
ma-203	172	22	differences	difference	NOUN
ma-203	172	23	for	for	ADP
ma-203	172	24	every	every	DET
ma-203	172	25	fixed	fix	VERB
ma-203	172	26	j	j	PROPN
ma-203	172	27	.let	.let	PUNCT
ma-203	172	28	s1,j	s1,j	PROPN
ma-203	172	29	,	,	PUNCT
ma-203	172	30	n	n	NOUN
ma-203	172	31	:	:	PUNCT
ma-203	172	32	=	=	SYM
ma-203	172	33	s1,j	s1,j	PROPN
ma-203	172	34	,	,	PUNCT
ma-203	172	35	n(0,∞	n(0,∞	NOUN
ma-203	172	36	)	)	PUNCT
ma-203	172	37	,	,	PUNCT
ma-203	172	38	s2,j	s2,j	PROPN
ma-203	172	39	,	,	PUNCT
ma-203	172	40	n	n	PRON
ma-203	172	41	:	:	PUNCT
ma-203	172	42	=	=	SYM
ma-203	172	43	s2,j	s2,j	PROPN
ma-203	172	44	,	,	PUNCT
ma-203	172	45	n(0,∞	n(0,∞	NOUN
ma-203	172	46	)	)	PUNCT
ma-203	172	47	and	and	CCONJ
ma-203	172	48	recall	recall	VERB
ma-203	172	49	that	that	SCONJ
ma-203	172	50	γ	γ	PROPN
ma-203	172	51	=	=	SYM
ma-203	172	52	e−θ	e−θ	PROPN
ma-203	172	53	.then	.then	PUNCT
ma-203	172	54	θ̂j	θ̂j	PROPN
ma-203	172	55	,	,	PUNCT
ma-203	172	56	n	n	PRON
ma-203	172	57	−	−	PROPN
ma-203	172	58	θ	θ	NOUN
ma-203	172	59	=	=	SYM
ma-203	172	60	s2,j	s2,j	PROPN
ma-203	172	61	,	,	PUNCT
ma-203	172	62	n	n	PRON
ma-203	172	63	s1,j	s1,j	NOUN
ma-203	172	64	,	,	PUNCT
ma-203	172	65	n	n	CCONJ
ma-203	172	66	(	(	PUNCT
ma-203	172	67	2.10	2.10	NUM
ma-203	172	68	)	)	PUNCT
ma-203	172	69	where	where	SCONJ
ma-203	172	70	θ̂n	θ̂n	NUM
ma-203	172	71	is	be	AUX
ma-203	172	72	the	the	DET
ma-203	172	73	conditional	conditional	ADJ
ma-203	172	74	least	least	ADJ
ma-203	172	75	squares	square	NOUN
ma-203	172	76	estimator	estimator	NOUN
ma-203	172	77	(	(	PUNCT
ma-203	172	78	clse	clse	PROPN
ma-203	172	79	)	)	PUNCT
ma-203	172	80	which	which	PRON
ma-203	172	81	minimizes	minimize	VERB
ma-203	172	82	n∑	n∑	NOUN
ma-203	172	83	k=1	k=1	PROPN
ma-203	172	84	ε2	ε2	PROPN
ma-203	172	85	j	j	PROPN
ma-203	172	86	,	,	PUNCT
ma-203	172	87	k	k	PROPN
ma-203	172	88	=	=	PUNCT
ma-203	172	89	n∑	n∑	NOUN
ma-203	172	90	k=1	k=1	PUNCT
ma-203	173	1	[	[	X
ma-203	173	2	qj	qj	PROPN
ma-203	173	3	,	,	PUNCT
ma-203	173	4	k	k	PROPN
ma-203	173	5	−	−	PROPN
ma-203	173	6	e(qj	e(qj	PROPN
ma-203	173	7	,	,	PUNCT
ma-203	173	8	k	k	PROPN
ma-203	173	9	|fk−1)]2	|fk−1)]2	PROPN
ma-203	173	10	=	=	PUNCT
ma-203	173	11	n∑	n∑	NOUN
ma-203	173	12	k=1	k=1	PUNCT
ma-203	174	1	[	[	X
ma-203	174	2	qj	qj	PROPN
ma-203	174	3	,	,	PUNCT
ma-203	174	4	k	k	PROPN
ma-203	174	5	−	−	PROPN
ma-203	174	6	ρ−	ρ−	PROPN
ma-203	174	7	γqj	γqj	ADJ
ma-203	174	8	,	,	PUNCT
ma-203	174	9	k−1]2	k−1]2	INTJ
ma-203	174	10	(	(	PUNCT
ma-203	174	11	2.11	2.11	NUM
ma-203	174	12	)	)	PUNCT
ma-203	174	13	and	and	CCONJ
ma-203	174	14	are	be	AUX
ma-203	174	15	given	give	VERB
ma-203	174	16	by	by	ADP
ma-203	174	17	γ̂j	γ̂j	NOUN
ma-203	174	18	,	,	PUNCT
ma-203	174	19	n	n	NOUN
ma-203	175	1	=	=	SYM
ma-203	175	2	∑n	∑n	PROPN
ma-203	175	3	k=1	k=1	PROPN
ma-203	175	4	qj	qj	PROPN
ma-203	175	5	,	,	PUNCT
ma-203	175	6	k−1	k−1	PROPN
ma-203	175	7	∑n	∑n	PROPN
ma-203	176	1	k=1	k=1	PROPN
ma-203	176	2	qj	qj	PROPN
ma-203	176	3	,	,	PUNCT
ma-203	176	4	k	k	PROPN
ma-203	176	5	−	−	PROPN
ma-203	176	6	n	n	CCONJ
ma-203	176	7	∑n	∑n	PROPN
ma-203	176	8	k=1	k=1	PROPN
ma-203	176	9	qj	qj	PROPN
ma-203	176	10	,	,	PUNCT
ma-203	176	11	k−1qj	k−1qj	PROPN
ma-203	176	12	,	,	PUNCT
ma-203	176	13	k	k	PROPN
ma-203	176	14	(	(	PUNCT
ma-203	176	15	∑n	∑n	PROPN
ma-203	176	16	k=1	k=1	PROPN
ma-203	176	17	qj	qj	PROPN
ma-203	176	18	,	,	PUNCT
ma-203	176	19	k−1)2	k−1)2	VERB
ma-203	176	20	−	−	PROPN
ma-203	176	21	n	n	NOUN
ma-203	176	22	∑n	∑n	PROPN
ma-203	177	1	k=1	k=1	PUNCT
ma-203	177	2	q	q	PROPN
ma-203	177	3	2	2	NUM
ma-203	177	4	j	j	PROPN
ma-203	177	5	,	,	PUNCT
ma-203	177	6	k−1	k−1	PROPN
ma-203	177	7	,	,	PUNCT
ma-203	177	8	ρ̂j	ρ̂j	X
ma-203	177	9	,	,	PUNCT
ma-203	177	10	n	n	NOUN
ma-203	177	11	=	=	SYM
ma-203	177	12	1	1	NUM
ma-203	177	13	n	n	NUM
ma-203	177	14	n∑	n∑	ADJ
ma-203	177	15	k=1	k=1	PROPN
ma-203	178	1	qj	qj	PROPN
ma-203	178	2	,	,	PUNCT
ma-203	178	3	k	k	PROPN
ma-203	178	4	−	−	PROPN
ma-203	178	5	γ̂n	γ̂n	NOUN
ma-203	178	6	1	1	NUM
ma-203	178	7	n	n	NUM
ma-203	178	8	n∑	n∑	NOUN
ma-203	178	9	k=1	k=1	PROPN
ma-203	178	10	qj	qj	PROPN
ma-203	178	11	,	,	PUNCT
ma-203	178	12	k−1	k−1	PROPN
ma-203	178	13	,	,	PUNCT
ma-203	178	14	θ̂j	θ̂j	PROPN
ma-203	178	15	,	,	PUNCT
ma-203	178	16	n	n	NOUN
ma-203	178	17	=	=	SYM
ma-203	178	18	−	−	PROPN
ma-203	178	19	log	log	NOUN
ma-203	178	20	γ̂j	γ̂j	NOUN
ma-203	178	21	,	,	PUNCT
ma-203	178	22	n	n	CCONJ
ma-203	178	23	,	,	PUNCT
ma-203	178	24	âj	âj	NOUN
ma-203	178	25	,	,	PUNCT
ma-203	178	26	n	n	NOUN
ma-203	178	27	=	=	PUNCT
ma-203	179	1	ρ̂nθ̂n	ρ̂nθ̂n	PROPN
ma-203	179	2	1−	1−	NUM
ma-203	179	3	γ̂n	γ̂n	NOUN
ma-203	179	4	.let	.let	PUNCT
ma-203	180	1	(	(	PUNCT
ma-203	180	2	s1	s1	NOUN
ma-203	180	3	,	,	PUNCT
ma-203	180	4	s2	s2	PROPN
ma-203	180	5	)	)	PUNCT
ma-203	180	6	have	have	VERB
ma-203	180	7	the	the	DET
ma-203	180	8	characteristic	characteristic	ADJ
ma-203	180	9	function	function	NOUN
ma-203	180	10	given	give	VERB
ma-203	180	11	by	by	ADP
ma-203	180	12	e[exp{iλ1s1	e[exp{iλ1s1	NOUN
ma-203	180	13	+	+	CCONJ
ma-203	180	14	iλ2s2	iλ2s2	PROPN
ma-203	180	15	}	}	PUNCT
ma-203	180	16	]	]	PUNCT
ma-203	180	17	:	:	PUNCT
ma-203	180	18	=	=	SYM
ma-203	180	19	exp	exp	NOUN
ma-203	180	20	{	{	PUNCT
ma-203	180	21	−	−	PROPN
ma-203	180	22	σα	σα	PROPN
ma-203	180	23	θ2γ(−α	θ2γ(−α	PROPN
ma-203	180	24	)	)	PUNCT
ma-203	180	25	∫	∫	PROPN
ma-203	181	1	∞	∞	PROPN
ma-203	181	2	0	0	PUNCT
ma-203	182	1	e	e	X
ma-203	182	2	(	(	PUNCT
ma-203	182	3	1−	1−	NUM
ma-203	182	4	exp{iλ1y	exp{iλ1y	NUM
ma-203	182	5	2	2	NUM
ma-203	182	6	+	+	CCONJ
ma-203	182	7	iλ2y	iλ2y	PROPN
ma-203	182	8	(	(	PUNCT
ma-203	182	9	α+1)/αvj,1	α+1)/αvj,1	NOUN
ma-203	182	10	}	}	PUNCT
ma-203	182	11	)	)	PUNCT
ma-203	182	12	×	×	NOUN
ma-203	182	13	e	e	NOUN
ma-203	182	14	(	(	PUNCT
ma-203	182	15	exp	exp	X
ma-203	182	16	{	{	PUNCT
ma-203	182	17	ie−2θλ1y	ie−2θλ1y	NUM
ma-203	182	18	2	2	NUM
ma-203	182	19	1−	1−	NUM
ma-203	182	20	e−2θ	e−2θ	NOUN
ma-203	183	1	+	+	CCONJ
ma-203	183	2	ie−θ(α+1)/αλ2y	ie−θ(α+1)/αλ2y	X
ma-203	183	3	(	(	PUNCT
ma-203	183	4	α+1)/αvj,2	α+1)/αvj,2	X
ma-203	183	5	(	(	PUNCT
ma-203	183	6	1−	1−	NUM
ma-203	183	7	eθ(α+1))1	eθ(α+1))1	NOUN
ma-203	183	8	/	/	SYM
ma-203	183	9	α	α	NOUN
ma-203	183	10	}	}	PUNCT
ma-203	183	11	)	)	PUNCT
ma-203	183	12	dy	dy	NOUN
ma-203	183	13	yα+1	yα+1	NOUN
ma-203	183	14	}	}	PUNCT
ma-203	183	15	(	(	PUNCT
ma-203	183	16	2.12	2.12	NUM
ma-203	183	17	)	)	PUNCT
ma-203	183	18	and	and	CCONJ
ma-203	183	19	vj	vj	INTJ
ma-203	183	20	,	,	PUNCT
ma-203	183	21	k	k	PROPN
ma-203	183	22	:	:	PUNCT
ma-203	183	23	=	=	SYM
ma-203	183	24	σ	σ	NUM
ma-203	183	25	∫	∫	PROPN
ma-203	184	1	k	k	PROPN
ma-203	184	2	k−1	k−1	PROPN
ma-203	184	3	e−θ(k−s)e−θ(s−k+1)/αdzj	e−θ(k−s)e−θ(s−k+1)/αdzj	PROPN
ma-203	184	4	,	,	PUNCT
ma-203	184	5	s	s	PART
ma-203	184	6	,	,	PUNCT
ma-203	184	7	k	k	PROPN
ma-203	185	1	=	=	SYM
ma-203	186	1	1	1	NUM
ma-203	186	2	,	,	PUNCT
ma-203	186	3	2	2	NUM
ma-203	186	4	,	,	PUNCT
ma-203	186	5	j	j	PROPN
ma-203	186	6	≥	≥	NUM
ma-203	186	7	1	1	NUM
ma-203	186	8	(	(	PUNCT
ma-203	186	9	2.13	2.13	NUM
ma-203	186	10	)	)	PUNCT
ma-203	186	11	which	which	PRON
ma-203	186	12	are	be	AUX
ma-203	186	13	i.i.d	i.i.d	ADJ
ma-203	186	14	.	.	PUNCT
ma-203	187	1	with	with	ADP
ma-203	187	2	the	the	DET
ma-203	187	3	same	same	ADJ
ma-203	187	4	distribution	distribution	NOUN
ma-203	187	5	as	as	ADP
ma-203	187	6	σ	σ	PROPN
ma-203	187	7	(	(	PUNCT
ma-203	187	8	e−θ	e−θ	PROPN
ma-203	187	9	−	−	PROPN
ma-203	187	10	1	1	NUM
ma-203	187	11	(	(	PUNCT
ma-203	187	12	α−	α−	ADP
ma-203	187	13	1)θ	1)θ	NUM
ma-203	187	14	)	)	PUNCT
ma-203	187	15	1	1	NUM
ma-203	187	16	/	/	SYM
ma-203	187	17	α	α	PROPN
ma-203	187	18	zj,1	zj,1	PROPN
ma-203	187	19	which	which	PRON
ma-203	187	20	is	be	AUX
ma-203	187	21	regularly	regularly	ADV
ma-203	187	22	varying	vary	VERB
ma-203	187	23	with	with	ADP
ma-203	187	24	index	index	NOUN
ma-203	187	25	α	α	NOUN
ma-203	187	26	.	.	PUNCT
ma-203	188	1	the	the	DET
ma-203	188	2	limit	limit	NOUN
ma-203	188	3	distribution	distribution	NOUN
ma-203	188	4	is	be	AUX
ma-203	188	5	normal	normal	ADJ
ma-203	188	6	only	only	ADV
ma-203	188	7	in	in	ADP
ma-203	188	8	the	the	DET
ma-203	188	9	gaussian	gaussian	ADJ
ma-203	188	10	case	case	NOUN
ma-203	188	11	α	α	X
ma-203	188	12	=	=	SYM
ma-203	188	13	2	2	NUM
ma-203	188	14	.	.	X
ma-203	188	15	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	188	16	eur	eur	PROPN
ma-203	188	17	.	.	PUNCT
ma-203	189	1	j.	j.	PROPN
ma-203	189	2	math	math	PROPN
ma-203	189	3	.	.	PUNCT
ma-203	190	1	anal	anal	PROPN
ma-203	190	2	.	.	PUNCT
ma-203	191	1	10.28924	10.28924	NUM
ma-203	191	2	/	/	SYM
ma-203	191	3	ada	ada	PROPN
ma-203	191	4	/	/	SYM
ma-203	191	5	ma.4.12	ma.4.12	PROPN
ma-203	191	6	8following	8following	NUM
ma-203	191	7	li	li	NOUN
ma-203	191	8	and	and	CCONJ
ma-203	191	9	ma	ma	PROPN
ma-203	192	1	[	[	X
ma-203	192	2	28	28	NUM
ma-203	192	3	]	]	X
ma-203	192	4	it	it	PRON
ma-203	192	5	can	can	AUX
ma-203	192	6	be	be	AUX
ma-203	192	7	shown	show	VERB
ma-203	192	8	that	that	SCONJ
ma-203	192	9	for	for	ADP
ma-203	192	10	every	every	DET
ma-203	192	11	fixed	fix	VERB
ma-203	192	12	j	j	PROPN
ma-203	192	13	,	,	PUNCT
ma-203	192	14	if	if	SCONJ
ma-203	192	15	we	we	PRON
ma-203	192	16	have	have	VERB
ma-203	192	17	1	1	NUM
ma-203	192	18	<	<	X
ma-203	192	19	α	α	X
ma-203	192	20	<	<	X
ma-203	192	21	(	(	PUNCT
ma-203	192	22	1	1	NUM
ma-203	192	23	+	+	CCONJ
ma-203	192	24	√	√	ADJ
ma-203	192	25	5)/2,then	5)/2,then	ADV
ma-203	192	26	we	we	PRON
ma-203	192	27	have	have	VERB
ma-203	192	28	as	as	ADP
ma-203	192	29	n	n	X
ma-203	192	30	→∞	→∞	PROPN
ma-203	192	31	(	(	PUNCT
ma-203	192	32	d−2	d−2	PROPN
ma-203	192	33	n	n	PRON
ma-203	192	34	s1,j	s1,j	NOUN
ma-203	192	35	,	,	PUNCT
ma-203	192	36	n	n	CCONJ
ma-203	192	37	,	,	PUNCT
ma-203	192	38	c	c	NOUN
ma-203	192	39	−1	−1	NOUN
ma-203	192	40	n	n	PRON
ma-203	192	41	s2,j	s2,j	PROPN
ma-203	192	42	,	,	PUNCT
ma-203	192	43	n	n	CCONJ
ma-203	192	44	)	)	PUNCT
ma-203	192	45	d→(s1	d→(s1	PROPN
ma-203	192	46	,	,	PUNCT
ma-203	192	47	s2	s2	PROPN
ma-203	192	48	)	)	PUNCT
ma-203	192	49	on	on	ADP
ma-203	192	50	r2	r2	PROPN
ma-203	192	51	where	where	SCONJ
ma-203	192	52	dn	dn	PROPN
ma-203	192	53	=	=	SYM
ma-203	192	54	n1	n1	PROPN
ma-203	192	55	/	/	SYM
ma-203	192	56	α	α	PROPN
ma-203	192	57	and	and	CCONJ
ma-203	192	58	cn	cn	PROPN
ma-203	192	59	=	=	NOUN
ma-203	192	60	n(α+1)/α2	n(α+1)/α2	NOUN
ma-203	193	1	=	=	SYM
ma-203	193	2	d	d	PROPN
ma-203	193	3	(	(	PUNCT
ma-203	193	4	α+1)/α	α+1)/α	PROPN
ma-203	193	5	n	n	PROPN
ma-203	193	6	.for	.for	PUNCT
ma-203	194	1	the	the	DET
ma-203	194	2	stable	stable	ADJ
ma-203	194	3	spde	spde	NOUN
ma-203	194	4	model	model	NOUN
ma-203	194	5	,	,	PUNCT
ma-203	194	6	we	we	PRON
ma-203	194	7	have	have	AUX
ma-203	194	8	the	the	DET
ma-203	194	9	following	following	ADJ
ma-203	194	10	result	result	NOUN
ma-203	194	11	on	on	ADP
ma-203	194	12	the	the	DET
ma-203	194	13	consistency	consistency	NOUN
ma-203	194	14	and	and	CCONJ
ma-203	194	15	the	the	DET
ma-203	194	16	limit	limit	NOUN
ma-203	194	17	dis	dis	PROPN
ma-203	194	18	-	-	PUNCT
ma-203	194	19	tribution	tribution	NOUN
ma-203	194	20	of	of	ADP
ma-203	194	21	the	the	DET
ma-203	194	22	clse	clse	NOUN
ma-203	194	23	:	:	PUNCT
ma-203	194	24	theorem	theorem	VERB
ma-203	194	25	2.1	2.1	NUM
ma-203	194	26	if	if	SCONJ
ma-203	194	27	we	we	PRON
ma-203	194	28	have	have	VERB
ma-203	194	29	1	1	NUM
ma-203	194	30	<	<	X
ma-203	194	31	α	α	X
ma-203	194	32	<	<	X
ma-203	194	33	(	(	PUNCT
ma-203	194	34	1	1	NUM
ma-203	194	35	+	+	CCONJ
ma-203	194	36	√	√	NUM
ma-203	194	37	5)/2	5)/2	NUM
ma-203	194	38	,	,	PUNCT
ma-203	194	39	then	then	ADV
ma-203	194	40	for	for	ADP
ma-203	194	41	every	every	DET
ma-203	194	42	fixed	fix	VERB
ma-203	194	43	j	j	PROPN
ma-203	194	44	≥	≥	X
ma-203	194	45	1a	1a	PROPN
ma-203	194	46	)	)	PUNCT
ma-203	194	47	θ̂j	θ̂j	PROPN
ma-203	194	48	,	,	PUNCT
ma-203	194	49	n	n	CCONJ
ma-203	194	50	→p	→p	PROPN
ma-203	194	51	θ	θ	PROPN
ma-203	194	52	as	as	ADP
ma-203	194	53	n	n	PROPN
ma-203	194	54	→∞.b	→∞.b	NUM
ma-203	194	55	)	)	PUNCT
ma-203	194	56	n(α−1)/α2	n(α−1)/α2	NUM
ma-203	194	57	(	(	PUNCT
ma-203	194	58	θ̂j	θ̂j	PROPN
ma-203	194	59	,	,	PUNCT
ma-203	194	60	n	n	CCONJ
ma-203	194	61	−	−	PROPN
ma-203	194	62	θ)→d	θ)→d	NOUN
ma-203	194	63	(	(	PUNCT
ma-203	194	64	σ2	σ2	PROPN
ma-203	194	65	ν2	ν2	PROPN
ma-203	194	66	j	j	PROPN
ma-203	194	67	)	)	PUNCT
ma-203	194	68	1	1	NUM
ma-203	194	69	/	/	SYM
ma-203	194	70	α	α	NOUN
ma-203	194	71	s2	s2	NOUN
ma-203	194	72	s1	s1	NOUN
ma-203	194	73	as	as	ADP
ma-203	194	74	n	n	PROPN
ma-203	194	75	→∞.	→∞.	PROPN
ma-203	194	76	c	c	X
ma-203	194	77	)	)	PUNCT
ma-203	194	78	if	if	SCONJ
ma-203	194	79	in	in	ADP
ma-203	194	80	addition	addition	NOUN
ma-203	194	81	,	,	PUNCT
ma-203	194	82	limj→∞	limj→∞	PROPN
ma-203	194	83	∣∣νj	∣∣νj	PROPN
ma-203	194	84	∣∣	∣∣	NUM
ma-203	194	85	=	=	SYM
ma-203	194	86	∞	∞	PROPN
ma-203	194	87	,	,	PUNCT
ma-203	194	88	then	then	ADV
ma-203	194	89	for	for	ADP
ma-203	194	90	every	every	DET
ma-203	194	91	fixed	fix	VERB
ma-203	194	92	n	n	X
ma-203	194	93	≥	≥	NOUN
ma-203	194	94	1	1	NUM
ma-203	194	95	,	,	PUNCT
ma-203	194	96	θ̂j	θ̂j	PROPN
ma-203	194	97	,	,	PUNCT
ma-203	194	98	n	n	PRON
ma-203	194	99	→p	→p	PROPN
ma-203	194	100	θ	θ	PROPN
ma-203	194	101	as	as	ADP
ma-203	194	102	j	j	PROPN
ma-203	194	103	→∞	→∞	PROPN
ma-203	194	104	and	and	CCONJ
ma-203	194	105	∣∣νj	∣∣νj	PROPN
ma-203	194	106	∣∣	∣∣	NUM
ma-203	194	107	(	(	PUNCT
ma-203	194	108	θ̂j	θ̂j	PROPN
ma-203	194	109	,	,	PUNCT
ma-203	194	110	n	n	CCONJ
ma-203	194	111	−	−	PROPN
ma-203	194	112	θ)→d	θ)→d	NOUN
ma-203	194	113	σ	σ	NOUN
ma-203	194	114	(	(	PUNCT
ma-203	194	115	n−(α−1)/α2	n−(α−1)/α2	NOUN
ma-203	194	116	)	)	PUNCT
ma-203	194	117	1	1	NUM
ma-203	194	118	/	/	SYM
ma-203	194	119	α	α	NOUN
ma-203	194	120	s2	s2	NOUN
ma-203	194	121	s1	s1	NOUN
ma-203	194	122	as	as	ADP
ma-203	194	123	j	j	PROPN
ma-203	194	124	→∞.where	→∞.where	X
ma-203	194	125	s2	s2	PROPN
ma-203	194	126	and	and	CCONJ
ma-203	194	127	s1	s1	NOUN
ma-203	194	128	are	be	AUX
ma-203	194	129	defined	define	VERB
ma-203	194	130	in	in	ADP
ma-203	194	131	(	(	PUNCT
ma-203	194	132	2.12	2.12	NUM
ma-203	194	133	)	)	PUNCT
ma-203	194	134	.	.	PUNCT
ma-203	195	1	remarks1	remarks1	NOUN
ma-203	195	2	)	)	PUNCT
ma-203	196	1	the	the	DET
ma-203	196	2	limit	limit	NOUN
ma-203	196	3	distribution	distribution	NOUN
ma-203	196	4	in	in	ADP
ma-203	196	5	the	the	DET
ma-203	196	6	case	case	NOUN
ma-203	196	7	(	(	PUNCT
ma-203	196	8	1	1	NUM
ma-203	196	9	+	+	CCONJ
ma-203	196	10	√	√	NUM
ma-203	196	11	5)/2	5)/2	NUM
ma-203	196	12	<	<	X
ma-203	196	13	α	α	X
ma-203	196	14	<	<	X
ma-203	196	15	2	2	NUM
ma-203	196	16	is	be	AUX
ma-203	196	17	still	still	ADV
ma-203	196	18	open.2	open.2	PRON
ma-203	196	19	)	)	PUNCT
ma-203	196	20	the	the	DET
ma-203	196	21	process	process	NOUN
ma-203	196	22	(	(	PUNCT
ma-203	196	23	xj	xj	NOUN
ma-203	196	24	)	)	PUNCT
ma-203	196	25	is	be	AUX
ma-203	196	26	exponentially	exponentially	ADV
ma-203	196	27	ergodic	ergodic	ADJ
ma-203	196	28	and	and	CCONJ
ma-203	196	29	hence	hence	ADV
ma-203	196	30	strongly	strongly	ADV
ma-203	196	31	mixing.3	mixing.3	PROPN
ma-203	196	32	)	)	PUNCT
ma-203	196	33	for	for	ADP
ma-203	196	34	the	the	DET
ma-203	196	35	gaussian	gaussian	ADJ
ma-203	196	36	case	case	NOUN
ma-203	196	37	(	(	PUNCT
ma-203	196	38	α	α	NOUN
ma-203	196	39	=	=	SYM
ma-203	196	40	2	2	NUM
ma-203	196	41	)	)	PUNCT
ma-203	196	42	,	,	PUNCT
ma-203	196	43	the	the	DET
ma-203	196	44	limit	limit	NOUN
ma-203	196	45	results	result	NOUN
ma-203	196	46	are	be	AUX
ma-203	196	47	based	base	VERB
ma-203	196	48	on	on	ADP
ma-203	196	49	ergodic	ergodic	ADJ
ma-203	196	50	theory	theory	NOUN
ma-203	196	51	and	and	CCONJ
ma-203	196	52	martingaleconvergence	martingaleconvergence	NOUN
ma-203	196	53	theorem	theorem	VERB
ma-203	196	54	.	.	PROPN
ma-203	197	1	for	for	ADP
ma-203	197	2	the	the	DET
ma-203	197	3	non	non	ADJ
ma-203	197	4	-	-	ADJ
ma-203	197	5	gaussian	gaussian	ADJ
ma-203	197	6	case	case	NOUN
ma-203	197	7	(	(	PUNCT
ma-203	197	8	1	1	NUM
ma-203	197	9	<	<	X
ma-203	197	10	α	α	X
ma-203	197	11	<	<	X
ma-203	197	12	2	2	NUM
ma-203	197	13	)	)	PUNCT
ma-203	197	14	,	,	PUNCT
ma-203	197	15	limit	limit	NOUN
ma-203	197	16	results	result	NOUN
ma-203	197	17	are	be	AUX
ma-203	197	18	obtained	obtain	VERB
ma-203	197	19	by	by	ADP
ma-203	197	20	thetheory	thetheory	NOUN
ma-203	197	21	of	of	ADP
ma-203	197	22	regular	regular	ADJ
ma-203	197	23	variation	variation	NOUN
ma-203	197	24	and	and	CCONJ
ma-203	197	25	convergence	convergence	NOUN
ma-203	197	26	of	of	ADP
ma-203	197	27	point	point	NOUN
ma-203	197	28	processes.4	processes.4	NOUN
ma-203	197	29	)	)	PUNCT
ma-203	198	1	let	let	VERB
ma-203	198	2	0	0	PUNCT
ma-203	198	3	<	<	X
ma-203	198	4	α	α	X
ma-203	198	5	<	<	X
ma-203	198	6	2	2	NUM
ma-203	198	7	and	and	CCONJ
ma-203	198	8	let	let	VERB
ma-203	198	9	zt	zt	PRON
ma-203	198	10	be	be	AUX
ma-203	198	11	a	a	DET
ma-203	198	12	one	one	NUM
ma-203	198	13	dimensional	dimensional	ADJ
ma-203	198	14	α	α	NOUN
ma-203	198	15	-	-	ADJ
ma-203	198	16	stable	stable	ADJ
ma-203	198	17	process	process	NOUN
ma-203	198	18	with	with	ADP
ma-203	198	19	levy	levy	NOUN
ma-203	198	20	measure	measure	NOUN
ma-203	198	21	ν(dz).then	ν(dz).then	ADV
ma-203	198	22	as	as	ADP
ma-203	198	23	n	n	PROPN
ma-203	198	24	→∞	→∞	PROPN
ma-203	198	25	,	,	PUNCT
ma-203	198	26	np	np	INTJ
ma-203	198	27	(	(	PUNCT
ma-203	198	28	n−1	n−1	PROPN
ma-203	198	29	/	/	SYM
ma-203	198	30	αzt	αzt	NOUN
ma-203	198	31	∈	∈	PROPN
ma-203	198	32	·	·	PUNCT
ma-203	198	33	)	)	PUNCT
ma-203	198	34	→v	→v	NUM
ma-203	198	35	tν	tν	NOUN
ma-203	198	36	(	(	PUNCT
ma-203	198	37	·	·	PUNCT
ma-203	198	38	)	)	PUNCT
ma-203	198	39	.	.	PUNCT
ma-203	199	1	we	we	PRON
ma-203	199	2	consider	consider	VERB
ma-203	199	3	the	the	DET
ma-203	199	4	stable	stable	ADJ
ma-203	199	5	cox	cox	PROPN
ma-203	199	6	-	-	PUNCT
ma-203	199	7	ingersoll	ingersoll	PROPN
ma-203	199	8	-	-	PUNCT
ma-203	199	9	ross	ross	PROPN
ma-203	199	10	model	model	NOUN
ma-203	199	11	as	as	ADP
ma-203	199	12	an	an	DET
ma-203	199	13	example	example	NOUN
ma-203	199	14	.	.	PUNCT
ma-203	200	1	xiong	xiong	PROPN
ma-203	200	2	and	and	CCONJ
ma-203	200	3	yang	yang	PROPN
ma-203	201	1	[	[	X
ma-203	201	2	41	41	NUM
ma-203	201	3	]	]	X
ma-203	201	4	studiedexistence	studiedexistence	NOUN
ma-203	201	5	and	and	CCONJ
ma-203	201	6	strong	strong	ADJ
ma-203	201	7	uniqueness	uniqueness	NOUN
ma-203	201	8	of	of	ADP
ma-203	201	9	the	the	DET
ma-203	201	10	following	follow	VERB
ma-203	201	11	spde	spde	NOUN
ma-203	201	12	:	:	PUNCT
ma-203	201	13	duk(t	duk(t	X
ma-203	201	14	)	)	PUNCT
ma-203	201	15	=	=	PUNCT
ma-203	201	16	(	(	PUNCT
ma-203	201	17	θνk	θνk	VERB
ma-203	201	18	+	+	CCONJ
ma-203	201	19	ρk)uk(t)dt	ρk)uk(t)dt	NOUN
ma-203	201	20	+	+	CCONJ
ma-203	201	21	σk(uk(t))1	σk(uk(t))1	PROPN
ma-203	201	22	/	/	SYM
ma-203	201	23	αdzk(t	αdzk(t	NOUN
ma-203	201	24	)	)	PUNCT
ma-203	201	25	,	,	PUNCT
ma-203	201	26	k	k	PROPN
ma-203	201	27	≥	≥	NUM
ma-203	201	28	1	1	NUM
ma-203	201	29	.	.	PUNCT
ma-203	202	1	the	the	DET
ma-203	202	2	existence	existence	NOUN
ma-203	202	3	of	of	ADP
ma-203	202	4	the	the	DET
ma-203	202	5	solution	solution	NOUN
ma-203	202	6	in	in	ADP
ma-203	202	7	the	the	DET
ma-203	202	8	case	case	NOUN
ma-203	202	9	of	of	ADP
ma-203	202	10	space	space	NOUN
ma-203	202	11	-	-	PUNCT
ma-203	202	12	time	time	NOUN
ma-203	202	13	white	white	ADJ
ma-203	202	14	noise	noise	NOUN
ma-203	202	15	is	be	AUX
ma-203	202	16	shown	show	VERB
ma-203	202	17	by	by	ADP
ma-203	202	18	considering	consider	VERB
ma-203	202	19	theweak	theweak	NOUN
ma-203	202	20	limit	limit	NOUN
ma-203	202	21	of	of	ADP
ma-203	202	22	a	a	DET
ma-203	202	23	sequence	sequence	NOUN
ma-203	202	24	of	of	ADP
ma-203	202	25	sde	sde	PROPN
ma-203	202	26	systems	system	NOUN
ma-203	202	27	which	which	PRON
ma-203	202	28	is	be	AUX
ma-203	202	29	obtained	obtain	VERB
ma-203	202	30	by	by	ADP
ma-203	202	31	replacing	replace	VERB
ma-203	202	32	the	the	DET
ma-203	202	33	laplacian	laplacian	ADJ
ma-203	202	34	operatorin	operatorin	NOUN
ma-203	202	35	the	the	DET
ma-203	202	36	spde	spde	NOUN
ma-203	202	37	by	by	ADP
ma-203	202	38	its	its	PRON
ma-203	202	39	discrete	discrete	ADJ
ma-203	202	40	version	version	NOUN
ma-203	202	41	.	.	PUNCT
ma-203	203	1	the	the	DET
ma-203	203	2	weak	weak	ADJ
ma-203	203	3	uniqueness	uniqueness	NOUN
ma-203	203	4	follows	follow	VERB
ma-203	203	5	from	from	ADP
ma-203	203	6	the	the	DET
ma-203	203	7	uniqueness	uniqueness	NOUN
ma-203	203	8	of	of	ADP
ma-203	203	9	solutionto	solutionto	NOUN
ma-203	203	10	the	the	DET
ma-203	203	11	martingale	martingale	ADJ
ma-203	203	12	problem	problem	NOUN
ma-203	203	13	for	for	ADP
ma-203	203	14	the	the	DET
ma-203	203	15	associated	associated	ADJ
ma-203	203	16	super	super	ADJ
ma-203	203	17	-	-	ADJ
ma-203	203	18	brownian	brownian	ADJ
ma-203	203	19	motion	motion	NOUN
ma-203	203	20	.	.	PUNCT
ma-203	204	1	in	in	ADP
ma-203	204	2	the	the	DET
ma-203	204	3	case	case	NOUN
ma-203	204	4	of	of	ADP
ma-203	204	5	α	α	NOUN
ma-203	204	6	-	-	ADJ
ma-203	204	7	stable	stable	ADJ
ma-203	204	8	noisethe	noisethe	ADJ
ma-203	204	9	existence	existence	NOUN
ma-203	204	10	and	and	CCONJ
ma-203	204	11	pathwise	pathwise	NOUN
ma-203	204	12	uniqueness	uniqueness	NOUN
ma-203	204	13	of	of	ADP
ma-203	204	14	the	the	DET
ma-203	204	15	solution	solution	NOUN
ma-203	204	16	is	be	AUX
ma-203	204	17	studied	study	VERB
ma-203	204	18	in	in	ADP
ma-203	204	19	xiong	xiong	PROPN
ma-203	204	20	and	and	CCONJ
ma-203	204	21	yang	yang	PROPN
ma-203	205	1	[	[	X
ma-203	205	2	41	41	NUM
ma-203	205	3	]	]	PUNCT
ma-203	205	4	.	.	PUNCT
ma-203	206	1	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	206	2	eur	eur	PROPN
ma-203	206	3	.	.	PUNCT
ma-203	207	1	j.	j.	PROPN
ma-203	207	2	math	math	PROPN
ma-203	207	3	.	.	PUNCT
ma-203	208	1	anal	anal	PROPN
ma-203	208	2	.	.	PUNCT
ma-203	209	1	10.28924	10.28924	NUM
ma-203	209	2	/	/	SYM
ma-203	209	3	ada	ada	PROPN
ma-203	209	4	/	/	SYM
ma-203	209	5	ma.4.12	ma.4.12	NOUN
ma-203	209	6	9	9	NUM
ma-203	209	7	3	3	NUM
ma-203	209	8	.	.	PUNCT
ma-203	209	9	interacting	interact	VERB
ma-203	209	10	particle	particle	NOUN
ma-203	209	11	systems	system	NOUN
ma-203	209	12	first	first	ADV
ma-203	209	13	consider	consider	VERB
ma-203	209	14	the	the	DET
ma-203	209	15	fractional	fractional	ADJ
ma-203	209	16	cox	cox	PROPN
ma-203	209	17	-	-	PUNCT
ma-203	209	18	ingersoll	ingersoll	PROPN
ma-203	209	19	-	-	PUNCT
ma-203	209	20	ross	ross	PROPN
ma-203	209	21	(	(	PUNCT
ma-203	209	22	fcir	fcir	NOUN
ma-203	209	23	)	)	PUNCT
ma-203	209	24	model	model	NOUN
ma-203	210	1	d	d	X
ma-203	210	2	yt	yt	NOUN
ma-203	211	1	=	=	PUNCT
ma-203	212	1	a(b	a(b	ADJ
ma-203	212	2	−	−	PROPN
ma-203	212	3	yt)dt	yt)dt	PROPN
ma-203	213	1	+	+	NUM
ma-203	213	2	σ	σ	PROPN
ma-203	213	3	√	√	PROPN
ma-203	213	4	ytdw	ytdw	NOUN
ma-203	213	5	h	h	PROPN
ma-203	213	6	t	t	PROPN
ma-203	213	7	(	(	PUNCT
ma-203	213	8	3.1	3.1	NUM
ma-203	213	9	)	)	PUNCT
ma-203	213	10	where	where	SCONJ
ma-203	213	11	wh	wh	PROPN
ma-203	213	12	t	t	PROPN
ma-203	213	13	is	be	AUX
ma-203	213	14	a	a	DET
ma-203	213	15	fractional	fractional	ADJ
ma-203	213	16	brownian	brownian	ADJ
ma-203	213	17	motion	motion	NOUN
ma-203	213	18	with	with	ADP
ma-203	213	19	hurst	hurst	PROPN
ma-203	213	20	parameter	parameter	PROPN
ma-203	213	21	h	h	PROPN
ma-203	213	22	>	>	X
ma-203	213	23	1/2.then	1/2.then	NUM
ma-203	213	24	by	by	ADP
ma-203	213	25	proposition	proposition	NOUN
ma-203	213	26	5.7	5.7	NUM
ma-203	213	27	of	of	ADP
ma-203	213	28	buchmann	buchmann	PROPN
ma-203	213	29	and	and	CCONJ
ma-203	213	30	kluppelberg	kluppelberg	PROPN
ma-203	214	1	[	[	X
ma-203	214	2	15	15	NUM
ma-203	214	3	]	]	PUNCT
ma-203	214	4	,	,	PUNCT
ma-203	214	5	we	we	PRON
ma-203	214	6	have	have	VERB
ma-203	214	7	yt	yt	NOUN
ma-203	214	8	=	=	SYM
ma-203	214	9	f	f	PROPN
ma-203	214	10	(	(	PUNCT
ma-203	214	11	xt	xt	PROPN
ma-203	214	12	)	)	PUNCT
ma-203	214	13	(	(	PUNCT
ma-203	214	14	3.2	3.2	NUM
ma-203	214	15	)	)	PUNCT
ma-203	214	16	where	where	SCONJ
ma-203	214	17	dxt	dxt	PROPN
ma-203	214	18	=	=	PUNCT
ma-203	214	19	a(b	a(b	NOUN
ma-203	214	20	−xt)dt	−xt)dt	SYM
ma-203	214	21	+	+	CCONJ
ma-203	214	22	dwh	dwh	PROPN
ma-203	214	23	t	t	PROPN
ma-203	214	24	,	,	PUNCT
ma-203	214	25	x0	x0	PROPN
ma-203	214	26	=	=	PUNCT
ma-203	214	27	f	f	PROPN
ma-203	214	28	−1(y0	−1(y0	NOUN
ma-203	214	29	)	)	PUNCT
ma-203	214	30	,	,	PUNCT
ma-203	214	31	t	t	PROPN
ma-203	214	32	∈	∈	PROPN
ma-203	215	1	[	[	X
ma-203	215	2	0	0	NUM
ma-203	215	3	,	,	PUNCT
ma-203	215	4	t	t	X
ma-203	215	5	]	]	PUNCT
ma-203	215	6	(	(	PUNCT
ma-203	215	7	3.3	3.3	NUM
ma-203	215	8	)	)	PUNCT
ma-203	215	9	and	and	CCONJ
ma-203	215	10	f	f	PROPN
ma-203	215	11	(	(	PUNCT
ma-203	215	12	x	x	X
ma-203	215	13	)	)	PUNCT
ma-203	215	14	=	=	SYM
ma-203	215	15	sgn(x)σ2x2/4.let	sgn(x)σ2x2/4.let	NOUN
ma-203	215	16	b	b	X
ma-203	215	17	=	=	SYM
ma-203	215	18	0	0	PROPN
ma-203	215	19	,	,	PUNCT
ma-203	215	20	σ	σ	NOUN
ma-203	215	21	=	=	SYM
ma-203	215	22	1	1	NUM
ma-203	215	23	and	and	CCONJ
ma-203	215	24	a	a	DET
ma-203	215	25	>	>	X
ma-203	215	26	0	0	NUM
ma-203	215	27	.	.	PUNCT
ma-203	215	28	then	then	ADV
ma-203	215	29	xt	xt	PROPN
ma-203	215	30	is	be	AUX
ma-203	215	31	described	describe	VERB
ma-203	215	32	by	by	ADP
ma-203	215	33	the	the	DET
ma-203	215	34	ornstein	ornstein	PROPN
ma-203	215	35	-	-	PUNCT
ma-203	215	36	uhlenbeck	uhlenbeck	PROPN
ma-203	215	37	sde	sde	PROPN
ma-203	215	38	dxt	dxt	PROPN
ma-203	215	39	=	=	PUNCT
ma-203	215	40	−axtdt	−axtdt	PROPN
ma-203	215	41	+	+	NUM
ma-203	215	42	dwh	dwh	PROPN
ma-203	215	43	t	t	PROPN
ma-203	215	44	,	,	PUNCT
ma-203	215	45	x0	x0	PROPN
ma-203	215	46	=	=	PUNCT
ma-203	215	47	f	f	PROPN
ma-203	216	1	−1(y0	−1(y0	NOUN
ma-203	216	2	)	)	PUNCT
ma-203	216	3	.	.	PUNCT
ma-203	217	1	(	(	PUNCT
ma-203	217	2	3.4	3.4	NUM
ma-203	217	3	)	)	PUNCT
ma-203	217	4	for	for	ADP
ma-203	217	5	h	h	NOUN
ma-203	217	6	=	=	SYM
ma-203	217	7	0.5	0.5	NUM
ma-203	217	8	,	,	PUNCT
ma-203	217	9	let	let	VERB
ma-203	217	10	us	we	PRON
ma-203	217	11	consider	consider	VERB
ma-203	217	12	maximum	maximum	ADJ
ma-203	217	13	likelihood	likelihood	NOUN
ma-203	217	14	estimator	estimator	NOUN
ma-203	217	15	(	(	PUNCT
ma-203	217	16	mle	mle	PROPN
ma-203	217	17	)	)	PUNCT
ma-203	217	18	for	for	ADP
ma-203	217	19	the	the	DET
ma-203	217	20	simple	simple	ADJ
ma-203	217	21	mean	mean	ADJ
ma-203	217	22	-	-	PUNCT
ma-203	217	23	field	field	NOUN
ma-203	217	24	model	model	NOUN
ma-203	217	25	dxj(t	dxj(t	PROPN
ma-203	217	26	)	)	PUNCT
ma-203	218	1	=	=	NOUN
ma-203	219	1	αxj(t)dt	αxj(t)dt	NUM
ma-203	220	1	−	−	PROPN
ma-203	220	2	β(xj(t)−	β(xj(t)−	PUNCT
ma-203	220	3	x̄n(t))dt	x̄n(t))dt	PROPN
ma-203	220	4	+	+	CCONJ
ma-203	220	5	dwj(t	dwj(t	PROPN
ma-203	220	6	)	)	PUNCT
ma-203	220	7	,	,	PUNCT
ma-203	220	8	xj(0	xj(0	PROPN
ma-203	220	9	)	)	PUNCT
ma-203	220	10	=	=	SYM
ma-203	220	11	xj(0	xj(0	PROPN
ma-203	220	12	)	)	PUNCT
ma-203	220	13	,	,	PUNCT
ma-203	220	14	j	j	PROPN
ma-203	220	15	=	=	SYM
ma-203	220	16	1	1	NUM
ma-203	220	17	,	,	PUNCT
ma-203	220	18	2	2	NUM
ma-203	220	19	,	,	PUNCT
ma-203	220	20	·	·	PUNCT
ma-203	220	21	·	·	PUNCT
ma-203	220	22	·	·	PUNCT
ma-203	220	23	,	,	PUNCT
ma-203	220	24	n	n	X
ma-203	220	25	(	(	PUNCT
ma-203	220	26	3.5	3.5	NUM
ma-203	220	27	)	)	PUNCT
ma-203	220	28	where	where	SCONJ
ma-203	220	29	x̄n(t	x̄n(t	NOUN
ma-203	220	30	)	)	PUNCT
ma-203	220	31	)	)	PUNCT
ma-203	221	1	=	=	SYM
ma-203	221	2	n−1	n−1	PROPN
ma-203	221	3	∑n	∑n	PROPN
ma-203	221	4	j=1xj(t	j=1xj(t	PROPN
ma-203	221	5	)	)	PUNCT
ma-203	221	6	,	,	PUNCT
ma-203	221	7	β	β	PROPN
ma-203	221	8	6=	6=	ADP
ma-203	221	9	α	α	PROPN
ma-203	221	10	,	,	PUNCT
ma-203	221	11	and	and	CCONJ
ma-203	221	12	α	α	X
ma-203	221	13	6=	6=	PROPN
ma-203	221	14	0	0	NUM
ma-203	221	15	.	.	PUNCT
ma-203	222	1	the	the	DET
ma-203	222	2	middle	middle	ADJ
ma-203	222	3	term	term	NOUN
ma-203	222	4	on	on	ADP
ma-203	222	5	the	the	DET
ma-203	222	6	right	right	ADJ
ma-203	222	7	side	side	NOUN
ma-203	222	8	of	of	ADP
ma-203	222	9	(	(	PUNCT
ma-203	222	10	3.5)can	3.5)can	NUM
ma-203	222	11	be	be	AUX
ma-203	222	12	viewed	view	VERB
ma-203	222	13	as	as	ADP
ma-203	222	14	an	an	DET
ma-203	222	15	interaction	interaction	NOUN
ma-203	222	16	among	among	ADP
ma-203	222	17	the	the	DET
ma-203	222	18	subsystems	subsystem	NOUN
ma-203	222	19	which	which	PRON
ma-203	222	20	create	create	VERB
ma-203	222	21	a	a	DET
ma-203	222	22	tendency	tendency	NOUN
ma-203	222	23	for	for	SCONJ
ma-203	222	24	the	the	DET
ma-203	222	25	subsystemsto	subsystemsto	NOUN
ma-203	222	26	relax	relax	VERB
ma-203	222	27	towards	towards	ADP
ma-203	222	28	the	the	DET
ma-203	222	29	center	center	NOUN
ma-203	222	30	of	of	ADP
ma-203	222	31	gravity	gravity	NOUN
ma-203	222	32	of	of	ADP
ma-203	222	33	the	the	DET
ma-203	222	34	ensemble	ensemble	NOUN
ma-203	222	35	.	.	PUNCT
ma-203	223	1	thus	thus	ADV
ma-203	223	2	the	the	DET
ma-203	223	3	system	system	NOUN
ma-203	223	4	provides	provide	VERB
ma-203	223	5	a	a	DET
ma-203	223	6	simple	simple	ADJ
ma-203	223	7	exampleof	exampleof	NOUN
ma-203	223	8	a	a	DET
ma-203	223	9	cooperative	cooperative	ADJ
ma-203	223	10	interaction	interaction	NOUN
ma-203	223	11	.	.	PUNCT
ma-203	224	1	mean	mean	ADJ
ma-203	224	2	-	-	PUNCT
ma-203	224	3	field	field	NOUN
ma-203	224	4	type	type	NOUN
ma-203	224	5	models	model	NOUN
ma-203	224	6	have	have	VERB
ma-203	224	7	applications	application	NOUN
ma-203	224	8	in	in	ADP
ma-203	224	9	physics	physics	NOUN
ma-203	224	10	,	,	PUNCT
ma-203	224	11	biology	biology	NOUN
ma-203	224	12	andeconomics	andeconomic	NOUN
ma-203	224	13	,	,	PUNCT
ma-203	224	14	see	see	VERB
ma-203	224	15	dawson	dawson	PROPN
ma-203	224	16	[	[	X
ma-203	224	17	19	19	NUM
ma-203	224	18	]	]	PUNCT
ma-203	224	19	.	.	PUNCT
ma-203	225	1	the	the	DET
ma-203	225	2	case	case	NOUN
ma-203	225	3	β	β	X
ma-203	225	4	=	=	SYM
ma-203	225	5	0	0	NUM
ma-203	225	6	corresponds	correspond	VERB
ma-203	225	7	to	to	ADP
ma-203	225	8	sampling	sample	VERB
ma-203	225	9	independent	independent	ADJ
ma-203	225	10	replications	replication	NOUN
ma-203	225	11	ofornstein	ofornstein	ADJ
ma-203	225	12	-	-	PUNCT
ma-203	225	13	uhlenbeck	uhlenbeck	NOUN
ma-203	225	14	processes	process	NOUN
ma-203	225	15	on	on	ADP
ma-203	225	16	[	[	X
ma-203	225	17	0	0	NUM
ma-203	225	18	,	,	PUNCT
ma-203	225	19	t	t	X
ma-203	225	20	]	]	PUNCT
ma-203	225	21	.	.	PUNCT
ma-203	226	1	our	our	PRON
ma-203	226	2	parameter	parameter	NOUN
ma-203	226	3	here	here	ADV
ma-203	226	4	is	be	AUX
ma-203	226	5	θ	θ	PROPN
ma-203	226	6	=	=	SYM
ma-203	226	7	(	(	PUNCT
ma-203	226	8	α	α	NOUN
ma-203	226	9	,	,	PUNCT
ma-203	226	10	β).suppose	β).suppose	PROPN
ma-203	226	11	1	1	NUM
ma-203	226	12	n	n	NOUN
ma-203	226	13	∑n	∑n	PROPN
ma-203	226	14	j=1	j=1	PROPN
ma-203	226	15	xj(0)→	xj(0)→	PUNCT
ma-203	226	16	ν0	ν0	PROPN
ma-203	226	17	almost	almost	ADV
ma-203	226	18	surely	surely	ADV
ma-203	226	19	and	and	CCONJ
ma-203	226	20	1	1	NUM
ma-203	226	21	n	n	PRON
ma-203	226	22	∑n	∑n	PROPN
ma-203	226	23	j=1	j=1	NOUN
ma-203	226	24	x	x	SYM
ma-203	226	25	2	2	NUM
ma-203	226	26	j	j	PROPN
ma-203	226	27	(	(	PUNCT
ma-203	226	28	0)→	0)→	NOUN
ma-203	226	29	γ2	γ2	NOUN
ma-203	226	30	0	0	NUM
ma-203	227	1	+	+	ADJ
ma-203	227	2	ν2	ν2	NOUN
ma-203	227	3	0	0	NUM
ma-203	227	4	almost	almost	ADV
ma-203	227	5	surely	surely	ADV
ma-203	227	6	as	as	ADP
ma-203	227	7	n	n	NOUN
ma-203	227	8	→∞.then	→∞.then	PUNCT
ma-203	227	9	the	the	DET
ma-203	227	10	estimator	estimator	NOUN
ma-203	227	11	θ̂n	θ̂n	ADP
ma-203	227	12	→p	→p	PROPN
ma-203	227	13	θ	θ	PROPN
ma-203	227	14	as	as	ADP
ma-203	227	15	n	n	PROPN
ma-203	227	16	→∞	→∞	PROPN
ma-203	227	17	and	and	CCONJ
ma-203	227	18	√n(θ̂n	√n(θ̂n	PROPN
ma-203	227	19	−	−	PROPN
ma-203	227	20	θ)→d	θ)→d	NOUN
ma-203	227	21	n	n	X
ma-203	227	22	(	(	PUNCT
ma-203	227	23	0	0	NUM
ma-203	227	24	,	,	PUNCT
ma-203	227	25	i−1(t	i−1(t	ADJ
ma-203	227	26	)	)	PUNCT
ma-203	227	27	)	)	PUNCT
ma-203	227	28	as	as	ADP
ma-203	227	29	n	n	PROPN
ma-203	227	30	→∞	→∞	PROPN
ma-203	227	31	where	where	SCONJ
ma-203	227	32	i(t	i(t	PUNCT
ma-203	227	33	)	)	PUNCT
ma-203	227	34	=	=	PUNCT
ma-203	227	35	(	(	PUNCT
ma-203	227	36	a(t	a(t	PROPN
ma-203	227	37	)	)	PUNCT
ma-203	227	38	−b(t	−b(t	NOUN
ma-203	227	39	)	)	PUNCT
ma-203	227	40	−b(t	−b(t	NOUN
ma-203	227	41	)	)	PUNCT
ma-203	227	42	b(t	b(t	PROPN
ma-203	227	43	)	)	PUNCT
ma-203	227	44	)	)	PUNCT
ma-203	227	45	with	with	ADP
ma-203	227	46	a(t	a(t	PROPN
ma-203	227	47	)	)	PUNCT
ma-203	227	48	:	:	PUNCT
ma-203	228	1	=	=	PUNCT
ma-203	228	2	ν2	ν2	NOUN
ma-203	228	3	0	0	NUM
ma-203	228	4	2α	2α	NOUN
ma-203	228	5	(	(	PUNCT
ma-203	228	6	e2αt	e2αt	NOUN
ma-203	228	7	−	−	PROPN
ma-203	228	8	1	1	NUM
ma-203	228	9	)	)	PUNCT
ma-203	228	10	+	+	CCONJ
ma-203	228	11	b(t	b(t	PROPN
ma-203	228	12	)	)	PUNCT
ma-203	228	13	,	,	PUNCT
ma-203	228	14	b(t	b(t	PROPN
ma-203	228	15	)	)	PUNCT
ma-203	228	16	:	:	PUNCT
ma-203	228	17	=	=	PUNCT
ma-203	228	18	e2(α−β)t	e2(α−β)t	VERB
ma-203	228	19	−	−	PROPN
ma-203	228	20	1	1	NUM
ma-203	228	21	4(α−	4(α−	NUM
ma-203	228	22	β)2	β)2	ADV
ma-203	228	23	−	−	PROPN
ma-203	228	24	t	t	PROPN
ma-203	228	25	2(α−	2(α−	NUM
ma-203	228	26	β	β	X
ma-203	228	27	)	)	PUNCT
ma-203	229	1	+	+	CCONJ
ma-203	229	2	γ2	γ2	NOUN
ma-203	229	3	0	0	NUM
ma-203	229	4	(	(	PUNCT
ma-203	229	5	e2(α−β)t	e2(α−β)t	VERB
ma-203	229	6	−	−	PROPN
ma-203	229	7	1	1	NUM
ma-203	229	8	)	)	PUNCT
ma-203	229	9	2(α−	2(α−	NUM
ma-203	229	10	β	β	NOUN
ma-203	229	11	)	)	PUNCT
ma-203	229	12	.	.	PUNCT
ma-203	230	1	the	the	DET
ma-203	230	2	case	case	NOUN
ma-203	230	3	β	β	X
ma-203	230	4	=	=	SYM
ma-203	230	5	0	0	NUM
ma-203	230	6	corresponds	correspond	VERB
ma-203	230	7	to	to	ADP
ma-203	230	8	sampling	sample	VERB
ma-203	230	9	independent	independent	ADJ
ma-203	230	10	replications	replication	NOUN
ma-203	230	11	of	of	ADP
ma-203	230	12	the	the	DET
ma-203	230	13	same	same	ADJ
ma-203	230	14	process	process	NOUN
ma-203	230	15	given	give	VERB
ma-203	230	16	below	below	ADV
ma-203	230	17	:	:	PUNCT
ma-203	230	18	dxj(t	dxj(t	X
ma-203	230	19	)	)	PUNCT
ma-203	230	20	=	=	PUNCT
ma-203	230	21	αxj(t)dt	αxj(t)dt	NUM
ma-203	230	22	+	+	NUM
ma-203	230	23	dwj(t	dwj(t	PROPN
ma-203	230	24	)	)	PUNCT
ma-203	230	25	,	,	PUNCT
ma-203	230	26	j	j	PROPN
ma-203	231	1	=	=	SYM
ma-203	231	2	1	1	NUM
ma-203	231	3	,	,	PUNCT
ma-203	231	4	2	2	NUM
ma-203	231	5	,	,	PUNCT
ma-203	231	6	·	·	PUNCT
ma-203	231	7	·	·	PUNCT
ma-203	231	8	·	·	PUNCT
ma-203	231	9	,	,	PUNCT
ma-203	231	10	n	n	X
ma-203	231	11	(	(	PUNCT
ma-203	231	12	3.6	3.6	NUM
ma-203	231	13	)	)	PUNCT
ma-203	231	14	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	231	15	eur	eur	NOUN
ma-203	231	16	.	.	PUNCT
ma-203	232	1	j.	j.	PROPN
ma-203	232	2	math	math	PROPN
ma-203	232	3	.	.	PUNCT
ma-203	233	1	anal	anal	PROPN
ma-203	233	2	.	.	PUNCT
ma-203	234	1	10.28924	10.28924	NUM
ma-203	234	2	/	/	SYM
ma-203	234	3	ada	ada	PROPN
ma-203	234	4	/	/	SYM
ma-203	234	5	ma.4.12	ma.4.12	NOUN
ma-203	234	6	10	10	NUM
ma-203	234	7	in	in	ADP
ma-203	234	8	the	the	DET
ma-203	234	9	classical	classical	ADJ
ma-203	234	10	case	case	NOUN
ma-203	234	11	when	when	SCONJ
ma-203	234	12	β	β	X
ma-203	234	13	=	=	SYM
ma-203	234	14	0	0	PROPN
ma-203	234	15	,	,	PUNCT
ma-203	234	16	the	the	DET
ma-203	234	17	mle	mle	NOUN
ma-203	234	18	is	be	AUX
ma-203	234	19	given	give	VERB
ma-203	234	20	by	by	ADP
ma-203	234	21	α̂n	α̂n	NUM
ma-203	234	22	=	=	SYM
ma-203	234	23	∑n	∑n	PROPN
ma-203	234	24	j=1	j=1	PROPN
ma-203	234	25	∫	∫	PROPN
ma-203	234	26	t	t	PROPN
ma-203	234	27	0	0	NUM
ma-203	235	1	xj(t)dxj(t)∑n	xj(t)dxj(t)∑n	PROPN
ma-203	236	1	j=1	j=1	PROPN
ma-203	236	2	∫	∫	PROPN
ma-203	236	3	t	t	PROPN
ma-203	236	4	0	0	NUM
ma-203	237	1	(	(	PUNCT
ma-203	237	2	xj(t))2dt	xj(t))2dt	PROPN
ma-203	237	3	.	.	PUNCT
ma-203	238	1	sampling	sample	VERB
ma-203	238	2	n	n	PRON
ma-203	238	3	independent	independent	ADJ
ma-203	238	4	ornstein	ornstein	PROPN
ma-203	238	5	-	-	PUNCT
ma-203	238	6	uhlenbeck	uhlenbeck	PROPN
ma-203	238	7	processes	process	NOUN
ma-203	238	8	on	on	ADP
ma-203	238	9	[	[	X
ma-203	238	10	0	0	NUM
ma-203	238	11	,	,	PUNCT
ma-203	238	12	t	t	NOUN
ma-203	238	13	]	]	PUNCT
ma-203	238	14	and	and	CCONJ
ma-203	238	15	letting	let	VERB
ma-203	238	16	n	n	X
ma-203	238	17	→	→	SYM
ma-203	238	18	∞	∞	NUM
ma-203	238	19	give	give	VERB
ma-203	238	20	weakconsistency	weakconsistency	NOUN
ma-203	238	21	and	and	CCONJ
ma-203	238	22	asymptotic	asymptotic	ADJ
ma-203	238	23	normality	normality	NOUN
ma-203	238	24	of	of	ADP
ma-203	238	25	the	the	DET
ma-203	238	26	mle	mle	NOUN
ma-203	238	27	:	:	PUNCT
ma-203	238	28	α̂n	α̂n	NUM
ma-203	238	29	→p	→p	PROPN
ma-203	238	30	α	α	NOUN
ma-203	238	31	and	and	CCONJ
ma-203	238	32	√n(α̂n−α)→d	√n(α̂n−α)→d	ADP
ma-203	238	33	n	n	PRON
ma-203	238	34	(	(	PUNCT
ma-203	238	35	0	0	NUM
ma-203	238	36	,	,	PUNCT
ma-203	238	37	2α	2α	NOUN
ma-203	238	38	ν2	ν2	NOUN
ma-203	238	39	0	0	NUM
ma-203	238	40	(	(	PUNCT
ma-203	238	41	e2αt−1	e2αt−1	PROPN
ma-203	238	42	)	)	PUNCT
ma-203	238	43	)	)	PUNCT
ma-203	238	44	as	as	ADP
ma-203	238	45	n	n	X
ma-203	238	46	→∞.	→∞.	X
ma-203	238	47	see	see	VERB
ma-203	238	48	also	also	ADV
ma-203	238	49	bishwal	bishwal	NOUN
ma-203	238	50	(	(	PUNCT
ma-203	238	51	2010	2010	NUM
ma-203	238	52	)	)	PUNCT
ma-203	238	53	for	for	ADP
ma-203	238	54	independent	independent	ADJ
ma-203	238	55	sampling	sampling	NOUN
ma-203	238	56	case.for	case.for	ADP
ma-203	238	57	h	h	PROPN
ma-203	238	58	≥	≥	NOUN
ma-203	238	59	0.5	0.5	NUM
ma-203	238	60	,	,	PUNCT
ma-203	238	61	let	let	VERB
ma-203	238	62	us	we	PRON
ma-203	238	63	consider	consider	VERB
ma-203	238	64	maximum	maximum	ADJ
ma-203	238	65	likelihood	likelihood	NOUN
ma-203	238	66	estimator	estimator	NOUN
ma-203	238	67	(	(	PUNCT
ma-203	238	68	mle	mle	PROPN
ma-203	238	69	)	)	PUNCT
ma-203	238	70	for	for	ADP
ma-203	238	71	the	the	DET
ma-203	238	72	fractional	fractional	ADJ
ma-203	238	73	mean	mean	ADJ
ma-203	238	74	-	-	PUNCT
ma-203	238	75	fieldmodel	fieldmodel	NOUN
ma-203	238	76	dxj(t	dxj(t	PROPN
ma-203	238	77	)	)	PUNCT
ma-203	239	1	=	=	NOUN
ma-203	240	1	αxj(t)dt	αxj(t)dt	NUM
ma-203	241	1	−	−	PROPN
ma-203	241	2	β(xj(t)−	β(xj(t)−	PUNCT
ma-203	241	3	x̄n(t))dt	x̄n(t))dt	PROPN
ma-203	241	4	+	+	CCONJ
ma-203	241	5	dwh	dwh	PROPN
ma-203	241	6	j	j	PROPN
ma-203	241	7	(	(	PUNCT
ma-203	241	8	t	t	PROPN
ma-203	241	9	)	)	PUNCT
ma-203	241	10	,	,	PUNCT
ma-203	241	11	xj(0	xj(0	PROPN
ma-203	241	12	)	)	PUNCT
ma-203	241	13	=	=	SYM
ma-203	241	14	xj(0	xj(0	PROPN
ma-203	241	15	)	)	PUNCT
ma-203	241	16	,	,	PUNCT
ma-203	241	17	j	j	PROPN
ma-203	241	18	=	=	SYM
ma-203	241	19	1	1	NUM
ma-203	241	20	,	,	PUNCT
ma-203	241	21	2	2	NUM
ma-203	241	22	,	,	PUNCT
ma-203	241	23	·	·	PUNCT
ma-203	241	24	·	·	PUNCT
ma-203	241	25	·	·	PUNCT
ma-203	241	26	,	,	PUNCT
ma-203	241	27	n	n	X
ma-203	241	28	(	(	PUNCT
ma-203	241	29	3.7	3.7	NUM
ma-203	241	30	)	)	PUNCT
ma-203	241	31	where	where	SCONJ
ma-203	241	32	x̄n(t	x̄n(t	NOUN
ma-203	241	33	)	)	PUNCT
ma-203	241	34	)	)	PUNCT
ma-203	242	1	=	=	SYM
ma-203	242	2	n−1	n−1	PROPN
ma-203	242	3	∑n	∑n	PROPN
ma-203	242	4	j=1xj(t	j=1xj(t	PROPN
ma-203	242	5	)	)	PUNCT
ma-203	242	6	,	,	PUNCT
ma-203	242	7	β	β	PROPN
ma-203	242	8	6=	6=	ADP
ma-203	242	9	α	α	PROPN
ma-203	242	10	,	,	PUNCT
ma-203	242	11	and	and	CCONJ
ma-203	242	12	α	α	X
ma-203	242	13	6=	6=	ADP
ma-203	242	14	0.the	0.the	DET
ma-203	242	15	case	case	NOUN
ma-203	242	16	β	β	X
ma-203	242	17	=	=	SYM
ma-203	242	18	0	0	NUM
ma-203	242	19	corresponds	correspond	VERB
ma-203	242	20	to	to	ADP
ma-203	242	21	sampling	sample	VERB
ma-203	242	22	independent	independent	ADJ
ma-203	242	23	replications	replication	NOUN
ma-203	242	24	of	of	ADP
ma-203	242	25	the	the	DET
ma-203	242	26	same	same	ADJ
ma-203	242	27	process	process	NOUN
ma-203	242	28	givenbelow	givenbelow	NOUN
ma-203	242	29	:	:	PUNCT
ma-203	242	30	dxj(t	dxj(t	X
ma-203	242	31	)	)	PUNCT
ma-203	242	32	=	=	PUNCT
ma-203	243	1	αxj(t)dt	αxj(t)dt	X
ma-203	243	2	+	+	NUM
ma-203	243	3	dwh	dwh	PROPN
ma-203	243	4	j	j	PROPN
ma-203	243	5	(	(	PUNCT
ma-203	243	6	t	t	PROPN
ma-203	243	7	)	)	PUNCT
ma-203	243	8	,	,	PUNCT
ma-203	243	9	j	j	PROPN
ma-203	244	1	=	=	SYM
ma-203	244	2	1	1	NUM
ma-203	244	3	,	,	PUNCT
ma-203	244	4	2	2	NUM
ma-203	244	5	,	,	PUNCT
ma-203	244	6	·	·	PUNCT
ma-203	244	7	·	·	PUNCT
ma-203	244	8	·	·	PUNCT
ma-203	244	9	,	,	PUNCT
ma-203	244	10	n	n	X
ma-203	244	11	(	(	PUNCT
ma-203	244	12	3.8)first	3.8)first	PROPN
ma-203	244	13	consider	consider	VERB
ma-203	244	14	the	the	DET
ma-203	244	15	fcir	fcir	NOUN
ma-203	244	16	model	model	NOUN
ma-203	244	17	d	d	PROPN
ma-203	244	18	yj(t	yj(t	PROPN
ma-203	244	19	)	)	PUNCT
ma-203	245	1	=	=	SYM
ma-203	246	1	a(b	a(b	ADP
ma-203	246	2	−	−	NUM
ma-203	246	3	yj(t))dt	yj(t))dt	PROPN
ma-203	246	4	+	+	CCONJ
ma-203	246	5	σ	σ	PROPN
ma-203	246	6	√	√	NUM
ma-203	246	7	yj(t)dw	yj(t)dw	PROPN
ma-203	246	8	h	h	PROPN
ma-203	246	9	j	j	PROPN
ma-203	246	10	(	(	PUNCT
ma-203	246	11	t	t	PROPN
ma-203	246	12	)	)	PUNCT
ma-203	246	13	,	,	PUNCT
ma-203	246	14	j	j	PROPN
ma-203	246	15	=	=	SYM
ma-203	246	16	1	1	NUM
ma-203	246	17	,	,	PUNCT
ma-203	246	18	2	2	NUM
ma-203	246	19	,	,	PUNCT
ma-203	246	20	·	·	PUNCT
ma-203	246	21	·	·	PUNCT
ma-203	246	22	·	·	PUNCT
ma-203	246	23	,	,	PUNCT
ma-203	246	24	n	n	X
ma-203	246	25	(	(	PUNCT
ma-203	246	26	3.9	3.9	NUM
ma-203	246	27	)	)	PUNCT
ma-203	246	28	where	where	SCONJ
ma-203	246	29	wh	wh	VERB
ma-203	246	30	j	j	PROPN
ma-203	246	31	(	(	PUNCT
ma-203	246	32	t	t	PROPN
ma-203	246	33	)	)	PUNCT
ma-203	246	34	is	be	AUX
ma-203	246	35	a	a	DET
ma-203	246	36	fractional	fractional	ADJ
ma-203	246	37	brownian	brownian	ADJ
ma-203	246	38	motion	motion	NOUN
ma-203	246	39	with	with	ADP
ma-203	246	40	hurst	hurst	PROPN
ma-203	246	41	parameter	parameter	PROPN
ma-203	246	42	h	h	PROPN
ma-203	246	43	>	>	X
ma-203	246	44	1/2.then	1/2.then	NUM
ma-203	246	45	by	by	ADP
ma-203	246	46	proposition	proposition	NOUN
ma-203	246	47	5.7	5.7	NUM
ma-203	246	48	of	of	ADP
ma-203	246	49	buchmann	buchmann	PROPN
ma-203	246	50	and	and	CCONJ
ma-203	246	51	kluppelberg	kluppelberg	PROPN
ma-203	246	52	[	[	X
ma-203	246	53	15	15	NUM
ma-203	246	54	]	]	PUNCT
ma-203	246	55	,	,	PUNCT
ma-203	246	56	we	we	PRON
ma-203	246	57	have	have	VERB
ma-203	246	58	yj(t	yj(t	X
ma-203	246	59	)	)	PUNCT
ma-203	246	60	=	=	SYM
ma-203	246	61	s(xj(t	s(xj(t	PROPN
ma-203	246	62	)	)	PUNCT
ma-203	246	63	)	)	PUNCT
ma-203	246	64	(	(	PUNCT
ma-203	246	65	3.10	3.10	NUM
ma-203	246	66	)	)	PUNCT
ma-203	246	67	where	where	SCONJ
ma-203	246	68	dxj(t	dxj(t	X
ma-203	246	69	)	)	PUNCT
ma-203	247	1	=	=	SYM
ma-203	247	2	a(b	a(b	ADJ
ma-203	247	3	−xj(t))dt	−xj(t))dt	NOUN
ma-203	247	4	+	+	CCONJ
ma-203	247	5	dwh	dwh	PROPN
ma-203	247	6	j	j	PROPN
ma-203	247	7	(	(	PUNCT
ma-203	247	8	t	t	PROPN
ma-203	247	9	)	)	PUNCT
ma-203	247	10	,	,	PUNCT
ma-203	247	11	xj(0	xj(0	PROPN
ma-203	247	12	)	)	PUNCT
ma-203	247	13	=	=	SYM
ma-203	247	14	s−1(yj(0	s−1(yj(0	PROPN
ma-203	247	15	)	)	PUNCT
ma-203	247	16	)	)	PUNCT
ma-203	247	17	,	,	PUNCT
ma-203	247	18	t	t	PROPN
ma-203	247	19	∈	∈	PROPN
ma-203	248	1	[	[	X
ma-203	248	2	0	0	NUM
ma-203	248	3	,	,	PUNCT
ma-203	248	4	t	t	X
ma-203	248	5	]	]	PUNCT
ma-203	248	6	,	,	PUNCT
ma-203	248	7	j	j	PROPN
ma-203	248	8	=	=	SYM
ma-203	248	9	1	1	NUM
ma-203	248	10	,	,	PUNCT
ma-203	248	11	2	2	NUM
ma-203	248	12	,	,	PUNCT
ma-203	248	13	·	·	PUNCT
ma-203	248	14	·	·	PUNCT
ma-203	248	15	·	·	PUNCT
ma-203	248	16	,	,	PUNCT
ma-203	248	17	n	n	X
ma-203	248	18	(	(	PUNCT
ma-203	248	19	3.11	3.11	NUM
ma-203	248	20	)	)	PUNCT
ma-203	248	21	and	and	CCONJ
ma-203	248	22	s(x	s(x	NOUN
ma-203	248	23	)	)	PUNCT
ma-203	248	24	=	=	PUNCT
ma-203	249	1	sgn(x)σ2x2/4	sgn(x)σ2x2/4	PROPN
ma-203	249	2	.	.	PUNCT
ma-203	250	1	here	here	ADV
ma-203	250	2	s	s	VERB
ma-203	250	3	is	be	AUX
ma-203	250	4	the	the	DET
ma-203	250	5	state	state	NOUN
ma-203	250	6	space	space	NOUN
ma-203	250	7	transform.let	transform.let	X
ma-203	250	8	b	b	NOUN
ma-203	250	9	=	=	SYM
ma-203	250	10	0	0	PROPN
ma-203	250	11	,	,	PUNCT
ma-203	250	12	σ	σ	NOUN
ma-203	250	13	=	=	SYM
ma-203	250	14	1	1	NUM
ma-203	250	15	and	and	CCONJ
ma-203	250	16	a	a	DET
ma-203	250	17	>	>	X
ma-203	250	18	0	0	NUM
ma-203	250	19	.	.	PUNCT
ma-203	251	1	then	then	ADV
ma-203	251	2	xj(t	xj(t	PUNCT
ma-203	251	3	)	)	PUNCT
ma-203	251	4	is	be	AUX
ma-203	251	5	described	describe	VERB
ma-203	251	6	by	by	ADP
ma-203	251	7	the	the	DET
ma-203	251	8	ornstein	ornstein	PROPN
ma-203	251	9	-	-	PUNCT
ma-203	251	10	uhlenbeck	uhlenbeck	PROPN
ma-203	251	11	sdes	sde	NOUN
ma-203	251	12	dxj(t	dxj(t	PROPN
ma-203	251	13	)	)	PUNCT
ma-203	252	1	=	=	SYM
ma-203	253	1	−axj(t)dt	−axj(t)dt	PROPN
ma-203	253	2	+	+	NUM
ma-203	253	3	dwh	dwh	PROPN
ma-203	253	4	j	j	PROPN
ma-203	253	5	(	(	PUNCT
ma-203	253	6	t	t	PROPN
ma-203	253	7	)	)	PUNCT
ma-203	253	8	,	,	PUNCT
ma-203	253	9	xj(0	xj(0	PROPN
ma-203	253	10	)	)	PUNCT
ma-203	253	11	=	=	SYM
ma-203	253	12	s−1(yj(0	s−1(yj(0	PROPN
ma-203	253	13	)	)	PUNCT
ma-203	253	14	)	)	PUNCT
ma-203	253	15	,	,	PUNCT
ma-203	253	16	j	j	PROPN
ma-203	253	17	=	=	SYM
ma-203	253	18	1	1	NUM
ma-203	253	19	,	,	PUNCT
ma-203	253	20	2	2	NUM
ma-203	253	21	,	,	PUNCT
ma-203	253	22	·	·	PUNCT
ma-203	253	23	·	·	PUNCT
ma-203	253	24	·	·	PUNCT
ma-203	253	25	,	,	PUNCT
ma-203	253	26	n	n	X
ma-203	253	27	(	(	PUNCT
ma-203	253	28	3.12	3.12	NUM
ma-203	253	29	)	)	PUNCT
ma-203	253	30	consider	consider	VERB
ma-203	253	31	the	the	DET
ma-203	253	32	model	model	NOUN
ma-203	253	33	of	of	ADP
ma-203	253	34	n	n	DET
ma-203	253	35	interacting	interact	VERB
ma-203	253	36	particles	particle	NOUN
ma-203	253	37	of	of	ADP
ma-203	253	38	fractional	fractional	ADJ
ma-203	253	39	diffusions	diffusion	NOUN
ma-203	253	40	satisfying	satisfy	VERB
ma-203	253	41	the	the	DET
ma-203	253	42	itô	itô	PROPN
ma-203	253	43	stochasticdifferential	stochasticdifferential	ADJ
ma-203	253	44	equations	equation	NOUN
ma-203	253	45	dxj(t	dxj(t	PROPN
ma-203	253	46	)	)	PUNCT
ma-203	254	1	=	=	PUNCT
ma-203	254	2	p∑	p∑	PRON
ma-203	255	1	l=1	l=1	X
ma-203	255	2	θlµj	θlµj	VERB
ma-203	255	3	l(x(t	l(x(t	PROPN
ma-203	255	4	)	)	PUNCT
ma-203	255	5	)	)	PUNCT
ma-203	256	1	+	+	CCONJ
ma-203	256	2	σj(x(t))dwh	σj(x(t))dwh	PROPN
ma-203	256	3	j	j	PROPN
ma-203	256	4	(	(	PUNCT
ma-203	256	5	t	t	PROPN
ma-203	256	6	)	)	PUNCT
ma-203	256	7	,	,	PUNCT
ma-203	256	8	j	j	PROPN
ma-203	256	9	=	=	SYM
ma-203	256	10	1	1	NUM
ma-203	256	11	,	,	PUNCT
ma-203	256	12	2	2	NUM
ma-203	256	13	,	,	PUNCT
ma-203	256	14	·	·	PUNCT
ma-203	256	15	·	·	PUNCT
ma-203	256	16	·	·	PUNCT
ma-203	256	17	,	,	PUNCT
ma-203	256	18	n	n	X
ma-203	256	19	(	(	PUNCT
ma-203	256	20	3.13	3.13	NUM
ma-203	256	21	)	)	PUNCT
ma-203	256	22	where	where	SCONJ
ma-203	256	23	x(t	x(t	PROPN
ma-203	256	24	)	)	PUNCT
ma-203	256	25	=	=	SYM
ma-203	256	26	(	(	PUNCT
ma-203	256	27	x1(t	x1(t	PROPN
ma-203	256	28	)	)	PUNCT
ma-203	256	29	,	,	PUNCT
ma-203	256	30	x2(t	x2(t	PROPN
ma-203	256	31	)	)	PUNCT
ma-203	256	32	,	,	PUNCT
ma-203	256	33	·	·	PUNCT
ma-203	256	34	·	·	PUNCT
ma-203	256	35	·	·	PUNCT
ma-203	256	36	,	,	PUNCT
ma-203	256	37	xn(t))′	xn(t))′	PROPN
ma-203	256	38	and	and	CCONJ
ma-203	256	39	(	(	PUNCT
ma-203	256	40	wh	wh	PROPN
ma-203	256	41	j	j	PROPN
ma-203	256	42	(	(	PUNCT
ma-203	256	43	t	t	PROPN
ma-203	256	44	)	)	PUNCT
ma-203	256	45	;	;	PUNCT
ma-203	256	46	t	t	PROPN
ma-203	256	47	≥	≥	PROPN
ma-203	256	48	0	0	NUM
ma-203	256	49	)	)	PUNCT
ma-203	256	50	,	,	PUNCT
ma-203	256	51	j	j	PROPN
ma-203	256	52	=	=	SYM
ma-203	256	53	1	1	NUM
ma-203	256	54	,	,	PUNCT
ma-203	256	55	2	2	NUM
ma-203	256	56	,	,	PUNCT
ma-203	256	57	·	·	PUNCT
ma-203	256	58	·	·	PUNCT
ma-203	256	59	·	·	PUNCT
ma-203	256	60	,	,	PUNCT
ma-203	256	61	n	n	PRON
ma-203	256	62	are	be	AUX
ma-203	256	63	independentfractional	independentfractional	ADJ
ma-203	256	64	wiener	wiener	NOUN
ma-203	256	65	processes	process	NOUN
ma-203	256	66	.	.	PUNCT
ma-203	257	1	here	here	ADV
ma-203	257	2	θl	θl	ADP
ma-203	257	3	(	(	PUNCT
ma-203	257	4	·	·	PUNCT
ma-203	257	5	)	)	PUNCT
ma-203	257	6	∈	∈	PROPN
ma-203	257	7	l2([0	l2([0	PROPN
ma-203	257	8	,	,	PUNCT
ma-203	257	9	t	t	X
ma-203	257	10	]	]	PUNCT
ma-203	257	11	,	,	PUNCT
ma-203	257	12	dt	dt	PROPN
ma-203	257	13	)	)	PUNCT
ma-203	257	14	,	,	PUNCT
ma-203	257	15	l	l	NOUN
ma-203	257	16	=	=	SYM
ma-203	257	17	1	1	NUM
ma-203	257	18	,	,	PUNCT
ma-203	257	19	.	.	PUNCT
ma-203	257	20	.	.	PUNCT
ma-203	257	21	.	.	PUNCT
ma-203	258	1	,	,	PUNCT
ma-203	258	2	p	p	NOUN
ma-203	258	3	are	be	AUX
ma-203	258	4	unknown	unknown	ADJ
ma-203	258	5	functions	function	NOUN
ma-203	258	6	to	to	PART
ma-203	258	7	beestimated	beestimate	VERB
ma-203	258	8	based	base	VERB
ma-203	258	9	on	on	ADP
ma-203	258	10	observation	observation	NOUN
ma-203	258	11	of	of	ADP
ma-203	258	12	the	the	DET
ma-203	258	13	process	process	NOUN
ma-203	258	14	x	x	PUNCT
ma-203	258	15	in	in	ADP
ma-203	258	16	the	the	DET
ma-203	258	17	time	time	NOUN
ma-203	258	18	interval	interval	NOUN
ma-203	258	19	[	[	X
ma-203	258	20	0	0	NUM
ma-203	258	21	,	,	PUNCT
ma-203	258	22	t	t	X
ma-203	258	23	]	]	PUNCT
ma-203	258	24	.	.	PUNCT
ma-203	259	1	let	let	VERB
ma-203	259	2	θ	θ	NOUN
ma-203	259	3	=	=	SYM
ma-203	259	4	(	(	PUNCT
ma-203	259	5	θ1	θ1	PROPN
ma-203	259	6	,	,	PUNCT
ma-203	259	7	θ2	θ2	PROPN
ma-203	259	8	,	,	PUNCT
ma-203	259	9	.	.	PUNCT
ma-203	259	10	.	.	PUNCT
ma-203	260	1	.	.	PUNCT
ma-203	261	1	,	,	PUNCT
ma-203	261	2	θp)and	θp)and	CCONJ
ma-203	261	3	µj(x	µj(x	PUNCT
ma-203	261	4	)	)	PUNCT
ma-203	262	1	=	=	SYM
ma-203	262	2	(	(	PUNCT
ma-203	262	3	µj1(x	µj1(x	NOUN
ma-203	262	4	)	)	PUNCT
ma-203	262	5	,	,	PUNCT
ma-203	262	6	µj2(x	µj2(x	PROPN
ma-203	262	7	)	)	PUNCT
ma-203	262	8	,	,	PUNCT
ma-203	262	9	.	.	PUNCT
ma-203	262	10	.	.	PUNCT
ma-203	263	1	.	.	PUNCT
ma-203	264	1	,	,	PUNCT
ma-203	264	2	µjp(x))′.	µjp(x))′.	PROPN
ma-203	264	3	the	the	DET
ma-203	264	4	processes	process	NOUN
ma-203	264	5	xj(t	xj(t	PUNCT
ma-203	264	6	)	)	PUNCT
ma-203	264	7	,	,	PUNCT
ma-203	264	8	j	j	PROPN
ma-203	264	9	=	=	SYM
ma-203	264	10	1	1	NUM
ma-203	264	11	,	,	PUNCT
ma-203	264	12	2	2	NUM
ma-203	264	13	,	,	PUNCT
ma-203	264	14	·	·	PUNCT
ma-203	264	15	·	·	PUNCT
ma-203	264	16	·	·	PUNCT
ma-203	264	17	,	,	PUNCT
ma-203	264	18	n	n	PRON
ma-203	264	19	are	be	AUX
ma-203	264	20	observed	observe	VERB
ma-203	264	21	on	on	ADP
ma-203	264	22	[	[	X
ma-203	264	23	0	0	NUM
ma-203	264	24	,	,	PUNCT
ma-203	264	25	t	t	X
ma-203	264	26	]	]	PUNCT
ma-203	264	27	.the	.the	DET
ma-203	264	28	functions	function	NOUN
ma-203	264	29	µj	µj	INTJ
ma-203	264	30	,	,	PUNCT
ma-203	264	31	σj	σj	ADJ
ma-203	264	32	;	;	PUNCT
ma-203	264	33	j	j	PROPN
ma-203	264	34	=	=	SYM
ma-203	264	35	1	1	NUM
ma-203	264	36	,	,	PUNCT
ma-203	264	37	2	2	NUM
ma-203	264	38	,	,	PUNCT
ma-203	264	39	·	·	PUNCT
ma-203	264	40	·	·	PUNCT
ma-203	264	41	·	·	PUNCT
ma-203	264	42	,	,	PUNCT
ma-203	264	43	n	n	PRON
ma-203	264	44	are	be	AUX
ma-203	264	45	assumed	assume	VERB
ma-203	264	46	to	to	PART
ma-203	264	47	be	be	AUX
ma-203	264	48	known	know	VERB
ma-203	264	49	such	such	ADJ
ma-203	264	50	that	that	SCONJ
ma-203	264	51	the	the	DET
ma-203	264	52	system	system	NOUN
ma-203	264	53	has	have	VERB
ma-203	264	54	a	a	DET
ma-203	264	55	uniquesolution	uniquesolution	NOUN
ma-203	264	56	.	.	PUNCT
ma-203	265	1	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	265	2	eur	eur	PROPN
ma-203	265	3	.	.	PUNCT
ma-203	266	1	j.	j.	PROPN
ma-203	266	2	math	math	PROPN
ma-203	266	3	.	.	PUNCT
ma-203	267	1	anal	anal	PROPN
ma-203	267	2	.	.	PUNCT
ma-203	268	1	10.28924	10.28924	NUM
ma-203	268	2	/	/	SYM
ma-203	268	3	ada	ada	NOUN
ma-203	268	4	/	/	SYM
ma-203	268	5	ma.4.12	ma.4.12	NOUN
ma-203	268	6	11we	11we	NOUN
ma-203	268	7	need	need	VERB
ma-203	268	8	the	the	DET
ma-203	268	9	following	following	ADJ
ma-203	268	10	assumption	assumption	NOUN
ma-203	268	11	and	and	CCONJ
ma-203	268	12	results	result	NOUN
ma-203	268	13	to	to	PART
ma-203	268	14	prove	prove	VERB
ma-203	268	15	the	the	DET
ma-203	268	16	main	main	ADJ
ma-203	268	17	results	result	NOUN
ma-203	268	18	.	.	PUNCT
ma-203	269	1	(	(	PUNCT
ma-203	269	2	a0	a0	NOUN
ma-203	269	3	)	)	PUNCT
ma-203	269	4	suppose	suppose	VERB
ma-203	269	5	that	that	SCONJ
ma-203	269	6	bj	bj	VERB
ma-203	269	7	l	l	NOUN
ma-203	269	8	:	:	PUNCT
ma-203	270	1	=	=	SYM
ma-203	270	2	µj	µj	X
ma-203	270	3	l(s)σ−1	l(s)σ−1	PROPN
ma-203	270	4	j	j	PROPN
ma-203	270	5	(	(	PUNCT
ma-203	270	6	s	s	PROPN
ma-203	270	7	)	)	PUNCT
ma-203	270	8	;	;	PUNCT
ma-203	270	9	j	j	PROPN
ma-203	270	10	=	=	SYM
ma-203	270	11	1	1	NUM
ma-203	270	12	,	,	PUNCT
ma-203	270	13	2	2	NUM
ma-203	270	14	,	,	PUNCT
ma-203	270	15	·	·	PUNCT
ma-203	270	16	·	·	PUNCT
ma-203	270	17	·	·	PUNCT
ma-203	270	18	,	,	PUNCT
ma-203	270	19	n	n	CCONJ
ma-203	270	20	;	;	PUNCT
ma-203	270	21	l	l	NOUN
ma-203	270	22	=	=	SYM
ma-203	270	23	1	1	NUM
ma-203	270	24	,	,	PUNCT
ma-203	270	25	2	2	NUM
ma-203	270	26	.	.	PUNCT
ma-203	270	27	.	.	PUNCT
ma-203	270	28	.	.	PUNCT
ma-203	271	1	,	,	PUNCT
ma-203	271	2	p	p	NOUN
ma-203	271	3	are	be	AUX
ma-203	271	4	measurable	measurable	ADJ
ma-203	271	5	and	and	CCONJ
ma-203	271	6	adaptedprocesses	adaptedprocesse	NOUN
ma-203	271	7	satisfying	satisfy	VERB
ma-203	271	8	1	1	NUM
ma-203	271	9	n	n	NOUN
ma-203	272	1	n∑	n∑	NOUN
ma-203	272	2	j=1	j=1	ADJ
ma-203	272	3	∫	∫	PROPN
ma-203	272	4	t	t	NOUN
ma-203	272	5	0	0	NUM
ma-203	272	6	bj	bj	NOUN
ma-203	272	7	l(s)bjm(s)ds	l(s)bjm(s)ds	X
ma-203	272	8	→	→	SYM
ma-203	272	9	clm(t	clm(t	PROPN
ma-203	272	10	)	)	PUNCT
ma-203	272	11	a.s	a.s	PROPN
ma-203	272	12	.	.	PROPN
ma-203	272	13	as	as	ADP
ma-203	272	14	n	n	PROPN
ma-203	272	15	→∞	→∞	PROPN
ma-203	272	16	l	l	NOUN
ma-203	272	17	,	,	PUNCT
ma-203	272	18	m	m	VERB
ma-203	272	19	=	=	NOUN
ma-203	272	20	1	1	NUM
ma-203	272	21	,	,	PUNCT
ma-203	272	22	2	2	NUM
ma-203	272	23	.	.	PUNCT
ma-203	272	24	.	.	PUNCT
ma-203	272	25	.	.	PUNCT
ma-203	273	1	,	,	PUNCT
ma-203	273	2	p	p	X
ma-203	273	3	where	where	SCONJ
ma-203	273	4	clm(t	clm(t	PROPN
ma-203	273	5	)	)	PUNCT
ma-203	273	6	are	be	AUX
ma-203	273	7	finite	finite	ADJ
ma-203	273	8	and	and	CCONJ
ma-203	273	9	continuous	continuous	ADJ
ma-203	273	10	nonrandom	nonrandom	NOUN
ma-203	273	11	functions	function	NOUN
ma-203	273	12	of	of	ADP
ma-203	273	13	t	t	PROPN
ma-203	273	14	∈	∈	PROPN
ma-203	274	1	[	[	X
ma-203	274	2	0	0	NUM
ma-203	274	3	,	,	PUNCT
ma-203	274	4	t	t	X
ma-203	274	5	]	]	PUNCT
ma-203	274	6	.	.	PUNCT
ma-203	275	1	thelimiting	thelimite	VERB
ma-203	275	2	matrix	matrix	NOUN
ma-203	275	3	i(t	i(t	NOUN
ma-203	275	4	)	)	PUNCT
ma-203	276	1	=	=	PUNCT
ma-203	276	2	(	(	PUNCT
ma-203	276	3	clm(t))l	clm(t))l	INTJ
ma-203	276	4	,	,	PUNCT
ma-203	276	5	m=1,2	m=1,2	NUM
ma-203	276	6	...	...	PUNCT
ma-203	276	7	,p	,p	PUNCT
ma-203	276	8	is	be	AUX
ma-203	276	9	positive	positive	ADJ
ma-203	276	10	definite	definite	ADJ
ma-203	276	11	,	,	PUNCT
ma-203	276	12	δ′i(t)δ	δ′i(t)δ	NOUN
ma-203	276	13	is	be	AUX
ma-203	276	14	increasing	increase	VERB
ma-203	276	15	for	for	ADP
ma-203	276	16	all	all	PRON
ma-203	276	17	δ	δ	PROPN
ma-203	276	18	∈	∈	PROPN
ma-203	276	19	rpand	rpand	PROPN
ma-203	276	20	i(0	i(0	PROPN
ma-203	276	21	)	)	PUNCT
ma-203	277	1	=	=	SYM
ma-203	277	2	0.in	0.in	NUM
ma-203	277	3	the	the	DET
ma-203	277	4	exchangeable	exchangeable	ADJ
ma-203	277	5	case	case	NOUN
ma-203	277	6	,	,	PUNCT
ma-203	277	7	(	(	PUNCT
ma-203	277	8	a0	a0	NOUN
ma-203	277	9	)	)	PUNCT
ma-203	277	10	follows	follow	VERB
ma-203	277	11	from	from	ADP
ma-203	277	12	mckean	mckean	ADJ
ma-203	277	13	-	-	PUNCT
ma-203	277	14	vlasov	vlasov	NOUN
ma-203	277	15	law	law	NOUN
ma-203	277	16	of	of	ADP
ma-203	277	17	large	large	ADJ
ma-203	277	18	numbers	number	NOUN
ma-203	277	19	.	.	PUNCT
ma-203	278	1	in	in	ADP
ma-203	278	2	particular,(a0	particular,(a0	X
ma-203	278	3	)	)	PUNCT
ma-203	278	4	will	will	AUX
ma-203	278	5	be	be	AUX
ma-203	278	6	satisfied	satisfied	ADJ
ma-203	278	7	when	when	SCONJ
ma-203	278	8	µj	µj	ADP
ma-203	278	9	l(x	l(x	PROPN
ma-203	278	10	)	)	PUNCT
ma-203	278	11	=	=	SYM
ma-203	278	12	µlxj	µlxj	NOUN
ma-203	278	13	and	and	CCONJ
ma-203	278	14	σj(x	σj(x	NOUN
ma-203	278	15	)	)	PUNCT
ma-203	279	1	=	=	SYM
ma-203	279	2	σ(xj	σ(xj	PROPN
ma-203	279	3	)	)	PUNCT
ma-203	279	4	which	which	PRON
ma-203	279	5	corresponds	correspond	VERB
ma-203	279	6	to	to	ADP
ma-203	279	7	the	the	DET
ma-203	279	8	independentreplicated	independentreplicate	VERB
ma-203	279	9	sampling	sampling	NOUN
ma-203	279	10	on	on	ADP
ma-203	279	11	[	[	X
ma-203	279	12	0	0	NUM
ma-203	279	13	,	,	PUNCT
ma-203	279	14	t	t	X
ma-203	279	15	]	]	PUNCT
ma-203	279	16	.	.	PUNCT
ma-203	280	1	see	see	VERB
ma-203	280	2	oelschlager	oelschlager	NOUN
ma-203	280	3	[	[	PRON
ma-203	280	4	29].we	29].we	NOUN
ma-203	280	5	also	also	ADV
ma-203	280	6	need	need	VERB
ma-203	280	7	the	the	DET
ma-203	280	8	following	follow	VERB
ma-203	280	9	version	version	NOUN
ma-203	280	10	of	of	ADP
ma-203	280	11	rebolledo	rebolledo	PROPN
ma-203	280	12	’s	’s	PART
ma-203	280	13	central	central	ADJ
ma-203	280	14	limit	limit	NOUN
ma-203	280	15	theorem	theorem	NOUN
ma-203	280	16	for	for	ADP
ma-203	280	17	martingales	martingale	NOUN
ma-203	280	18	,	,	PUNCT
ma-203	280	19	seerebolledo	seerebolledo	VERB
ma-203	280	20	[	[	X
ma-203	280	21	34	34	NUM
ma-203	280	22	]	]	X
ma-203	280	23	:	:	PUNCT
ma-203	280	24	theorem	theorem	VERB
ma-203	280	25	3.1	3.1	NUM
ma-203	280	26	let	let	VERB
ma-203	280	27	mn	mn	PROPN
ma-203	280	28	,	,	PUNCT
ma-203	280	29	n	n	PROPN
ma-203	280	30	∈	∈	PROPN
ma-203	280	31	z+	z+	PUNCT
ma-203	280	32	be	be	AUX
ma-203	280	33	a	a	DET
ma-203	280	34	sequence	sequence	NOUN
ma-203	280	35	of	of	ADP
ma-203	280	36	locally	locally	ADV
ma-203	280	37	square	square	ADJ
ma-203	280	38	integrable	integrable	ADJ
ma-203	280	39	martingales	martingale	NOUN
ma-203	280	40	with	with	ADP
ma-203	280	41	mn(0	mn(0	NOUN
ma-203	280	42	)	)	PUNCT
ma-203	280	43	=	=	SYM
ma-203	281	1	0	0	X
ma-203	281	2	.	.	PUNCT
ma-203	281	3	suppose	suppose	VERB
ma-203	281	4	the	the	DET
ma-203	281	5	following	follow	VERB
ma-203	281	6	condition	condition	NOUN
ma-203	281	7	holds	hold	VERB
ma-203	281	8	:	:	PUNCT
ma-203	281	9	∑	∑	PUNCT
ma-203	281	10	s≤t	s≤t	PROPN
ma-203	281	11	e{|∆mn(s)|2i(|∆mn(s)|	e{|∆mn(s)|2i(|∆mn(s)|	PROPN
ma-203	281	12	>	>	PUNCT
ma-203	281	13	ε	ε	PROPN
ma-203	281	14	)	)	PUNCT
ma-203	281	15	}	}	PUNCT
ma-203	281	16	→	→	SYM
ma-203	281	17	0	0	NUM
ma-203	281	18	for	for	ADP
ma-203	281	19	all	all	DET
ma-203	281	20	t	t	NOUN
ma-203	281	21	∈	∈	PROPN
ma-203	282	1	[	[	X
ma-203	282	2	0	0	NUM
ma-203	282	3	,	,	PUNCT
ma-203	282	4	t	t	X
ma-203	282	5	]	]	PUNCT
ma-203	282	6	,	,	PUNCT
ma-203	282	7	ε	ε	PROPN
ma-203	282	8	>	>	X
ma-203	282	9	0	0	NUM
ma-203	282	10	;	;	PUNCT
ma-203	282	11	and	and	CCONJ
ma-203	282	12	〈	〈	PROPN
ma-203	282	13	mn〉(t)→	mn〉(t)→	ADJ
ma-203	282	14	c(t	c(t	PROPN
ma-203	282	15	)	)	PUNCT
ma-203	282	16	a.s	a.s	PROPN
ma-203	282	17	.	.	PROPN
ma-203	283	1	for	for	ADP
ma-203	283	2	all	all	DET
ma-203	283	3	t	t	NOUN
ma-203	283	4	∈	∈	PROPN
ma-203	284	1	[	[	X
ma-203	284	2	0	0	NUM
ma-203	284	3	,	,	PUNCT
ma-203	284	4	t	t	X
ma-203	284	5	]	]	PUNCT
ma-203	284	6	,	,	PUNCT
ma-203	284	7	where	where	SCONJ
ma-203	284	8	c(t	c(t	NOUN
ma-203	284	9	)	)	PUNCT
ma-203	284	10	is	be	AUX
ma-203	284	11	a	a	DET
ma-203	284	12	continuous	continuous	ADJ
ma-203	284	13	increasing	increase	VERB
ma-203	284	14	function	function	NOUN
ma-203	284	15	with	with	ADP
ma-203	284	16	c(0	c(0	NOUN
ma-203	284	17	)	)	PUNCT
ma-203	284	18	=	=	SYM
ma-203	284	19	0	0	X
ma-203	284	20	.	.	PUNCT
ma-203	285	1	then	then	ADV
ma-203	285	2	mn	mn	PROPN
ma-203	286	1	→d	→d	PROPN
ma-203	286	2	m	m	PROPN
ma-203	286	3	,	,	PUNCT
ma-203	286	4	a	a	DET
ma-203	286	5	continuous	continuous	ADJ
ma-203	286	6	gaussian	gaussian	ADJ
ma-203	286	7	martingale	martingale	NOUN
ma-203	286	8	with	with	ADP
ma-203	286	9	zero	zero	NUM
ma-203	286	10	mean	mean	NOUN
ma-203	286	11	and	and	CCONJ
ma-203	286	12	covariance	covariance	NOUN
ma-203	286	13	function	function	NOUN
ma-203	286	14	k(s	k(s	PROPN
ma-203	286	15	,	,	PUNCT
ma-203	286	16	t	t	PROPN
ma-203	286	17	)	)	PUNCT
ma-203	286	18	=	=	PUNCT
ma-203	287	1	c(s	c(s	PROPN
ma-203	287	2	∧	∧	PROPN
ma-203	287	3	t	t	PROPN
ma-203	287	4	)	)	PUNCT
ma-203	287	5	,	,	PUNCT
ma-203	287	6	s	s	PROPN
ma-203	287	7	,	,	PUNCT
ma-203	287	8	t	t	PROPN
ma-203	287	9	∈	∈	PROPN
ma-203	288	1	[	[	X
ma-203	288	2	0	0	NUM
ma-203	288	3	,	,	PUNCT
ma-203	288	4	t	t	NOUN
ma-203	288	5	]	]	PUNCT
ma-203	289	1	where	where	SCONJ
ma-203	289	2	∆ms	∆ms	ADP
ma-203	289	3	=	=	NOUN
ma-203	289	4	ms	ms	PROPN
ma-203	289	5	−ms−	−ms−	PROPN
ma-203	289	6	denotes	denote	VERB
ma-203	289	7	the	the	DET
ma-203	289	8	jump	jump	NOUN
ma-203	289	9	of	of	ADP
ma-203	289	10	m	m	NOUN
ma-203	289	11	at	at	ADP
ma-203	289	12	the	the	DET
ma-203	289	13	point	point	NOUN
ma-203	289	14	s.the	s.the	DET
ma-203	289	15	model	model	NOUN
ma-203	289	16	is	be	AUX
ma-203	289	17	given	give	VERB
ma-203	289	18	by	by	ADP
ma-203	289	19	dxj(t	dxj(t	PROPN
ma-203	289	20	)	)	PUNCT
ma-203	290	1	=	=	PUNCT
ma-203	290	2	p∑	p∑	ADJ
ma-203	291	1	l=1	l=1	X
ma-203	291	2	θlµj	θlµj	VERB
ma-203	291	3	l(x(t	l(x(t	PROPN
ma-203	291	4	)	)	PUNCT
ma-203	291	5	)	)	PUNCT
ma-203	292	1	+	+	CCONJ
ma-203	292	2	σj(x(t))dwh	σj(x(t))dwh	PROPN
ma-203	292	3	j	j	PROPN
ma-203	292	4	(	(	PUNCT
ma-203	292	5	t	t	PROPN
ma-203	292	6	)	)	PUNCT
ma-203	292	7	,	,	PUNCT
ma-203	292	8	j	j	PROPN
ma-203	292	9	=	=	SYM
ma-203	292	10	1	1	NUM
ma-203	292	11	,	,	PUNCT
ma-203	292	12	2	2	NUM
ma-203	292	13	,	,	PUNCT
ma-203	292	14	·	·	PUNCT
ma-203	292	15	·	·	PUNCT
ma-203	292	16	·	·	PUNCT
ma-203	292	17	,	,	PUNCT
ma-203	292	18	n	n	X
ma-203	292	19	(	(	PUNCT
ma-203	292	20	3.14	3.14	NUM
ma-203	292	21	)	)	PUNCT
ma-203	292	22	where	where	SCONJ
ma-203	292	23	x(t	x(t	PROPN
ma-203	292	24	)	)	PUNCT
ma-203	292	25	=	=	SYM
ma-203	292	26	(	(	PUNCT
ma-203	292	27	x1(t	x1(t	PROPN
ma-203	292	28	)	)	PUNCT
ma-203	292	29	,	,	PUNCT
ma-203	292	30	x2(t	x2(t	PROPN
ma-203	292	31	)	)	PUNCT
ma-203	292	32	,	,	PUNCT
ma-203	292	33	·	·	PUNCT
ma-203	292	34	·	·	PUNCT
ma-203	292	35	·	·	PUNCT
ma-203	292	36	,	,	PUNCT
ma-203	292	37	xn(t))′	xn(t))′	PROPN
ma-203	292	38	and	and	CCONJ
ma-203	292	39	(	(	PUNCT
ma-203	292	40	wh	wh	PROPN
ma-203	292	41	j	j	PROPN
ma-203	292	42	(	(	PUNCT
ma-203	292	43	t	t	PROPN
ma-203	292	44	)	)	PUNCT
ma-203	292	45	;	;	PUNCT
ma-203	292	46	t	t	PROPN
ma-203	292	47	≥	≥	PROPN
ma-203	292	48	0	0	NUM
ma-203	292	49	)	)	PUNCT
ma-203	292	50	,	,	PUNCT
ma-203	292	51	j	j	PROPN
ma-203	292	52	=	=	SYM
ma-203	292	53	1	1	NUM
ma-203	292	54	,	,	PUNCT
ma-203	292	55	2	2	NUM
ma-203	292	56	,	,	PUNCT
ma-203	292	57	·	·	PUNCT
ma-203	292	58	·	·	PUNCT
ma-203	292	59	·	·	PUNCT
ma-203	292	60	,	,	PUNCT
ma-203	292	61	n	n	PRON
ma-203	292	62	are	be	AUX
ma-203	292	63	independentfractional	independentfractional	ADJ
ma-203	292	64	wiener	wiener	NOUN
ma-203	292	65	processes	process	NOUN
ma-203	292	66	.	.	PUNCT
ma-203	293	1	here	here	ADV
ma-203	293	2	θ	θ	X
ma-203	293	3	=	=	SYM
ma-203	293	4	(	(	PUNCT
ma-203	293	5	θ1	θ1	PROPN
ma-203	293	6	,	,	PUNCT
ma-203	293	7	θ2	θ2	PROPN
ma-203	293	8	,	,	PUNCT
ma-203	293	9	.	.	PUNCT
ma-203	293	10	.	.	PUNCT
ma-203	294	1	.	.	PUNCT
ma-203	295	1	,	,	PUNCT
ma-203	295	2	θp	θp	ADP
ma-203	295	3	)	)	PUNCT
ma-203	295	4	is	be	AUX
ma-203	295	5	the	the	DET
ma-203	295	6	unknown	unknown	ADJ
ma-203	295	7	parameter	parameter	NOUN
ma-203	295	8	.	.	PUNCT
ma-203	296	1	the	the	DET
ma-203	296	2	functions	function	NOUN
ma-203	296	3	µj	µj	ADP
ma-203	296	4	l	l	NOUN
ma-203	296	5	,	,	PUNCT
ma-203	296	6	σj	σj	VERB
ma-203	296	7	,	,	PUNCT
ma-203	296	8	j	j	PROPN
ma-203	296	9	=	=	SYM
ma-203	296	10	1	1	NUM
ma-203	296	11	,	,	PUNCT
ma-203	296	12	.	.	PUNCT
ma-203	296	13	.	.	PUNCT
ma-203	297	1	.	.	PUNCT
ma-203	298	1	,	,	PUNCT
ma-203	298	2	n	n	CCONJ
ma-203	298	3	;	;	PUNCT
ma-203	298	4	l	l	NOUN
ma-203	298	5	=	=	SYM
ma-203	298	6	1	1	NUM
ma-203	298	7	,	,	PUNCT
ma-203	298	8	.	.	PUNCT
ma-203	298	9	.	.	PUNCT
ma-203	298	10	.	.	PUNCT
ma-203	299	1	,	,	PUNCT
ma-203	299	2	p	p	NOUN
ma-203	299	3	are	be	AUX
ma-203	299	4	assumed	assume	VERB
ma-203	299	5	to	to	PART
ma-203	299	6	be	be	AUX
ma-203	299	7	known	know	VERB
ma-203	299	8	such	such	ADJ
ma-203	299	9	that	that	SCONJ
ma-203	299	10	there	there	PRON
ma-203	299	11	exists	exist	VERB
ma-203	299	12	a	a	DET
ma-203	299	13	unique	unique	ADJ
ma-203	299	14	solution	solution	NOUN
ma-203	299	15	x(t	x(t	PROPN
ma-203	299	16	)	)	PUNCT
ma-203	299	17	to	to	ADP
ma-203	299	18	the	the	PRON
ma-203	299	19	above	above	ADJ
ma-203	299	20	sde.our	sde.our	NUM
ma-203	299	21	aim	aim	NOUN
ma-203	299	22	is	be	AUX
ma-203	299	23	to	to	PART
ma-203	299	24	estimate	estimate	VERB
ma-203	299	25	the	the	DET
ma-203	299	26	parameter	parameter	NOUN
ma-203	299	27	θ	θ	PROPN
ma-203	299	28	based	base	VERB
ma-203	299	29	on	on	ADP
ma-203	299	30	n	n	PRON
ma-203	299	31	particles	particle	NOUN
ma-203	299	32	q1	q1	PROPN
ma-203	299	33	(	(	PUNCT
ma-203	299	34	·	·	PUNCT
ma-203	299	35	)	)	PUNCT
ma-203	299	36	,	,	PUNCT
ma-203	299	37	q2	q2	NOUN
ma-203	299	38	(	(	PUNCT
ma-203	299	39	·	·	PUNCT
ma-203	299	40	)	)	PUNCT
ma-203	299	41	,	,	PUNCT
ma-203	299	42	·	·	PUNCT
ma-203	299	43	·	·	PUNCT
ma-203	299	44	·	·	PUNCT
ma-203	299	45	,	,	PUNCT
ma-203	299	46	qn	qn	INTJ
ma-203	299	47	(	(	PUNCT
ma-203	299	48	·	·	PUNCT
ma-203	299	49	)	)	PUNCT
ma-203	299	50	of	of	ADP
ma-203	299	51	q(t	q(t	NOUN
ma-203	299	52	)	)	PUNCT
ma-203	299	53	on	on	ADP
ma-203	299	54	[	[	X
ma-203	299	55	0	0	NUM
ma-203	299	56	,	,	PUNCT
ma-203	299	57	t	t	X
ma-203	299	58	]	]	PUNCT
ma-203	299	59	.	.	PUNCT
ma-203	300	1	we	we	PRON
ma-203	300	2	denote	denote	VERB
ma-203	300	3	this	this	DET
ma-203	300	4	data	datum	NOUN
ma-203	300	5	by	by	ADP
ma-203	300	6	qn	qn	PROPN
ma-203	300	7	,	,	PUNCT
ma-203	300	8	t	t	PROPN
ma-203	300	9	.the	.the	PUNCT
ma-203	300	10	radon	radon	PROPN
ma-203	300	11	-	-	PUNCT
ma-203	300	12	nikodym	nikodym	PROPN
ma-203	300	13	derivative	derivative	NOUN
ma-203	300	14	(	(	PUNCT
ma-203	300	15	likelihood	likelihood	NOUN
ma-203	300	16	)	)	PUNCT
ma-203	300	17	is	be	AUX
ma-203	300	18	given	give	VERB
ma-203	300	19	by	by	ADP
ma-203	300	20	λθn(qn	λθn(qn	PROPN
ma-203	300	21	,	,	PUNCT
ma-203	300	22	t	t	PROPN
ma-203	300	23	)	)	PUNCT
ma-203	300	24	:	:	PUNCT
ma-203	301	1	=	=	PUNCT
ma-203	301	2	dpθ	dpθ	NOUN
ma-203	301	3	dp0	dp0	PROPN
ma-203	301	4	(	(	PUNCT
ma-203	301	5	qn	qn	PROPN
ma-203	301	6	,	,	PUNCT
ma-203	301	7	t	t	NOUN
ma-203	301	8	)	)	PUNCT
ma-203	301	9	=	=	SYM
ma-203	301	10	exp	exp	NOUN
ma-203	301	11	{	{	PUNCT
ma-203	301	12	∑p	∑p	ADJ
ma-203	301	13	l=1	l=1	PROPN
ma-203	301	14	θl	θl	ADP
ma-203	301	15	∑n	∑n	PROPN
ma-203	301	16	j=1	j=1	PROPN
ma-203	301	17	∫	∫	PROPN
ma-203	301	18	t	t	PROPN
ma-203	301	19	0	0	NUM
ma-203	301	20	µj	µj	PROPN
ma-203	302	1	l(q(t))σ−2	l(q(t))σ−2	PROPN
ma-203	302	2	j	j	PROPN
ma-203	302	3	(	(	PUNCT
ma-203	302	4	q(t))dqj(t	q(t))dqj(t	PROPN
ma-203	302	5	)	)	PUNCT
ma-203	302	6	−1	−1	NOUN
ma-203	302	7	2	2	NUM
ma-203	302	8	∑p	∑p	ADJ
ma-203	302	9	l=1	l=1	PROPN
ma-203	303	1	∑p	∑p	ADJ
ma-203	303	2	m=1	m=1	PROPN
ma-203	303	3	θlθm	θlθm	NOUN
ma-203	304	1	∑n	∑n	PROPN
ma-203	304	2	j=1	j=1	PROPN
ma-203	304	3	∫	∫	PROPN
ma-203	304	4	t	t	PROPN
ma-203	304	5	0	0	NUM
ma-203	305	1	µj	µj	PROPN
ma-203	306	1	l(q(t))σ−2	l(q(t))σ−2	PROPN
ma-203	306	2	j	j	PROPN
ma-203	306	3	(	(	PUNCT
ma-203	306	4	q(t))µjm(q(t))dt	q(t))µjm(q(t))dt	NOUN
ma-203	306	5	}	}	PUNCT
ma-203	306	6	.	.	PUNCT
ma-203	307	1	(	(	PUNCT
ma-203	307	2	3.15	3.15	NUM
ma-203	307	3	)	)	PUNCT
ma-203	307	4	4	4	NUM
ma-203	307	5	.	.	NOUN
ma-203	307	6	approximate	approximate	ADJ
ma-203	307	7	maximum	maximum	ADJ
ma-203	307	8	likelihood	likelihood	NOUN
ma-203	307	9	estimation	estimation	NOUN
ma-203	307	10	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	NOUN
ma-203	307	11	eur	eur	PROPN
ma-203	307	12	.	.	PUNCT
ma-203	308	1	j.	j.	PROPN
ma-203	308	2	math	math	PROPN
ma-203	308	3	.	.	PUNCT
ma-203	309	1	anal	anal	PROPN
ma-203	309	2	.	.	PUNCT
ma-203	310	1	10.28924	10.28924	NUM
ma-203	310	2	/	/	SYM
ma-203	310	3	ada	ada	PROPN
ma-203	310	4	/	/	SYM
ma-203	310	5	ma.4.12	ma.4.12	PROPN
ma-203	310	6	12the	12the	ADP
ma-203	310	7	approximate	approximate	ADJ
ma-203	310	8	maximum	maximum	ADJ
ma-203	310	9	likelihood	likelihood	NOUN
ma-203	310	10	estimator	estimator	NOUN
ma-203	310	11	is	be	AUX
ma-203	310	12	defined	define	VERB
ma-203	310	13	as	as	ADP
ma-203	310	14	θ̂n	θ̂n	NUM
ma-203	310	15	=	=	PUNCT
ma-203	310	16	arg	arg	NOUN
ma-203	310	17	max	max	PROPN
ma-203	310	18	θ	θ	PROPN
ma-203	310	19	λθn(qn	λθn(qn	PROPN
ma-203	310	20	,	,	PUNCT
ma-203	310	21	t	t	PROPN
ma-203	310	22	)	)	PUNCT
ma-203	310	23	.extending	.extende	VERB
ma-203	311	1	kasonga	kasonga	NOUN
ma-203	312	1	[	[	X
ma-203	312	2	24	24	NUM
ma-203	312	3	]	]	PUNCT
ma-203	312	4	,	,	PUNCT
ma-203	312	5	using	use	VERB
ma-203	312	6	mckean	mckean	ADJ
ma-203	312	7	-	-	PUNCT
ma-203	312	8	vlasov	vlasov	NOUN
ma-203	312	9	law	law	NOUN
ma-203	312	10	of	of	ADP
ma-203	312	11	large	large	ADJ
ma-203	312	12	numbers	number	NOUN
ma-203	312	13	and	and	CCONJ
ma-203	312	14	rebolledo	rebolledo	PROPN
ma-203	312	15	’s	’s	PART
ma-203	312	16	centrallimit	centrallimit	NOUN
ma-203	312	17	theorem	theorem	NOUN
ma-203	312	18	for	for	ADP
ma-203	312	19	martingales	martingale	NOUN
ma-203	312	20	,	,	PUNCT
ma-203	312	21	we	we	PRON
ma-203	312	22	obtain	obtain	VERB
ma-203	312	23	the	the	DET
ma-203	312	24	consistency	consistency	NOUN
ma-203	312	25	and	and	CCONJ
ma-203	312	26	asymptotic	asymptotic	ADJ
ma-203	312	27	normality	normality	NOUN
ma-203	312	28	of	of	ADP
ma-203	312	29	the	the	DET
ma-203	312	30	approx	approx	PROPN
ma-203	312	31	-	-	PUNCT
ma-203	312	32	imate	imate	PROPN
ma-203	312	33	maximum	maximum	ADJ
ma-203	312	34	likelihood	likelihood	NOUN
ma-203	312	35	estimator	estimator	NOUN
ma-203	312	36	θ̂n	θ̂n	NUM
ma-203	312	37	which	which	PRON
ma-203	312	38	is	be	AUX
ma-203	312	39	given	give	VERB
ma-203	312	40	below	below	ADV
ma-203	312	41	:	:	PUNCT
ma-203	312	42	theorem	theorem	VERB
ma-203	312	43	4.1	4.1	NUM
ma-203	312	44	under	under	ADP
ma-203	312	45	(	(	PUNCT
ma-203	312	46	a0	a0	NOUN
ma-203	312	47	)	)	PUNCT
ma-203	312	48	,	,	PUNCT
ma-203	312	49	we	we	PRON
ma-203	312	50	have	have	VERB
ma-203	312	51	a	a	PRON
ma-203	312	52	)	)	PUNCT
ma-203	312	53	θ̂n	θ̂n	ADP
ma-203	312	54	→p	→p	PROPN
ma-203	312	55	θ	θ	PROPN
ma-203	312	56	as	as	ADP
ma-203	312	57	n	n	PROPN
ma-203	312	58	→∞.	→∞.	PROPN
ma-203	312	59	b	b	NOUN
ma-203	312	60	)	)	PUNCT
ma-203	312	61	√	√	PROPN
ma-203	312	62	n(θ̂n	n(θ̂n	NUM
ma-203	312	63	−	−	PROPN
ma-203	312	64	θ)→d	θ)→d	NOUN
ma-203	312	65	n	n	X
ma-203	312	66	(	(	PUNCT
ma-203	312	67	0	0	NUM
ma-203	312	68	,	,	PUNCT
ma-203	312	69	i−1(t	i−1(t	ADJ
ma-203	312	70	)	)	PUNCT
ma-203	312	71	)	)	PUNCT
ma-203	312	72	as	as	ADP
ma-203	312	73	n	n	PROPN
ma-203	312	74	→∞	→∞	PROPN
ma-203	312	75	where	where	SCONJ
ma-203	312	76	i(t	i(t	PROPN
ma-203	312	77	)	)	PUNCT
ma-203	312	78	is	be	AUX
ma-203	312	79	the	the	DET
ma-203	312	80	fisher	fisher	PROPN
ma-203	312	81	information	information	NOUN
ma-203	312	82	.	.	PUNCT
ma-203	313	1	5	5	X
ma-203	313	2	.	.	X
ma-203	313	3	berry	berry	VERB
ma-203	313	4	-	-	PUNCT
ma-203	313	5	esseen	esseen	VERB
ma-203	313	6	inequality	inequality	NOUN
ma-203	313	7	in	in	ADP
ma-203	313	8	this	this	DET
ma-203	313	9	section	section	NOUN
ma-203	313	10	we	we	PRON
ma-203	313	11	consider	consider	VERB
ma-203	313	12	the	the	DET
ma-203	313	13	case	case	NOUN
ma-203	313	14	h	h	NOUN
ma-203	313	15	=	=	SYM
ma-203	313	16	0.5	0.5	NUM
ma-203	313	17	and	and	CCONJ
ma-203	313	18	α	α	NOUN
ma-203	313	19	=	=	SYM
ma-203	313	20	2	2	NUM
ma-203	313	21	,	,	PUNCT
ma-203	313	22	i.e.	i.e.	X
ma-203	313	23	,	,	PUNCT
ma-203	313	24	the	the	DET
ma-203	313	25	standard	standard	ADJ
ma-203	313	26	brownian	brownian	ADJ
ma-203	313	27	motion	motion	NOUN
ma-203	313	28	case	case	NOUN
ma-203	313	29	.	.	PUNCT
ma-203	314	1	dxj(t	dxj(t	X
ma-203	314	2	)	)	PUNCT
ma-203	314	3	=	=	SYM
ma-203	315	1	fj(θ	fj(θ	NOUN
ma-203	315	2	,	,	PUNCT
ma-203	315	3	x(t	x(t	PROPN
ma-203	315	4	)	)	PUNCT
ma-203	315	5	)	)	PUNCT
ma-203	316	1	+	+	CCONJ
ma-203	316	2	σj(x(t))dwj(t	σj(x(t))dwj(t	NOUN
ma-203	316	3	)	)	PUNCT
ma-203	316	4	,	,	PUNCT
ma-203	316	5	xj(0	xj(0	PROPN
ma-203	316	6	)	)	PUNCT
ma-203	316	7	=	=	PUNCT
ma-203	317	1	x0	x0	PROPN
ma-203	317	2	j	j	PROPN
ma-203	317	3	,	,	PUNCT
ma-203	317	4	j	j	PROPN
ma-203	317	5	=	=	SYM
ma-203	317	6	1	1	NUM
ma-203	317	7	,	,	PUNCT
ma-203	317	8	2	2	NUM
ma-203	317	9	,	,	PUNCT
ma-203	317	10	·	·	PUNCT
ma-203	317	11	·	·	PUNCT
ma-203	317	12	·	·	PUNCT
ma-203	317	13	,	,	PUNCT
ma-203	317	14	nwe	nwe	PROPN
ma-203	317	15	assume	assume	VERB
ma-203	317	16	the	the	DET
ma-203	317	17	following	follow	VERB
ma-203	317	18	conditions	condition	NOUN
ma-203	317	19	for	for	ADP
ma-203	317	20	j	j	PROPN
ma-203	317	21	=	=	SYM
ma-203	317	22	1	1	NUM
ma-203	317	23	,	,	PUNCT
ma-203	317	24	2	2	NUM
ma-203	317	25	,	,	PUNCT
ma-203	317	26	·	·	PUNCT
ma-203	317	27	·	·	PUNCT
ma-203	317	28	·	·	PUNCT
ma-203	317	29	,	,	PUNCT
ma-203	317	30	n	n	CCONJ
ma-203	317	31	:	:	PUNCT
ma-203	317	32	(	(	PUNCT
ma-203	317	33	a1	a1	NOUN
ma-203	317	34	)	)	PUNCT
ma-203	317	35	|fj(θ	|fj(θ	PROPN
ma-203	317	36	,	,	PUNCT
ma-203	317	37	x)|	x)|	PROPN
ma-203	317	38	≤	≤	PROPN
ma-203	317	39	aj(θ)(1	aj(θ)(1	PROPN
ma-203	317	40	+	+	CCONJ
ma-203	317	41	|x	|x	NOUN
ma-203	317	42	|	|	ADV
ma-203	317	43	)	)	PUNCT
ma-203	317	44	,	,	PUNCT
ma-203	317	45	|fj(θ	|fj(θ	PROPN
ma-203	317	46	,	,	PUNCT
ma-203	317	47	x)−	x)−	PROPN
ma-203	317	48	fj(θ	fj(θ	PROPN
ma-203	317	49	,	,	PUNCT
ma-203	317	50	y)|	y)|	PROPN
ma-203	317	51	≤	≤	NOUN
ma-203	317	52	aj(θ)|x	aj(θ)|x	NOUN
ma-203	317	53	−	−	PROPN
ma-203	317	54	y	y	PROPN
ma-203	317	55	|.(a2	|.(a2	PROPN
ma-203	317	56	)	)	PUNCT
ma-203	318	1	|fj(θ	|fj(θ	ADP
ma-203	318	2	,	,	PUNCT
ma-203	318	3	x)−	x)−	PROPN
ma-203	318	4	fj(φ	fj(φ	NOUN
ma-203	318	5	,	,	PUNCT
ma-203	318	6	y)|	y)|	PROPN
ma-203	318	7	≤	≤	PROPN
ma-203	318	8	bj(x)|θ	bj(x)|θ	PROPN
ma-203	319	1	−	−	PROPN
ma-203	319	2	φ|	φ|	PROPN
ma-203	319	3	for	for	ADP
ma-203	319	4	all	all	DET
ma-203	319	5	θ	θ	PROPN
ma-203	319	6	,	,	PUNCT
ma-203	319	7	φ	φ	PROPN
ma-203	319	8	∈	∈	PROPN
ma-203	319	9	θ	θ	PROPN
ma-203	319	10	,	,	PUNCT
ma-203	319	11	x	x	PRON
ma-203	319	12	,	,	PUNCT
ma-203	319	13	y	y	PROPN
ma-203	319	14	∈	∈	PROPN
ma-203	319	15	rwhere	rwhere	VERB
ma-203	319	16	supθ∈θ	supθ∈θ	PROPN
ma-203	319	17	|aj(θ)|	|aj(θ)|	PROPN
ma-203	319	18	=	=	PUNCT
ma-203	319	19	a	a	DET
ma-203	319	20	<	<	X
ma-203	319	21	∞	∞	PROPN
ma-203	319	22	,	,	PUNCT
ma-203	319	23	e|bj(x0	e|bj(x0	NOUN
ma-203	319	24	j	j	PROPN
ma-203	319	25	)	)	PUNCT
ma-203	319	26	|r	|r	PROPN
ma-203	320	1	<	<	X
ma-203	320	2	∞	∞	PROPN
ma-203	320	3	for	for	ADP
ma-203	320	4	any	any	DET
ma-203	320	5	integer	integer	NOUN
ma-203	320	6	r.(a3	r.(a3	PROPN
ma-203	320	7	)	)	PUNCT
ma-203	320	8	the	the	DET
ma-203	320	9	diffusion	diffusion	NOUN
ma-203	320	10	process	process	NOUN
ma-203	320	11	x	x	PRON
ma-203	320	12	is	be	AUX
ma-203	320	13	stationary	stationary	ADJ
ma-203	320	14	and	and	CCONJ
ma-203	320	15	ergodic	ergodic	ADJ
ma-203	320	16	with	with	ADP
ma-203	320	17	invariant	invariant	ADJ
ma-203	320	18	measure	measure	NOUN
ma-203	320	19	ν	ν	NOUN
ma-203	320	20	,	,	PUNCT
ma-203	320	21	i.e.	i.e.	X
ma-203	320	22	,	,	PUNCT
ma-203	320	23	for	for	ADP
ma-203	320	24	any	any	DET
ma-203	320	25	gjwith	gjwith	NOUN
ma-203	320	26	e[gj	e[gj	PROPN
ma-203	320	27	(	(	PUNCT
ma-203	320	28	·	·	PUNCT
ma-203	320	29	)	)	PUNCT
ma-203	320	30	]	]	PUNCT
ma-203	321	1	<	<	X
ma-203	321	2	∞	∞	PROPN
ma-203	321	3	,	,	PUNCT
ma-203	321	4	1	1	NUM
ma-203	321	5	n	n	NOUN
ma-203	321	6	∑n	∑n	PROPN
ma-203	321	7	j=1	j=1	PROPN
ma-203	321	8	∑m	∑m	PROPN
ma-203	321	9	i=1	i=1	PROPN
ma-203	321	10	gj(xti	gj(xti	PROPN
ma-203	321	11	)	)	PUNCT
ma-203	321	12	→	→	SYM
ma-203	321	13	eν	eν	X
ma-203	321	14	[	[	X
ma-203	321	15	g(x0	g(x0	NOUN
ma-203	321	16	)	)	PUNCT
ma-203	321	17	]	]	PUNCT
ma-203	322	1	a.s	a.s	PROPN
ma-203	322	2	.	.	PROPN
ma-203	322	3	as	as	ADP
ma-203	322	4	n	n	PROPN
ma-203	322	5	→∞	→∞	PROPN
ma-203	322	6	and	and	CCONJ
ma-203	322	7	h	h	PROPN
ma-203	322	8	→	→	SYM
ma-203	322	9	0.(a4	0.(a4	PROPN
ma-203	322	10	)	)	PUNCT
ma-203	323	1	supt≥0	supt≥0	PROPN
ma-203	323	2	e|xj(t)|r	e|xj(t)|r	X
ma-203	324	1	<	<	X
ma-203	324	2	∞	∞	NUM
ma-203	324	3	for	for	ADP
ma-203	324	4	all	all	DET
ma-203	324	5	r	r	NOUN
ma-203	324	6	≥	≥	NOUN
ma-203	324	7	0.(a5	0.(a5	NUM
ma-203	324	8	)	)	PUNCT
ma-203	324	9	e|fj(θ	e|fj(θ	NOUN
ma-203	324	10	,	,	PUNCT
ma-203	324	11	x0	x0	PROPN
ma-203	324	12	j	j	PROPN
ma-203	324	13	)	)	PUNCT
ma-203	325	1	−	−	PROPN
ma-203	325	2	fj(θ0	fj(θ0	PROPN
ma-203	325	3	,	,	PUNCT
ma-203	325	4	x	x	PROPN
ma-203	325	5	0	0	NUM
ma-203	325	6	j	j	PROPN
ma-203	325	7	)	)	PUNCT
ma-203	325	8	|2	|2	NUM
ma-203	325	9	=	=	SYM
ma-203	325	10	0	0	NUM
ma-203	325	11	iff	iff	PROPN
ma-203	325	12	θ	θ	PROPN
ma-203	325	13	=	=	SYM
ma-203	325	14	θ0.(a6	θ0.(a6	PROPN
ma-203	325	15	)	)	PUNCT
ma-203	325	16	fj	fj	PROPN
ma-203	325	17	is	be	AUX
ma-203	325	18	twice	twice	ADV
ma-203	325	19	continuously	continuously	ADV
ma-203	325	20	differentiable	differentiable	ADJ
ma-203	325	21	function	function	NOUN
ma-203	325	22	in	in	ADP
ma-203	325	23	x	x	PUNCT
ma-203	325	24	for	for	ADP
ma-203	325	25	all	all	DET
ma-203	325	26	θ.(a7	θ.(a7	PROPN
ma-203	325	27	)	)	PUNCT
ma-203	325	28	fj	fj	PROPN
ma-203	325	29	(	(	PUNCT
ma-203	325	30	·	·	PUNCT
ma-203	325	31	,	,	PUNCT
ma-203	325	32	x	x	X
ma-203	325	33	)	)	PUNCT
ma-203	325	34	and	and	CCONJ
ma-203	325	35	all	all	DET
ma-203	325	36	its	its	PRON
ma-203	325	37	derivatives	derivative	NOUN
ma-203	325	38	are	be	AUX
ma-203	325	39	three	three	NUM
ma-203	325	40	times	time	NOUN
ma-203	325	41	continuously	continuously	ADV
ma-203	325	42	differentiable	differentiable	VERB
ma-203	325	43	with	with	ADP
ma-203	325	44	respect	respect	NOUN
ma-203	325	45	to	to	ADP
ma-203	325	46	θfor	θfor	PROPN
ma-203	325	47	all	all	DET
ma-203	325	48	x	x	PROPN
ma-203	325	49	∈	∈	PROPN
ma-203	325	50	r.	r.	PROPN
ma-203	325	51	moreover	moreover	ADV
ma-203	325	52	,	,	PUNCT
ma-203	325	53	these	these	DET
ma-203	325	54	derivatives	derivative	NOUN
ma-203	325	55	upto	upto	VERB
ma-203	325	56	third	third	ADJ
ma-203	325	57	order	order	NOUN
ma-203	325	58	with	with	ADP
ma-203	325	59	respect	respect	NOUN
ma-203	325	60	to	to	ADP
ma-203	325	61	θ	θ	PROPN
ma-203	325	62	are	be	AUX
ma-203	325	63	of	of	ADP
ma-203	325	64	polynomialgrowth	polynomialgrowth	NOUN
ma-203	325	65	in	in	ADP
ma-203	325	66	x	x	X
ma-203	325	67	uniformly	uniformly	ADV
ma-203	325	68	in	in	ADP
ma-203	325	69	θ.the	θ.the	DET
ma-203	325	70	fisher	fisher	PROPN
ma-203	325	71	information	information	NOUN
ma-203	325	72	is	be	AUX
ma-203	325	73	given	give	VERB
ma-203	325	74	by	by	ADP
ma-203	325	75	0	0	NUM
ma-203	325	76	<	<	X
ma-203	325	77	i(θ	i(θ	PROPN
ma-203	325	78	)	)	PUNCT
ma-203	325	79	:	:	PUNCT
ma-203	325	80	=	=	SYM
ma-203	325	81	∫∞	∫∞	NOUN
ma-203	325	82	−∞(f	−∞(f	NOUN
ma-203	325	83	′j	′j	NOUN
ma-203	325	84	(	(	PUNCT
ma-203	325	85	θ	θ	PROPN
ma-203	325	86	,	,	PUNCT
ma-203	325	87	x))2dν(x	x))2dν(x	NOUN
ma-203	325	88	)	)	PUNCT
ma-203	326	1	<	<	X
ma-203	326	2	∞	∞	NUM
ma-203	326	3	and	and	CCONJ
ma-203	326	4	for	for	ADP
ma-203	326	5	any	any	DET
ma-203	326	6	δ	δ	PROPN
ma-203	326	7	>	>	X
ma-203	326	8	0	0	PROPN
ma-203	326	9	,	,	PUNCT
ma-203	326	10	orany	orany	ADJ
ma-203	326	11	compact	compact	ADJ
ma-203	326	12	θ̄	θ̄	X
ma-203	326	13	⊂	⊂	PROPN
ma-203	326	14	θ	θ	PROPN
ma-203	326	15	,	,	PUNCT
ma-203	326	16	inf	inf	NOUN
ma-203	326	17	θ0∈θ̄	θ0∈θ̄	ADJ
ma-203	326	18	sup	sup	NOUN
ma-203	326	19	|θ−θ0|>δ	|θ−θ0|>δ	NOUN
ma-203	326	20	eθ0	eθ0	X
ma-203	326	21	|f	|f	PROPN
ma-203	326	22	′j	′j	ADJ
ma-203	326	23	(	(	PUNCT
ma-203	326	24	θ	θ	PROPN
ma-203	326	25	,	,	PUNCT
ma-203	326	26	x0)−	x0)−	X
ma-203	326	27	f	f	X
ma-203	326	28	′j	′j	NOUN
ma-203	326	29	(	(	PUNCT
ma-203	326	30	θ0	θ0	PROPN
ma-203	326	31	,	,	PUNCT
ma-203	326	32	xj(0))|2	xj(0))|2	X
ma-203	326	33	>	>	X
ma-203	326	34	0	0	X
ma-203	326	35	.	.	PUNCT
ma-203	327	1	(	(	PUNCT
ma-203	327	2	a8	a8	PROPN
ma-203	327	3	)	)	PUNCT
ma-203	327	4	the	the	DET
ma-203	327	5	malliavin	malliavin	NOUN
ma-203	327	6	covariance	covariance	NOUN
ma-203	327	7	of	of	ADP
ma-203	327	8	the	the	DET
ma-203	327	9	process	process	NOUN
ma-203	327	10	is	be	AUX
ma-203	327	11	nondegenerate	nondegenerate	ADJ
ma-203	327	12	.	.	PUNCT
ma-203	328	1	let	let	VERB
ma-203	328	2	fj	fj	PROPN
ma-203	328	3	=	=	PUNCT
ma-203	328	4	µj	µj	PROPN
ma-203	328	5	/	/	SYM
ma-203	328	6	σj	σj	PROPN
ma-203	328	7	,	,	PUNCT
ma-203	328	8	j	j	PROPN
ma-203	328	9	=	=	SYM
ma-203	328	10	1	1	NUM
ma-203	328	11	,	,	PUNCT
ma-203	328	12	2	2	NUM
ma-203	328	13	,	,	PUNCT
ma-203	328	14	·	·	PUNCT
ma-203	328	15	·	·	PUNCT
ma-203	328	16	·	·	PUNCT
ma-203	328	17	,	,	PUNCT
ma-203	328	18	n.	n.	PROPN
ma-203	328	19	the	the	DET
ma-203	328	20	model	model	NOUN
ma-203	328	21	is	be	AUX
ma-203	328	22	given	give	VERB
ma-203	328	23	by	by	ADP
ma-203	328	24	dxj(t	dxj(t	PROPN
ma-203	328	25	)	)	PUNCT
ma-203	329	1	=	=	PUNCT
ma-203	329	2	p∑	p∑	ADJ
ma-203	330	1	l=1	l=1	X
ma-203	330	2	θlµj	θlµj	VERB
ma-203	330	3	l(x(t	l(x(t	PROPN
ma-203	330	4	)	)	PUNCT
ma-203	330	5	)	)	PUNCT
ma-203	331	1	+	+	CCONJ
ma-203	331	2	σj(x(t))dwj(t	σj(x(t))dwj(t	PROPN
ma-203	331	3	)	)	PUNCT
ma-203	331	4	,	,	PUNCT
ma-203	331	5	j	j	PROPN
ma-203	332	1	=	=	SYM
ma-203	332	2	1	1	NUM
ma-203	332	3	,	,	PUNCT
ma-203	332	4	2	2	NUM
ma-203	332	5	,	,	PUNCT
ma-203	332	6	·	·	PUNCT
ma-203	332	7	·	·	PUNCT
ma-203	332	8	·	·	PUNCT
ma-203	332	9	,	,	PUNCT
ma-203	332	10	n.	n.	PROPN
ma-203	332	11	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	332	12	eur	eur	PROPN
ma-203	332	13	.	.	PUNCT
ma-203	333	1	j.	j.	PROPN
ma-203	333	2	math	math	PROPN
ma-203	333	3	.	.	PUNCT
ma-203	334	1	anal	anal	PROPN
ma-203	334	2	.	.	PUNCT
ma-203	335	1	10.28924	10.28924	NUM
ma-203	335	2	/	/	SYM
ma-203	335	3	ada	ada	PROPN
ma-203	335	4	/	/	SYM
ma-203	335	5	ma.4.12	ma.4.12	NOUN
ma-203	335	6	13the	13the	ADJ
ma-203	335	7	radon	radon	PROPN
ma-203	335	8	-	-	PUNCT
ma-203	335	9	nikodym	nikodym	ADJ
ma-203	335	10	derivative	derivative	NOUN
ma-203	335	11	(	(	PUNCT
ma-203	335	12	likelihood	likelihood	NOUN
ma-203	335	13	)	)	PUNCT
ma-203	335	14	is	be	AUX
ma-203	335	15	given	give	VERB
ma-203	335	16	by	by	ADP
ma-203	335	17	lθn(xn	lθn(xn	NOUN
ma-203	335	18	,	,	PUNCT
ma-203	335	19	t	t	NOUN
ma-203	335	20	)	)	PUNCT
ma-203	335	21	:	:	PUNCT
ma-203	335	22	=	=	PUNCT
ma-203	335	23	dpθ	dpθ	NOUN
ma-203	335	24	dp0	dp0	PROPN
ma-203	335	25	(	(	PUNCT
ma-203	335	26	xn	xn	PROPN
ma-203	335	27	,	,	PUNCT
ma-203	335	28	t	t	NOUN
ma-203	335	29	)	)	PUNCT
ma-203	335	30	=	=	SYM
ma-203	335	31	exp	exp	NOUN
ma-203	335	32	{	{	PUNCT
ma-203	335	33	∑p	∑p	ADJ
ma-203	335	34	l=1	l=1	PROPN
ma-203	335	35	θl	θl	ADP
ma-203	335	36	∑n	∑n	PROPN
ma-203	335	37	j=1	j=1	PROPN
ma-203	335	38	∫	∫	PROPN
ma-203	335	39	t	t	PROPN
ma-203	335	40	0	0	NUM
ma-203	335	41	µj	µj	PROPN
ma-203	336	1	l(x(t))σ−2	l(x(t))σ−2	PROPN
ma-203	336	2	j	j	PROPN
ma-203	336	3	(	(	PUNCT
ma-203	336	4	x(t))dxj(t	x(t))dxj(t	PROPN
ma-203	336	5	)	)	PUNCT
ma-203	336	6	−1	−1	NOUN
ma-203	336	7	2	2	NUM
ma-203	336	8	∑p	∑p	ADJ
ma-203	336	9	l=1	l=1	PROPN
ma-203	337	1	∑p	∑p	ADJ
ma-203	337	2	m=1	m=1	PROPN
ma-203	337	3	θlθm	θlθm	NOUN
ma-203	338	1	∑n	∑n	PROPN
ma-203	338	2	j=1	j=1	PROPN
ma-203	338	3	∫	∫	PROPN
ma-203	338	4	t	t	PROPN
ma-203	338	5	0	0	NUM
ma-203	339	1	µj	µj	PROPN
ma-203	340	1	l(x(t))σ−2	l(x(t))σ−2	PROPN
ma-203	340	2	j	j	PROPN
ma-203	340	3	(	(	PUNCT
ma-203	340	4	x(t))µjm(x(t))dt	x(t))µjm(x(t))dt	PROPN
ma-203	340	5	}	}	PUNCT
ma-203	340	6	.	.	PUNCT
ma-203	341	1	we	we	PRON
ma-203	341	2	observe	observe	VERB
ma-203	341	3	the	the	DET
ma-203	341	4	process	process	NOUN
ma-203	341	5	{	{	PUNCT
ma-203	341	6	xt	xt	ADP
ma-203	341	7	}	}	PUNCT
ma-203	341	8	at	at	ADP
ma-203	341	9	times	time	NOUN
ma-203	341	10	0	0	X
ma-203	342	1	=	=	SYM
ma-203	342	2	t0	t0	PROPN
ma-203	342	3	<	<	X
ma-203	342	4	t1	t1	X
ma-203	342	5	<	<	X
ma-203	342	6	·	·	PUNCT
ma-203	342	7	·	·	PUNCT
ma-203	342	8	·	·	PUNCT
ma-203	343	1	tm	tm	NOUN
ma-203	343	2	=	=	PROPN
ma-203	343	3	t	t	PROPN
ma-203	343	4	with	with	ADP
ma-203	343	5	ti	ti	NOUN
ma-203	343	6	−	−	PROPN
ma-203	343	7	ti−1	ti−1	NOUN
ma-203	343	8	=	=	SYM
ma-203	343	9	t	t	NOUN
ma-203	343	10	m	m	NOUN
ma-203	344	1	=	=	ADJ
ma-203	344	2	h	h	NOUN
ma-203	344	3	,	,	PUNCT
ma-203	344	4	i	i	PRON
ma-203	344	5	=	=	NOUN
ma-203	344	6	1	1	NUM
ma-203	344	7	,	,	PUNCT
ma-203	344	8	2	2	NUM
ma-203	344	9	·	·	PUNCT
ma-203	344	10	·	·	PUNCT
ma-203	344	11	·	·	PUNCT
ma-203	344	12	,	,	PUNCT
ma-203	344	13	n.	n.	NOUN
ma-203	344	14	we	we	PRON
ma-203	344	15	assume	assume	VERB
ma-203	344	16	equispaced	equispace	VERB
ma-203	344	17	sampling	sample	VERB
ma-203	344	18	for	for	ADP
ma-203	344	19	simplicity	simplicity	NOUN
ma-203	344	20	with	with	ADP
ma-203	344	21	t	t	PROPN
ma-203	344	22	being	be	AUX
ma-203	344	23	fixed	fix	VERB
ma-203	344	24	,	,	PUNCT
ma-203	344	25	m	m	VERB
ma-203	344	26	→∞	→∞	PROPN
ma-203	344	27	and	and	CCONJ
ma-203	344	28	n	n	CCONJ
ma-203	344	29	→∞.the	→∞.the	DET
ma-203	344	30	dataset	dataset	NOUN
ma-203	344	31	is	be	AUX
ma-203	344	32	n	n	DET
ma-203	344	33	particles	particle	NOUN
ma-203	344	34	x1	x1	PROPN
ma-203	344	35	(	(	PUNCT
ma-203	344	36	·	·	PUNCT
ma-203	344	37	)	)	PUNCT
ma-203	344	38	,	,	PUNCT
ma-203	344	39	x2	x2	PROPN
ma-203	344	40	(	(	PUNCT
ma-203	344	41	·	·	PUNCT
ma-203	344	42	)	)	PUNCT
ma-203	344	43	,	,	PUNCT
ma-203	344	44	·	·	PUNCT
ma-203	344	45	·	·	PUNCT
ma-203	344	46	·	·	PUNCT
ma-203	344	47	,	,	PUNCT
ma-203	344	48	xn	xn	PROPN
ma-203	344	49	(	(	PUNCT
ma-203	344	50	·	·	PUNCT
ma-203	344	51	)	)	PUNCT
ma-203	344	52	of	of	ADP
ma-203	344	53	x(t	x(t	PROPN
ma-203	344	54	)	)	PUNCT
ma-203	344	55	on	on	ADP
ma-203	344	56	[	[	X
ma-203	344	57	0	0	NUM
ma-203	344	58	,	,	PUNCT
ma-203	344	59	t	t	X
ma-203	344	60	]	]	PUNCT
ma-203	344	61	.	.	PUNCT
ma-203	345	1	the	the	DET
ma-203	345	2	approximate	approximate	ADJ
ma-203	345	3	log	log	NOUN
ma-203	345	4	-	-	PUNCT
ma-203	345	5	likelihood	likelihood	NOUN
ma-203	345	6	based	base	VERB
ma-203	345	7	on	on	ADP
ma-203	345	8	observations	observation	NOUN
ma-203	345	9	xj(t1	xj(t1	NUM
ma-203	345	10	)	)	PUNCT
ma-203	345	11	,	,	PUNCT
ma-203	345	12	xj(t2	xj(t2	NOUN
ma-203	345	13	)	)	PUNCT
ma-203	345	14	,	,	PUNCT
ma-203	345	15	.	.	PUNCT
ma-203	345	16	.	.	PUNCT
ma-203	345	17	.	.	PUNCT
ma-203	346	1	,	,	PUNCT
ma-203	346	2	xj(tn	xj(tn	PROPN
ma-203	346	3	)	)	PUNCT
ma-203	346	4	,	,	PUNCT
ma-203	346	5	j	j	PROPN
ma-203	346	6	=	=	SYM
ma-203	346	7	1	1	NUM
ma-203	346	8	,	,	PUNCT
ma-203	346	9	2	2	NUM
ma-203	346	10	,	,	PUNCT
ma-203	346	11	·	·	PUNCT
ma-203	346	12	·	·	PUNCT
ma-203	346	13	·	·	PUNCT
ma-203	346	14	,	,	PUNCT
ma-203	346	15	n	n	CCONJ
ma-203	346	16	with	with	ADP
ma-203	346	17	ti	ti	X
ma-203	346	18	=	=	NOUN
ma-203	346	19	it	it	PRON
ma-203	346	20	/	/	SYM
ma-203	346	21	m	m	VERB
ma-203	346	22	=	=	NOUN
ma-203	346	23	ihis	ihis	PROPN
ma-203	346	24	defined	define	VERB
ma-203	346	25	as	as	ADP
ma-203	346	26	kn	kn	PROPN
ma-203	346	27	,	,	PUNCT
ma-203	346	28	m(θ	m(θ	PROPN
ma-203	346	29	)	)	PUNCT
ma-203	346	30	=	=	PUNCT
ma-203	347	1	∑p	∑p	ADJ
ma-203	348	1	l=1	l=1	NOUN
ma-203	348	2	θl	θl	ADP
ma-203	348	3	∑n	∑n	PROPN
ma-203	348	4	j=1	j=1	ADJ
ma-203	348	5	∑m	∑m	PROPN
ma-203	349	1	i=1	i=1	PROPN
ma-203	350	1	µj	µj	INTJ
ma-203	350	2	l(x(ti−1))σ−2	l(x(ti−1))σ−2	PROPN
ma-203	350	3	j	j	PROPN
ma-203	350	4	(	(	PUNCT
ma-203	350	5	x(ti−1))(xj(ti)−xj(ti−1	x(ti−1))(xj(ti)−xj(ti−1	PROPN
ma-203	350	6	)	)	PUNCT
ma-203	350	7	−	−	PROPN
ma-203	350	8	1	1	NUM
ma-203	350	9	2	2	NUM
ma-203	350	10	∑p	∑p	ADJ
ma-203	350	11	l=1	l=1	PROPN
ma-203	351	1	∑p	∑p	INTJ
ma-203	351	2	k=1	k=1	INTJ
ma-203	351	3	θlθk	θlθk	INTJ
ma-203	352	1	∑n	∑n	PROPN
ma-203	353	1	j=1	j=1	NOUN
ma-203	353	2	∑m	∑m	PROPN
ma-203	353	3	i=1	i=1	PROPN
ma-203	354	1	µj	µj	INTJ
ma-203	354	2	l(x(ti−1))σ−2	l(x(ti−1))σ−2	PROPN
ma-203	354	3	j	j	PROPN
ma-203	354	4	(	(	PUNCT
ma-203	354	5	x(ti−1)))µjk(x(ti−1))(ti	x(ti−1)))µjk(x(ti−1))(ti	NUM
ma-203	354	6	−	−	PROPN
ma-203	354	7	ti−1	ti−1	NOUN
ma-203	354	8	)	)	PUNCT
ma-203	354	9	.	.	PUNCT
ma-203	355	1	we	we	PRON
ma-203	355	2	start	start	VERB
ma-203	355	3	with	with	ADP
ma-203	355	4	some	some	DET
ma-203	355	5	preliminary	preliminary	ADJ
ma-203	355	6	lemmas	lemma	NOUN
ma-203	355	7	.	.	PUNCT
ma-203	356	1	the	the	DET
ma-203	356	2	first	first	ADJ
ma-203	356	3	lemma	lemma	PROPN
ma-203	356	4	is	be	AUX
ma-203	356	5	from	from	ADP
ma-203	356	6	michel	michel	PROPN
ma-203	356	7	and	and	CCONJ
ma-203	356	8	pfanzagl	pfanzagl	NOUN
ma-203	356	9	(	(	PUNCT
ma-203	356	10	1971)which	1971)which	NOUN
ma-203	356	11	will	will	AUX
ma-203	356	12	be	be	AUX
ma-203	356	13	needed	need	VERB
ma-203	356	14	to	to	PART
ma-203	356	15	prove	prove	VERB
ma-203	356	16	our	our	PRON
ma-203	356	17	main	main	ADJ
ma-203	356	18	results	result	NOUN
ma-203	356	19	.	.	PUNCT
ma-203	357	1	lemma	lemma	PROPN
ma-203	357	2	5.1	5.1	NUM
ma-203	357	3	let	let	VERB
ma-203	357	4	ξ	ξ	NOUN
ma-203	357	5	,	,	PUNCT
ma-203	357	6	ζ	ζ	NOUN
ma-203	357	7	and	and	CCONJ
ma-203	357	8	η	η	PROPN
ma-203	357	9	be	be	VERB
ma-203	357	10	any	any	DET
ma-203	357	11	three	three	NUM
ma-203	357	12	random	random	ADJ
ma-203	357	13	variables	variable	NOUN
ma-203	357	14	on	on	ADP
ma-203	357	15	a	a	DET
ma-203	357	16	probability	probability	NOUN
ma-203	357	17	space	space	NOUN
ma-203	357	18	(	(	PUNCT
ma-203	357	19	ω	ω	PROPN
ma-203	357	20	,	,	PUNCT
ma-203	357	21	f	f	PROPN
ma-203	357	22	,	,	PUNCT
ma-203	357	23	p	p	NOUN
ma-203	357	24	)	)	PUNCT
ma-203	357	25	with	with	ADP
ma-203	357	26	p	p	PROPN
ma-203	357	27	(	(	PUNCT
ma-203	357	28	η	η	X
ma-203	357	29	>	>	X
ma-203	357	30	0	0	NUM
ma-203	357	31	)	)	PUNCT
ma-203	357	32	=	=	SYM
ma-203	358	1	1	1	X
ma-203	358	2	.	.	PUNCT
ma-203	358	3	then	then	ADV
ma-203	358	4	,	,	PUNCT
ma-203	358	5	for	for	ADP
ma-203	358	6	any	any	DET
ma-203	358	7	ε	ε	PROPN
ma-203	358	8	>	>	X
ma-203	358	9	0	0	PROPN
ma-203	358	10	,	,	PUNCT
ma-203	358	11	we	we	PRON
ma-203	358	12	have	have	VERB
ma-203	358	13	(	(	PUNCT
ma-203	358	14	a	a	X
ma-203	358	15	)	)	PUNCT
ma-203	358	16	sup	sup	NOUN
ma-203	358	17	x∈r	x∈r	PROPN
ma-203	358	18	|p{ξ	|p{ξ	PROPN
ma-203	358	19	+	+	CCONJ
ma-203	358	20	ζ	ζ	NOUN
ma-203	358	21	≤	≤	NUM
ma-203	358	22	x	x	X
ma-203	358	23	}	}	PUNCT
ma-203	358	24	−φ(x)|	−φ(x)|	VERB
ma-203	358	25	≤	≤	NUM
ma-203	358	26	sup	sup	NOUN
ma-203	358	27	x∈r	x∈r	PROPN
ma-203	358	28	|p{ξ	|p{ξ	PROPN
ma-203	359	1	≤	≤	ADV
ma-203	359	2	x	x	SYM
ma-203	359	3	}	}	PUNCT
ma-203	359	4	−φ(x)|+	−φ(x)|+	NOUN
ma-203	359	5	p	p	X
ma-203	359	6	(	(	PUNCT
ma-203	359	7	|ζ|	|ζ|	PROPN
ma-203	359	8	>	>	X
ma-203	359	9	ε	ε	PROPN
ma-203	359	10	)	)	PUNCT
ma-203	360	1	+	+	CCONJ
ma-203	360	2	ε	ε	PROPN
ma-203	360	3	,	,	PUNCT
ma-203	360	4	(	(	PUNCT
ma-203	360	5	b	b	NOUN
ma-203	360	6	)	)	PUNCT
ma-203	360	7	sup	sup	NOUN
ma-203	360	8	x∈r	x∈r	PROPN
ma-203	360	9	|p	|p	PROPN
ma-203	360	10	{	{	PUNCT
ma-203	360	11	ξ	ξ	PROPN
ma-203	360	12	η	η	PROPN
ma-203	360	13	≤	≤	PROPN
ma-203	360	14	x	x	X
ma-203	360	15	}	}	PUNCT
ma-203	360	16	−φ(x)|	−φ(x)|	VERB
ma-203	360	17	≤	≤	NUM
ma-203	360	18	sup	sup	NOUN
ma-203	360	19	x∈r	x∈r	PROPN
ma-203	360	20	|p{ξ	|p{ξ	PROPN
ma-203	360	21	≤	≤	ADV
ma-203	360	22	x	x	SYM
ma-203	360	23	}	}	PUNCT
ma-203	360	24	−φ(x)|+	−φ(x)|+	NOUN
ma-203	360	25	p{|η	p{|η	NOUN
ma-203	360	26	−	−	PROPN
ma-203	360	27	1|	1|	NUM
ma-203	360	28	>	>	X
ma-203	360	29	ε}+	ε}+	PROPN
ma-203	360	30	ε	ε	PROPN
ma-203	360	31	.	.	PUNCT
ma-203	361	1	the	the	DET
ma-203	361	2	strong	strong	ADJ
ma-203	361	3	rate	rate	NOUN
ma-203	361	4	of	of	ADP
ma-203	361	5	convergence	convergence	NOUN
ma-203	361	6	of	of	ADP
ma-203	361	7	particle	particle	NOUN
ma-203	361	8	approximations	approximation	NOUN
ma-203	361	9	of	of	ADP
ma-203	361	10	mckean	mckean	PROPN
ma-203	361	11	-	-	PUNCT
ma-203	361	12	vlasov	vlasov	PROPN
ma-203	361	13	sdes	sde	NOUN
ma-203	361	14	with	with	ADP
ma-203	361	15	lipschitzcoefficients	lipschitzcoefficient	NOUN
ma-203	361	16	is	be	AUX
ma-203	361	17	o(n−1/2	o(n−1/2	ADJ
ma-203	361	18	)	)	PUNCT
ma-203	361	19	where	where	SCONJ
ma-203	361	20	n	n	PRON
ma-203	361	21	is	be	AUX
ma-203	361	22	the	the	DET
ma-203	361	23	number	number	NOUN
ma-203	361	24	of	of	ADP
ma-203	361	25	particles	particle	NOUN
ma-203	361	26	.	.	PUNCT
ma-203	362	1	this	this	DET
ma-203	362	2	rate	rate	NOUN
ma-203	362	3	is	be	AUX
ma-203	362	4	driven	drive	VERB
ma-203	362	5	by	by	ADP
ma-203	362	6	the	the	DET
ma-203	362	7	statisticalerror	statisticalerror	NOUN
ma-203	362	8	.	.	PUNCT
ma-203	363	1	the	the	DET
ma-203	363	2	bias	bias	NOUN
ma-203	363	3	is	be	AUX
ma-203	363	4	of	of	ADP
ma-203	363	5	the	the	DET
ma-203	363	6	order	order	NOUN
ma-203	363	7	o(n−1	o(n−1	NOUN
ma-203	363	8	)	)	PUNCT
ma-203	363	9	.	.	PUNCT
ma-203	364	1	talay	talay	VERB
ma-203	364	2	and	and	CCONJ
ma-203	364	3	tubaro	tubaro	NOUN
ma-203	364	4	[	[	X
ma-203	364	5	37	37	NUM
ma-203	364	6	]	]	PUNCT
ma-203	364	7	showed	show	VERB
ma-203	364	8	that	that	SCONJ
ma-203	364	9	for	for	ADP
ma-203	364	10	smooth	smooth	ADJ
ma-203	364	11	coefficientsthe	coefficientsthe	NOUN
ma-203	364	12	the	the	DET
ma-203	364	13	weak	weak	ADJ
ma-203	364	14	error	error	NOUN
ma-203	364	15	is	be	AUX
ma-203	364	16	o(h	o(h	ADJ
ma-203	364	17	)	)	PUNCT
ma-203	364	18	.	.	PUNCT
ma-203	365	1	bencheikh	bencheikh	NOUN
ma-203	365	2	and	and	CCONJ
ma-203	365	3	jourdain	jourdain	NOUN
ma-203	366	1	[	[	X
ma-203	366	2	2	2	X
ma-203	366	3	]	]	PUNCT
ma-203	366	4	showed	show	VERB
ma-203	366	5	that	that	SCONJ
ma-203	366	6	weak	weak	ADJ
ma-203	366	7	error	error	NOUN
ma-203	366	8	between	between	ADP
ma-203	366	9	a	a	DET
ma-203	366	10	sdewith	sdewith	NOUN
ma-203	366	11	nonlinear	nonlinear	NOUN
ma-203	366	12	in	in	ADP
ma-203	366	13	the	the	DET
ma-203	366	14	sense	sense	NOUN
ma-203	366	15	of	of	ADP
ma-203	366	16	mckean	mckean	PROPN
ma-203	366	17	given	give	VERB
ma-203	366	18	by	by	ADP
ma-203	366	19	moments	moment	NOUN
ma-203	366	20	and	and	CCONJ
ma-203	366	21	its	its	PRON
ma-203	366	22	approximation	approximation	NOUN
ma-203	366	23	by	by	ADP
ma-203	366	24	the	the	DET
ma-203	366	25	eulerdiscretization	eulerdiscretization	NOUN
ma-203	366	26	with	with	ADP
ma-203	366	27	time	time	NOUN
ma-203	366	28	step	step	NOUN
ma-203	366	29	h	h	NOUN
ma-203	366	30	of	of	ADP
ma-203	366	31	a	a	DET
ma-203	366	32	system	system	NOUN
ma-203	366	33	of	of	ADP
ma-203	366	34	n	n	DET
ma-203	366	35	interacting	interact	VERB
ma-203	366	36	particles	particle	NOUN
ma-203	366	37	is	be	AUX
ma-203	366	38	o(n−1	o(n−1	PRON
ma-203	366	39	+	+	CCONJ
ma-203	366	40	h).from	h).from	PRON
ma-203	366	41	talay	talay	NOUN
ma-203	366	42	and	and	CCONJ
ma-203	366	43	tubaro	tubaro	NOUN
ma-203	366	44	[	[	X
ma-203	366	45	37	37	NUM
ma-203	366	46	]	]	PUNCT
ma-203	366	47	and	and	CCONJ
ma-203	366	48	bencheikh	bencheikh	NOUN
ma-203	366	49	and	and	CCONJ
ma-203	366	50	jourdain	jourdain	NOUN
ma-203	367	1	[	[	X
ma-203	367	2	2	2	NUM
ma-203	367	3	]	]	PUNCT
ma-203	367	4	,	,	PUNCT
ma-203	367	5	we	we	PRON
ma-203	367	6	have	have	AUX
ma-203	367	7	lemma	lemma	PROPN
ma-203	367	8	5.2	5.2	NUM
ma-203	367	9	let	let	VERB
ma-203	367	10	fj	fj	PROPN
ma-203	367	11	=	=	SYM
ma-203	367	12	µj	µj	PROPN
ma-203	367	13	/	/	SYM
ma-203	367	14	σj	σj	NOUN
ma-203	367	15	.	.	PUNCT
ma-203	368	1	then	then	ADV
ma-203	368	2	sup	sup	NOUN
ma-203	368	3	t∈π	t∈π	VERB
ma-203	368	4	|e[fj(x	|e[fj(x	PROPN
ma-203	368	5	n	n	PROPN
ma-203	368	6	t	t	PROPN
ma-203	368	7	)	)	PUNCT
ma-203	369	1	]	]	PUNCT
ma-203	369	2	−	−	PROPN
ma-203	369	3	e[fj(x	e[fj(x	PROPN
ma-203	369	4	n	n	CCONJ
ma-203	369	5	,	,	PUNCT
ma-203	369	6	m	m	PROPN
ma-203	369	7	t	t	NOUN
ma-203	369	8	)	)	PUNCT
ma-203	370	1	]	]	X
ma-203	370	2	|	|	X
ma-203	370	3	≤	≤	NUM
ma-203	370	4	c	c	PROPN
ma-203	370	5	t	t	PROPN
ma-203	370	6	m	m	PROPN
ma-203	370	7	,	,	PUNCT
ma-203	370	8	j	j	PROPN
ma-203	370	9	≥	≥	NUM
ma-203	370	10	1	1	NUM
ma-203	370	11	.	.	PUNCT
ma-203	371	1	the	the	DET
ma-203	371	2	following	follow	VERB
ma-203	371	3	lemma	lemma	PROPN
ma-203	371	4	follows	follow	VERB
ma-203	371	5	from	from	ADP
ma-203	371	6	yoshida	yoshida	PROPN
ma-203	372	1	[	[	X
ma-203	372	2	43,44	43,44	X
ma-203	372	3	]	]	X
ma-203	372	4	.	.	PUNCT
ma-203	373	1	lemma	lemma	PROPN
ma-203	373	2	5.3	5.3	NUM
ma-203	373	3	let	let	VERB
ma-203	373	4	in(θ	in(θ	NOUN
ma-203	373	5	)	)	PUNCT
ma-203	373	6	:	:	PUNCT
ma-203	374	1	=	=	SYM
ma-203	374	2	1	1	NUM
ma-203	374	3	ni(θ0	ni(θ0	NOUN
ma-203	374	4	)	)	PUNCT
ma-203	374	5	∑n	∑n	PROPN
ma-203	374	6	j=1	j=1	PROPN
ma-203	374	7	∫	∫	PROPN
ma-203	374	8	t	t	PROPN
ma-203	374	9	0	0	NUM
ma-203	375	1	µ2	µ2	PROPN
ma-203	375	2	j	j	PROPN
ma-203	375	3	(	(	PUNCT
ma-203	375	4	θ	θ	PROPN
ma-203	375	5	,	,	PUNCT
ma-203	375	6	xt)dt	xt)dt	PUNCT
ma-203	375	7	.	.	PUNCT
ma-203	376	1	then	then	ADV
ma-203	376	2	under	under	ADP
ma-203	376	3	the	the	DET
ma-203	376	4	conditions	condition	NOUN
ma-203	376	5	(	(	PUNCT
ma-203	376	6	a1)-(a8	a1)-(a8	ADV
ma-203	376	7	)	)	PUNCT
ma-203	376	8	,	,	PUNCT
ma-203	376	9	sup	sup	NOUN
ma-203	376	10	θ∈θ	θ∈θ	NOUN
ma-203	376	11	e[in(θ)−	e[in(θ)−	PROPN
ma-203	376	12	1]2	1]2	NUM
ma-203	376	13	≤	≤	NUM
ma-203	376	14	cn−1	cn−1	PROPN
ma-203	376	15	.	.	PUNCT
ma-203	377	1	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	377	2	eur	eur	PROPN
ma-203	377	3	.	.	PUNCT
ma-203	378	1	j.	j.	PROPN
ma-203	378	2	math	math	PROPN
ma-203	378	3	.	.	PUNCT
ma-203	379	1	anal	anal	PROPN
ma-203	379	2	.	.	PUNCT
ma-203	380	1	10.28924	10.28924	NUM
ma-203	380	2	/	/	SYM
ma-203	380	3	ada	ada	PROPN
ma-203	380	4	/	/	SYM
ma-203	380	5	ma.4.12	ma.4.12	NOUN
ma-203	380	6	14the	14the	NOUN
ma-203	380	7	following	follow	VERB
ma-203	380	8	lemma	lemma	PROPN
ma-203	380	9	follows	follow	VERB
ma-203	380	10	from	from	ADP
ma-203	380	11	theorem	theorem	NOUN
ma-203	380	12	1	1	NUM
ma-203	380	13	in	in	ADP
ma-203	380	14	yoshida	yoshida	PROPN
ma-203	381	1	[	[	X
ma-203	381	2	44	44	NUM
ma-203	381	3	]	]	PUNCT
ma-203	381	4	.	.	PUNCT
ma-203	382	1	lemma	lemma	PROPN
ma-203	382	2	5.4	5.4	NUM
ma-203	382	3	let	let	VERB
ma-203	382	4	mn	mn	PROPN
ma-203	382	5	:	:	PUNCT
ma-203	382	6	=	=	PROPN
ma-203	382	7	1√	1√	PROPN
ma-203	382	8	ni(θ0	ni(θ0	NOUN
ma-203	382	9	)	)	PUNCT
ma-203	383	1	∑n	∑n	PROPN
ma-203	383	2	j=1	j=1	PROPN
ma-203	383	3	∫	∫	PROPN
ma-203	383	4	t	t	PROPN
ma-203	383	5	0	0	NUM
ma-203	383	6	µj(θ0	µj(θ0	PROPN
ma-203	383	7	,	,	PUNCT
ma-203	383	8	xt)dwt	xt)dwt	PROPN
ma-203	383	9	.	.	PUNCT
ma-203	384	1	then	then	ADV
ma-203	384	2	under	under	ADP
ma-203	384	3	the	the	DET
ma-203	384	4	conditions	condition	NOUN
ma-203	384	5	(	(	PUNCT
ma-203	384	6	a1)-(a8	a1)-(a8	ADV
ma-203	384	7	)	)	PUNCT
ma-203	384	8	,	,	PUNCT
ma-203	384	9	sup	sup	NOUN
ma-203	384	10	x∈r	x∈r	PROPN
ma-203	384	11	|pθ0	|pθ0	NUM
ma-203	384	12	{	{	PUNCT
ma-203	384	13	mn	mn	PROPN
ma-203	384	14	≤	≤	PROPN
ma-203	384	15	x	x	X
ma-203	384	16	}	}	PUNCT
ma-203	384	17	−φ(x)|	−φ(x)|	VERB
ma-203	384	18	≤	≤	PROPN
ma-203	384	19	cn−1/2	cn−1/2	PROPN
ma-203	384	20	.	.	PUNCT
ma-203	385	1	in	in	ADP
ma-203	385	2	this	this	DET
ma-203	385	3	section	section	NOUN
ma-203	385	4	,	,	PUNCT
ma-203	385	5	our	our	PRON
ma-203	385	6	main	main	ADJ
ma-203	385	7	result	result	NOUN
ma-203	385	8	is	be	AUX
ma-203	385	9	the	the	DET
ma-203	385	10	following	follow	VERB
ma-203	385	11	theorem	theorem	NOUN
ma-203	385	12	.	.	PUNCT
ma-203	385	13	theorem	theorem	VERB
ma-203	385	14	5.5	5.5	NUM
ma-203	385	15	under	under	ADP
ma-203	385	16	the	the	DET
ma-203	385	17	conditions	condition	NOUN
ma-203	385	18	(	(	PUNCT
ma-203	385	19	a1)–(a8	a1)–(a8	ADJ
ma-203	385	20	)	)	PUNCT
ma-203	385	21	,	,	PUNCT
ma-203	385	22	we	we	PRON
ma-203	385	23	have	have	VERB
ma-203	385	24	sup	sup	NOUN
ma-203	385	25	x∈r	x∈r	PROPN
ma-203	385	26	∣∣∣pθ0	∣∣∣pθ0	PROPN
ma-203	385	27	{	{	PUNCT
ma-203	385	28	√	√	ADV
ma-203	385	29	ni(θ0)(θm	ni(θ0)(θm	PROPN
ma-203	385	30	,	,	PUNCT
ma-203	385	31	n	n	CCONJ
ma-203	385	32	−	−	PROPN
ma-203	385	33	θ0	θ0	NOUN
ma-203	385	34	)	)	PUNCT
ma-203	385	35	≤	≤	NUM
ma-203	385	36	x	x	PUNCT
ma-203	385	37	}	}	PUNCT
ma-203	385	38	−φ(x	−φ(x	NOUN
ma-203	385	39	)	)	PUNCT
ma-203	385	40	∣∣∣	∣∣∣	NOUN
ma-203	386	1	=	=	SYM
ma-203	386	2	o	o	PROPN
ma-203	386	3	(	(	PUNCT
ma-203	386	4	n−1/2	n−1/2	PROPN
ma-203	386	5	∨	∨	PROPN
ma-203	386	6	t	t	PROPN
ma-203	386	7	m	m	PROPN
ma-203	386	8	)	)	PUNCT
ma-203	386	9	.	.	PUNCT
ma-203	387	1	proof	proof	NOUN
ma-203	387	2	by	by	ADP
ma-203	387	3	taylor	taylor	PROPN
ma-203	387	4	expansion	expansion	NOUN
ma-203	387	5	,	,	PUNCT
ma-203	387	6	we	we	PRON
ma-203	387	7	have	have	VERB
ma-203	387	8	k′m	k′m	NOUN
ma-203	387	9	,	,	PUNCT
ma-203	387	10	n(θm	n(θm	PROPN
ma-203	387	11	,	,	PUNCT
ma-203	387	12	n	n	CCONJ
ma-203	387	13	)	)	PUNCT
ma-203	387	14	=	=	SYM
ma-203	387	15	k′m	k′m	PROPN
ma-203	387	16	,	,	PUNCT
ma-203	387	17	n(θ0	n(θ0	NOUN
ma-203	387	18	)	)	PUNCT
ma-203	387	19	+	+	CCONJ
ma-203	387	20	(	(	PUNCT
ma-203	387	21	θm	θm	PROPN
ma-203	387	22	,	,	PUNCT
ma-203	387	23	n	n	CCONJ
ma-203	387	24	−	−	PROPN
ma-203	388	1	θ0)k′′m	θ0)k′′m	NOUN
ma-203	388	2	,	,	PUNCT
ma-203	388	3	n(θ̄m	n(θ̄m	NOUN
ma-203	388	4	,	,	PUNCT
ma-203	388	5	n	n	CCONJ
ma-203	388	6	)	)	PUNCT
ma-203	389	1	where	where	SCONJ
ma-203	389	2	∣∣θ̄m	∣∣θ̄m	NOUN
ma-203	389	3	,	,	PUNCT
ma-203	389	4	n	n	CCONJ
ma-203	389	5	−	−	NOUN
ma-203	389	6	θ∣∣	θ∣∣	ADJ
ma-203	389	7	≤	≤	NOUN
ma-203	389	8	|θm	|θm	NUM
ma-203	389	9	,	,	PUNCT
ma-203	389	10	n	n	PRON
ma-203	389	11	−	−	PROPN
ma-203	389	12	θ0|	θ0|	PROPN
ma-203	389	13	.	.	PUNCT
ma-203	390	1	since	since	SCONJ
ma-203	390	2	k′m	k′m	PROPN
ma-203	390	3	,	,	PUNCT
ma-203	390	4	n(θm	n(θm	PROPN
ma-203	390	5	,	,	PUNCT
ma-203	390	6	n	n	CCONJ
ma-203	390	7	)	)	PUNCT
ma-203	390	8	=	=	SYM
ma-203	390	9	0	0	NUM
ma-203	390	10	,	,	PUNCT
ma-203	390	11	hence	hence	ADV
ma-203	390	12	we	we	PRON
ma-203	390	13	have	have	VERB
ma-203	390	14	√	√	VERB
ma-203	390	15	ni(θ0)(θm	ni(θ0)(θm	NOUN
ma-203	390	16	,	,	PUNCT
ma-203	390	17	n	n	CCONJ
ma-203	390	18	−	−	PROPN
ma-203	390	19	θ0	θ0	PROPN
ma-203	390	20	)	)	PUNCT
ma-203	390	21	=	=	SYM
ma-203	391	1	−	−	PROPN
ma-203	391	2	1√	1√	PROPN
ma-203	391	3	ni(θ0	ni(θ0	NOUN
ma-203	391	4	)	)	PUNCT
ma-203	391	5	k′m	k′m	NOUN
ma-203	391	6	,	,	PUNCT
ma-203	391	7	n(θ0	n(θ0	NOUN
ma-203	391	8	)	)	PUNCT
ma-203	391	9	1	1	NUM
ma-203	391	10	ni(θ0)k	ni(θ0)k	NOUN
ma-203	392	1	′′	′′	PROPN
ma-203	392	2	m	m	PROPN
ma-203	392	3	,	,	PUNCT
ma-203	392	4	n(θ̄m	n(θ̄m	NOUN
ma-203	392	5	,	,	PUNCT
ma-203	392	6	n	n	CCONJ
ma-203	392	7	)	)	PUNCT
ma-203	392	8	=	=	SYM
ma-203	392	9	−	−	PROPN
ma-203	392	10	1√	1√	PROPN
ma-203	392	11	ni(θ0	ni(θ0	NOUN
ma-203	392	12	)	)	PUNCT
ma-203	392	13	∑n	∑n	PROPN
ma-203	392	14	j=1	j=1	PROPN
ma-203	392	15	∑m	∑m	PROPN
ma-203	392	16	i=1	i=1	PROPN
ma-203	392	17	µ	µ	ADJ
ma-203	392	18	′	′	NUM
ma-203	392	19	j(θ0	j(θ0	NOUN
ma-203	392	20	,	,	PUNCT
ma-203	392	21	xti−1	xti−1	PROPN
ma-203	392	22	)	)	PUNCT
ma-203	392	23	∆wi	∆wi	PROPN
ma-203	392	24	1	1	NUM
ma-203	392	25	ni(θ0	ni(θ0	NOUN
ma-203	392	26	)	)	PUNCT
ma-203	392	27	∑n	∑n	PROPN
ma-203	392	28	j=1	j=1	PROPN
ma-203	392	29	∑m	∑m	PROPN
ma-203	392	30	i=1	i=1	PROPN
ma-203	392	31	µ	µ	X
ma-203	392	32	′′	′′	PROPN
ma-203	392	33	j	j	PROPN
ma-203	392	34	(	(	PUNCT
ma-203	392	35	θ̄m	θ̄m	PROPN
ma-203	392	36	,	,	PUNCT
ma-203	392	37	n	n	CCONJ
ma-203	392	38	,	,	PUNCT
ma-203	392	39	xti−1	xti−1	PROPN
ma-203	392	40	)	)	PUNCT
ma-203	392	41	∆ti	∆ti	NOUN
ma-203	393	1	=	=	NUM
ma-203	393	2	:	:	PUNCT
ma-203	393	3	um	um	INTJ
ma-203	393	4	,	,	PUNCT
ma-203	393	5	n	n	PRON
ma-203	393	6	vm	vm	PROPN
ma-203	393	7	,	,	PUNCT
ma-203	393	8	n	n	PRON
ma-203	393	9	note	note	VERB
ma-203	393	10	that	that	SCONJ
ma-203	393	11	vm	vm	PROPN
ma-203	393	12	,	,	PUNCT
ma-203	393	13	n	n	NOUN
ma-203	393	14	=	=	SYM
ma-203	393	15	1	1	NUM
ma-203	393	16	ni(θ0	ni(θ0	PROPN
ma-203	393	17	)	)	PUNCT
ma-203	393	18	n∑	n∑	NOUN
ma-203	394	1	j=1	j=1	NOUN
ma-203	394	2	m∑	m∑	VERB
ma-203	394	3	i=1	i=1	PROPN
ma-203	394	4	µ′′j	µ′′j	NOUN
ma-203	394	5	(	(	PUNCT
ma-203	394	6	θ̄m	θ̄m	PROPN
ma-203	394	7	,	,	PUNCT
ma-203	394	8	n	n	CCONJ
ma-203	394	9	,	,	PUNCT
ma-203	394	10	xti−1	xti−1	PROPN
ma-203	394	11	)	)	PUNCT
ma-203	394	12	∆ti	∆ti	NOUN
ma-203	394	13	=	=	SYM
ma-203	394	14	1	1	NUM
ma-203	394	15	ni(θ0	ni(θ0	NOUN
ma-203	394	16	)	)	PUNCT
ma-203	394	17	n∑	n∑	NOUN
ma-203	394	18	j=1	j=1	NOUN
ma-203	394	19	m∑	m∑	VERB
ma-203	394	20	i=1	i=1	PROPN
ma-203	394	21	µ′j(θ̄m	µ′j(θ̄m	PROPN
ma-203	394	22	,	,	PUNCT
ma-203	394	23	n	n	CCONJ
ma-203	394	24	,	,	PUNCT
ma-203	394	25	xti−1	xti−1	PROPN
ma-203	394	26	)	)	PUNCT
ma-203	394	27	2∆ti	2∆ti	PROPN
ma-203	394	28	.	.	PUNCT
ma-203	395	1	let	let	VERB
ma-203	395	2	lim	lim	PROPN
ma-203	395	3	vm	vm	PROPN
ma-203	395	4	,	,	PUNCT
ma-203	395	5	n	n	PROPN
ma-203	395	6	=	=	SYM
ma-203	395	7	vn	vn	X
ma-203	395	8	in	in	ADP
ma-203	395	9	l2	l2	NOUN
ma-203	395	10	as	as	ADP
ma-203	395	11	t	t	NOUN
ma-203	395	12	m	m	PROPN
ma-203	395	13	→	→	SYM
ma-203	395	14	0	0	NUM
ma-203	395	15	.	.	NOUN
ma-203	395	16	similar	similar	ADJ
ma-203	395	17	to	to	ADP
ma-203	395	18	lemma	lemma	PROPN
ma-203	395	19	5.3	5.3	NUM
ma-203	395	20	,	,	PUNCT
ma-203	395	21	it	it	PRON
ma-203	395	22	can	can	AUX
ma-203	395	23	be	be	AUX
ma-203	395	24	shown	show	VERB
ma-203	395	25	that	that	SCONJ
ma-203	395	26	e(vn	e(vn	PROPN
ma-203	395	27	−	−	PROPN
ma-203	395	28	1)2	1)2	NUM
ma-203	395	29	≤	≤	NUM
ma-203	395	30	cn−1	cn−1	PROPN
ma-203	395	31	(	(	PUNCT
ma-203	395	32	see	see	AUX
ma-203	395	33	also	also	ADV
ma-203	395	34	pardoux	pardoux	VERB
ma-203	395	35	and	and	CCONJ
ma-203	395	36	veretennikov	veretennikov	NOUN
ma-203	395	37	(	(	PUNCT
ma-203	395	38	2001	2001	NUM
ma-203	395	39	)	)	PUNCT
ma-203	395	40	and	and	CCONJ
ma-203	395	41	yoshida	yoshida	PROPN
ma-203	395	42	(	(	PUNCT
ma-203	395	43	2011	2011	NUM
ma-203	395	44	)	)	PUNCT
ma-203	395	45	)	)	PUNCT
ma-203	395	46	.	.	PUNCT
ma-203	396	1	it	it	PRON
ma-203	396	2	can	can	AUX
ma-203	396	3	be	be	AUX
ma-203	396	4	shown	show	VERB
ma-203	396	5	that	that	SCONJ
ma-203	396	6	e(vm	e(vm	PROPN
ma-203	396	7	,	,	PUNCT
ma-203	396	8	n	n	PRON
ma-203	396	9	−	−	PROPN
ma-203	396	10	vn)2	vn)2	PROPN
ma-203	396	11	≤	≤	PROPN
ma-203	396	12	c	c	PROPN
ma-203	396	13	t	t	AUX
ma-203	396	14	m	m	AUX
ma-203	396	15	(	(	PUNCT
ma-203	396	16	see	see	VERB
ma-203	396	17	altmeyer	altmeyer	NOUN
ma-203	396	18	and	and	CCONJ
ma-203	396	19	chorowski	chorowski	ADJ
ma-203	396	20	(	(	PUNCT
ma-203	396	21	2018	2018	NUM
ma-203	396	22	)	)	PUNCT
ma-203	396	23	)	)	PUNCT
ma-203	396	24	.	.	PUNCT
ma-203	397	1	hence	hence	ADV
ma-203	397	2	e(vm	e(vm	PROPN
ma-203	397	3	,	,	PUNCT
ma-203	397	4	n	n	PRON
ma-203	397	5	−	−	PROPN
ma-203	397	6	1)2	1)2	NUM
ma-203	397	7	=	=	SYM
ma-203	397	8	e[(vm	e[(vm	PROPN
ma-203	397	9	,	,	PUNCT
ma-203	397	10	n	n	CCONJ
ma-203	397	11	−	−	PROPN
ma-203	397	12	vn	vn	PROPN
ma-203	397	13	)	)	PUNCT
ma-203	397	14	+	+	CCONJ
ma-203	397	15	(	(	PUNCT
ma-203	397	16	vn	vn	INTJ
ma-203	397	17	−	−	PROPN
ma-203	397	18	1)]2	1)]2	PROPN
ma-203	397	19	≤	≤	PROPN
ma-203	397	20	c(n−1	c(n−1	PROPN
ma-203	397	21	∨	∨	PROPN
ma-203	397	22	t	t	PROPN
ma-203	397	23	m	m	PROPN
ma-203	397	24	)	)	PUNCT
ma-203	397	25	.	.	PUNCT
ma-203	398	1	further	far	ADV
ma-203	398	2	by	by	ADP
ma-203	398	3	lemma	lemma	PROPN
ma-203	398	4	5.1	5.1	NUM
ma-203	398	5	(	(	PUNCT
ma-203	398	6	b	b	NOUN
ma-203	398	7	)	)	PUNCT
ma-203	398	8	,	,	PUNCT
ma-203	398	9	we	we	PRON
ma-203	398	10	have	have	VERB
ma-203	398	11	sup	sup	NOUN
ma-203	398	12	x∈r	x∈r	PROPN
ma-203	398	13	∣∣∣pθ	∣∣∣pθ	PROPN
ma-203	398	14	{	{	PUNCT
ma-203	398	15	√ni(θ)(θm	√ni(θ)(θm	NUM
ma-203	398	16	,	,	PUNCT
ma-203	398	17	n	n	CCONJ
ma-203	398	18	−	−	PROPN
ma-203	398	19	θ	θ	NOUN
ma-203	398	20	)	)	PUNCT
ma-203	398	21	≤	≤	NOUN
ma-203	398	22	x	x	PUNCT
ma-203	398	23	}	}	PUNCT
ma-203	398	24	−φ(x	−φ(x	NOUN
ma-203	398	25	)	)	PUNCT
ma-203	398	26	∣∣∣	∣∣∣	NOUN
ma-203	399	1	=	=	SYM
ma-203	399	2	sup	sup	NOUN
ma-203	399	3	x∈r	x∈r	PROPN
ma-203	399	4	∣∣∣∣pθ	∣∣∣∣pθ	PROPN
ma-203	399	5	{	{	PUNCT
ma-203	399	6	um	um	INTJ
ma-203	399	7	,	,	PUNCT
ma-203	399	8	nvm	nvm	PROPN
ma-203	399	9	,	,	PUNCT
ma-203	399	10	n	n	PRON
ma-203	399	11	≤	≤	NOUN
ma-203	399	12	x	x	X
ma-203	399	13	}	}	PUNCT
ma-203	399	14	−φ(x	−φ(x	NOUN
ma-203	399	15	)	)	PUNCT
ma-203	399	16	∣∣∣∣	∣∣∣∣	NOUN
ma-203	399	17	=	=	PUNCT
ma-203	399	18	sup	sup	NOUN
ma-203	399	19	x∈r	x∈r	PROPN
ma-203	399	20	|pθ	|pθ	X
ma-203	399	21	{	{	PUNCT
ma-203	399	22	um	um	INTJ
ma-203	399	23	,	,	PUNCT
ma-203	399	24	n	n	NOUN
ma-203	399	25	≤	≤	NOUN
ma-203	399	26	x	x	SYM
ma-203	399	27	}	}	PUNCT
ma-203	399	28	−φ(x)|+	−φ(x)|+	VERB
ma-203	399	29	pθ	pθ	INTJ
ma-203	399	30	{	{	PUNCT
ma-203	399	31	|vm	|vm	NOUN
ma-203	399	32	,	,	PUNCT
ma-203	399	33	n	n	PROPN
ma-203	399	34	−	−	PROPN
ma-203	399	35	1|	1|	NUM
ma-203	399	36	≥	≥	NOUN
ma-203	399	37	ε}+	ε}+	PROPN
ma-203	399	38	ε	ε	PROPN
ma-203	399	39	≤	≤	PROPN
ma-203	399	40	c(n−1/2	c(n−1/2	PROPN
ma-203	399	41	∨	∨	PROPN
ma-203	399	42	t	t	PROPN
ma-203	399	43	2	2	NUM
ma-203	399	44	m	m	NOUN
ma-203	399	45	)	)	PUNCT
ma-203	400	1	+	+	NUM
ma-203	400	2	ε−2c(n−1	ε−2c(n−1	PROPN
ma-203	400	3	∨	∨	PROPN
ma-203	400	4	t	t	PROPN
ma-203	400	5	m	m	PROPN
ma-203	400	6	)	)	PUNCT
ma-203	401	1	+	+	CCONJ
ma-203	401	2	ε	ε	PROPN
ma-203	401	3	.	.	PUNCT
ma-203	401	4	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	401	5	eur	eur	PROPN
ma-203	401	6	.	.	PUNCT
ma-203	402	1	j.	j.	PROPN
ma-203	402	2	math	math	PROPN
ma-203	402	3	.	.	PUNCT
ma-203	403	1	anal	anal	PROPN
ma-203	403	2	.	.	PUNCT
ma-203	404	1	10.28924	10.28924	NUM
ma-203	404	2	/	/	SYM
ma-203	404	3	ada	ada	PROPN
ma-203	404	4	/	/	SYM
ma-203	404	5	ma.4.12	ma.4.12	NOUN
ma-203	404	6	15since	15since	NUM
ma-203	404	7	by	by	ADP
ma-203	404	8	lemma	lemma	PROPN
ma-203	404	9	5.1	5.1	NUM
ma-203	404	10	(	(	PUNCT
ma-203	404	11	a	a	NOUN
ma-203	404	12	)	)	PUNCT
ma-203	404	13	,	,	PUNCT
ma-203	404	14	lemma	lemma	PROPN
ma-203	404	15	5.2	5.2	NUM
ma-203	404	16	and	and	CCONJ
ma-203	404	17	lemma	lemma	PROPN
ma-203	404	18	5.4	5.4	NUM
ma-203	404	19	,	,	PUNCT
ma-203	404	20	we	we	PRON
ma-203	404	21	have	have	VERB
ma-203	404	22	sup	sup	PROPN
ma-203	404	23	x∈r	x∈r	PROPN
ma-203	404	24	|pθ	|pθ	X
ma-203	404	25	{	{	PUNCT
ma-203	404	26	um	um	INTJ
ma-203	404	27	,	,	PUNCT
ma-203	404	28	n	n	NOUN
ma-203	404	29	≤	≤	NOUN
ma-203	404	30	x	x	X
ma-203	404	31	}	}	PUNCT
ma-203	404	32	−φ(x)|	−φ(x)|	VERB
ma-203	404	33	≤	≤	NUM
ma-203	404	34	sup	sup	NOUN
ma-203	404	35	x∈r	x∈r	PROPN
ma-203	404	36	|pθ	|pθ	X
ma-203	404	37	{	{	PUNCT
ma-203	404	38	mn	mn	PROPN
ma-203	404	39	≤	≤	NUM
ma-203	404	40	x	x	SYM
ma-203	404	41	}	}	PUNCT
ma-203	404	42	−φ(x)|+	−φ(x)|+	ADJ
ma-203	404	43	pθ	pθ	NOUN
ma-203	404	44	{	{	PUNCT
ma-203	404	45	|um	|um	NOUN
ma-203	404	46	,	,	PUNCT
ma-203	404	47	n	n	PRON
ma-203	404	48	−mn|	−mn|	PROPN
ma-203	404	49	≥	≥	NUM
ma-203	404	50	ε}+	ε}+	PROPN
ma-203	404	51	ε	ε	PROPN
ma-203	404	52	≤	≤	PROPN
ma-203	404	53	cn−1/2	cn−1/2	PROPN
ma-203	405	1	+	+	CCONJ
ma-203	405	2	ε−2e	ε−2e	X
ma-203	405	3	|um	|um	X
ma-203	405	4	,	,	PUNCT
ma-203	405	5	n	n	PRON
ma-203	405	6	−mn|2	−mn|2	NUM
ma-203	405	7	+	+	NUM
ma-203	406	1	ε	ε	PROPN
ma-203	406	2	≤	≤	PROPN
ma-203	406	3	cn−1/2	cn−1/2	PROPN
ma-203	406	4	+	+	NUM
ma-203	406	5	ε−2c	ε−2c	PROPN
ma-203	406	6	t	t	PROPN
ma-203	406	7	m	m	PROPN
ma-203	406	8	+	+	PROPN
ma-203	406	9	ε	ε	AUX
ma-203	406	10	.	.	PUNCT
ma-203	406	11	choosing	choose	VERB
ma-203	406	12	ε	ε	PROPN
ma-203	406	13	=	=	SYM
ma-203	406	14	n−1/2	n−1/2	PROPN
ma-203	406	15	,	,	PUNCT
ma-203	406	16	we	we	PRON
ma-203	406	17	have	have	VERB
ma-203	406	18	the	the	DET
ma-203	406	19	result	result	NOUN
ma-203	406	20	.	.	PUNCT
ma-203	407	1	remarks	remark	NOUN
ma-203	407	2	we	we	PRON
ma-203	407	3	considered	consider	VERB
ma-203	407	4	fractional	fractional	ADJ
ma-203	407	5	levy	levy	NOUN
ma-203	407	6	process	process	NOUN
ma-203	407	7	driving	drive	VERB
ma-203	407	8	term	term	NOUN
ma-203	407	9	in	in	ADP
ma-203	407	10	this	this	DET
ma-203	407	11	paper	paper	NOUN
ma-203	407	12	whose	whose	DET
ma-203	407	13	incrementsare	incrementsare	NOUN
ma-203	407	14	stationary	stationary	NOUN
ma-203	407	15	.	.	PUNCT
ma-203	408	1	using	use	VERB
ma-203	408	2	fractional	fractional	ADJ
ma-203	408	3	levy	levy	NOUN
ma-203	408	4	process	process	NOUN
ma-203	408	5	as	as	SCONJ
ma-203	408	6	the	the	DET
ma-203	408	7	driving	drive	VERB
ma-203	408	8	term	term	NOUN
ma-203	408	9	which	which	PRON
ma-203	408	10	include	include	VERB
ma-203	408	11	jumps	jump	NOUN
ma-203	408	12	,	,	PUNCT
ma-203	408	13	maximumquasi	maximumquasi	NOUN
ma-203	408	14	-	-	PUNCT
ma-203	408	15	likelihood	likelihood	NOUN
ma-203	408	16	estimation	estimation	NOUN
ma-203	408	17	in	in	ADP
ma-203	408	18	fractional	fractional	ADJ
ma-203	408	19	levy	levy	NOUN
ma-203	408	20	stochastic	stochastic	ADJ
ma-203	408	21	volatility	volatility	NOUN
ma-203	408	22	model	model	NOUN
ma-203	408	23	was	be	AUX
ma-203	408	24	studied	study	VERB
ma-203	408	25	in	in	ADP
ma-203	408	26	bishwal	bishwal	NOUN
ma-203	408	27	[	[	X
ma-203	408	28	9].recently	9].recently	ADV
ma-203	408	29	,	,	PUNCT
ma-203	408	30	sub	sub	ADJ
ma-203	408	31	-	-	ADJ
ma-203	408	32	fractional	fractional	ADJ
ma-203	408	33	brownian	brownian	NOUN
ma-203	408	34	(	(	PUNCT
ma-203	408	35	sub	sub	NOUN
ma-203	408	36	-	-	ADJ
ma-203	408	37	fbm	fbm	ADJ
ma-203	408	38	)	)	PUNCT
ma-203	408	39	motion	motion	NOUN
ma-203	408	40	which	which	PRON
ma-203	408	41	is	be	AUX
ma-203	408	42	a	a	DET
ma-203	408	43	centered	center	VERB
ma-203	408	44	gaussian	gaussian	ADJ
ma-203	408	45	process	process	NOUN
ma-203	408	46	withcovariance	withcovariance	NOUN
ma-203	408	47	function	function	NOUN
ma-203	408	48	ch(s	ch(s	PROPN
ma-203	408	49	,	,	PUNCT
ma-203	408	50	t	t	PROPN
ma-203	408	51	)	)	PUNCT
ma-203	409	1	=	=	PUNCT
ma-203	410	1	s2h	s2h	NOUN
ma-203	410	2	+	+	PROPN
ma-203	410	3	t2h	t2h	PROPN
ma-203	410	4	−	−	PROPN
ma-203	410	5	1	1	NUM
ma-203	410	6	2	2	NUM
ma-203	410	7	[	[	PUNCT
ma-203	410	8	(	(	PUNCT
ma-203	410	9	s	s	NOUN
ma-203	410	10	+	+	NOUN
ma-203	410	11	t)2h	t)2h	NOUN
ma-203	410	12	+	+	CCONJ
ma-203	410	13	|s	|s	PROPN
ma-203	410	14	−	−	PROPN
ma-203	410	15	t|2h	t|2h	NOUN
ma-203	410	16	]	]	PUNCT
ma-203	410	17	,	,	PUNCT
ma-203	410	18	s	s	X
ma-203	410	19	,	,	PUNCT
ma-203	410	20	t	t	X
ma-203	410	21	>	>	X
ma-203	410	22	0	0	PUNCT
ma-203	411	1	for	for	ADP
ma-203	411	2	0	0	NUM
ma-203	411	3	<	<	X
ma-203	411	4	h	h	X
ma-203	411	5	<	<	X
ma-203	411	6	1	1	NUM
ma-203	411	7	introduced	introduce	VERB
ma-203	411	8	by	by	ADP
ma-203	411	9	bojdecki	bojdecki	ADJ
ma-203	411	10	,	,	PUNCT
ma-203	411	11	gorostiza	gorostiza	ADJ
ma-203	411	12	and	and	CCONJ
ma-203	411	13	talarczyk	talarczyk	X
ma-203	411	14	[	[	X
ma-203	411	15	14	14	NUM
ma-203	411	16	]	]	PUNCT
ma-203	411	17	has	have	AUX
ma-203	411	18	received	receive	VERB
ma-203	411	19	some	some	PRON
ma-203	411	20	attentionrecently	attentionrecently	ADV
ma-203	411	21	in	in	ADP
ma-203	411	22	finite	finite	ADJ
ma-203	411	23	dimensional	dimensional	ADJ
ma-203	411	24	models	model	NOUN
ma-203	411	25	.	.	PUNCT
ma-203	412	1	the	the	DET
ma-203	412	2	interesting	interesting	ADJ
ma-203	412	3	feature	feature	NOUN
ma-203	412	4	of	of	ADP
ma-203	412	5	this	this	DET
ma-203	412	6	process	process	NOUN
ma-203	412	7	is	be	AUX
ma-203	412	8	that	that	SCONJ
ma-203	412	9	this	this	PRON
ma-203	412	10	processhas	processha	VERB
ma-203	412	11	some	some	PRON
ma-203	412	12	of	of	ADP
ma-203	412	13	the	the	DET
ma-203	412	14	main	main	ADJ
ma-203	412	15	properties	property	NOUN
ma-203	412	16	of	of	ADP
ma-203	412	17	fbm	fbm	NOUN
ma-203	412	18	,	,	PUNCT
ma-203	412	19	but	but	CCONJ
ma-203	412	20	the	the	DET
ma-203	412	21	increments	increment	NOUN
ma-203	412	22	of	of	ADP
ma-203	412	23	the	the	DET
ma-203	412	24	process	process	NOUN
ma-203	412	25	are	be	AUX
ma-203	412	26	nonstationary	nonstationary	ADJ
ma-203	412	27	,	,	PUNCT
ma-203	412	28	more	more	ADV
ma-203	412	29	weakly	weakly	ADV
ma-203	412	30	correlated	correlate	VERB
ma-203	412	31	on	on	ADP
ma-203	412	32	non	non	ADJ
ma-203	412	33	-	-	ADJ
ma-203	412	34	overlapping	overlapping	ADJ
ma-203	412	35	time	time	NOUN
ma-203	412	36	intervals	interval	NOUN
ma-203	412	37	than	than	ADP
ma-203	412	38	that	that	PRON
ma-203	412	39	of	of	ADP
ma-203	412	40	fbm	fbm	NOUN
ma-203	412	41	,	,	PUNCT
ma-203	412	42	and	and	CCONJ
ma-203	412	43	its	its	PRON
ma-203	412	44	covariancedecays	covariancedecay	NOUN
ma-203	412	45	polynomially	polynomially	ADV
ma-203	412	46	at	at	ADP
ma-203	412	47	a	a	DET
ma-203	412	48	higher	high	ADJ
ma-203	412	49	rate	rate	NOUN
ma-203	412	50	as	as	ADP
ma-203	412	51	the	the	DET
ma-203	412	52	distance	distance	NOUN
ma-203	412	53	between	between	ADP
ma-203	412	54	the	the	DET
ma-203	412	55	intervals	interval	NOUN
ma-203	412	56	tends	tend	VERB
ma-203	412	57	to	to	PART
ma-203	412	58	infinity	infinity	VERB
ma-203	412	59	.	.	PUNCT
ma-203	413	1	itwould	itwould	AUX
ma-203	413	2	be	be	AUX
ma-203	413	3	interesting	interesting	ADJ
ma-203	413	4	to	to	PART
ma-203	413	5	see	see	VERB
ma-203	413	6	extension	extension	NOUN
ma-203	413	7	of	of	ADP
ma-203	413	8	this	this	DET
ma-203	413	9	paper	paper	NOUN
ma-203	413	10	to	to	ADP
ma-203	413	11	sub	sub	VERB
ma-203	413	12	-	-	ADJ
ma-203	413	13	fbm	fbm	ADJ
ma-203	413	14	case	case	NOUN
ma-203	413	15	.	.	PUNCT
ma-203	414	1	we	we	PRON
ma-203	414	2	generalize	generalize	VERB
ma-203	414	3	sub	sub	ADJ
ma-203	414	4	-	-	ADJ
ma-203	414	5	fbm	fbm	ADJ
ma-203	414	6	tosub	tosub	NOUN
ma-203	414	7	-	-	PUNCT
ma-203	414	8	fractional	fractional	ADJ
ma-203	414	9	levy	levy	NOUN
ma-203	414	10	process	process	NOUN
ma-203	414	11	(	(	PUNCT
ma-203	414	12	sub	sub	ADJ
ma-203	414	13	-	-	ADJ
ma-203	414	14	flp).sub	flp).sub	ADJ
ma-203	414	15	-	-	PUNCT
ma-203	414	16	fractional	fractional	ADJ
ma-203	414	17	levy	levy	NOUN
ma-203	414	18	process	process	NOUN
ma-203	414	19	(	(	PUNCT
ma-203	414	20	sflp	sflp	PROPN
ma-203	414	21	)	)	PUNCT
ma-203	414	22	is	be	AUX
ma-203	414	23	defined	define	VERB
ma-203	414	24	as	as	ADP
ma-203	414	25	sh	sh	PROPN
ma-203	414	26	,	,	PUNCT
ma-203	414	27	t	t	NOUN
ma-203	414	28	=	=	SYM
ma-203	414	29	1	1	NUM
ma-203	414	30	γ(h	γ(h	NOUN
ma-203	414	31	+	+	CCONJ
ma-203	414	32	1	1	NUM
ma-203	414	33	2	2	NUM
ma-203	414	34	)	)	PUNCT
ma-203	414	35	∫	∫	NOUN
ma-203	415	1	r	r	NOUN
ma-203	415	2	[	[	X
ma-203	415	3	(	(	PUNCT
ma-203	415	4	t	t	PROPN
ma-203	415	5	−	−	PROPN
ma-203	415	6	s	s	PART
ma-203	415	7	)	)	PUNCT
ma-203	415	8	h−1/2	h−1/2	PROPN
ma-203	415	9	+	+	CCONJ
ma-203	415	10	−	−	PROPN
ma-203	415	11	(	(	PUNCT
ma-203	415	12	−s	−s	NOUN
ma-203	415	13	)	)	PUNCT
ma-203	415	14	h−1/2	h−1/2	NOUN
ma-203	416	1	+	+	NUM
ma-203	416	2	]	]	X
ma-203	416	3	dms	dms	NOUN
ma-203	416	4	,	,	PUNCT
ma-203	416	5	t	t	PROPN
ma-203	416	6	∈	∈	PROPN
ma-203	416	7	r	r	NOUN
ma-203	416	8	where	where	SCONJ
ma-203	416	9	mt	mt	PROPN
ma-203	416	10	,	,	PUNCT
ma-203	416	11	t	t	PROPN
ma-203	416	12	∈	∈	PROPN
ma-203	416	13	r	r	NOUN
ma-203	416	14	is	be	AUX
ma-203	416	15	a	a	DET
ma-203	416	16	levy	levy	NOUN
ma-203	416	17	process	process	NOUN
ma-203	416	18	on	on	ADP
ma-203	416	19	r	r	NOUN
ma-203	416	20	with	with	ADP
ma-203	416	21	e(m1	e(m1	NOUN
ma-203	416	22	)	)	PUNCT
ma-203	416	23	=	=	SYM
ma-203	416	24	0	0	NUM
ma-203	416	25	,	,	PUNCT
ma-203	416	26	e(m2	e(m2	X
ma-203	416	27	1	1	NUM
ma-203	416	28	)	)	PUNCT
ma-203	416	29	<	<	X
ma-203	416	30	∞	∞	PROPN
ma-203	416	31	and	and	CCONJ
ma-203	416	32	without	without	ADP
ma-203	416	33	browniancomponent	browniancomponent	ADJ
ma-203	416	34	.	.	PUNCT
ma-203	417	1	sflp	sflp	PROPN
ma-203	417	2	has	have	VERB
ma-203	417	3	the	the	DET
ma-203	417	4	following	following	NOUN
ma-203	417	5	properties:1	properties:1	VERB
ma-203	417	6	)	)	PUNCT
ma-203	417	7	the	the	DET
ma-203	417	8	covariance	covariance	NOUN
ma-203	417	9	of	of	ADP
ma-203	417	10	the	the	DET
ma-203	417	11	process	process	NOUN
ma-203	417	12	is	be	AUX
ma-203	417	13	given	give	VERB
ma-203	417	14	by	by	ADP
ma-203	417	15	cov(sh	cov(sh	NOUN
ma-203	417	16	,	,	PUNCT
ma-203	417	17	t	t	PROPN
ma-203	417	18	,	,	PUNCT
ma-203	417	19	sh	sh	PROPN
ma-203	417	20	,	,	PUNCT
ma-203	417	21	s	s	PART
ma-203	417	22	)	)	PUNCT
ma-203	417	23	=	=	SYM
ma-203	418	1	s2h	s2h	NOUN
ma-203	418	2	+	+	PROPN
ma-203	418	3	t2h	t2h	PROPN
ma-203	418	4	+	+	CCONJ
ma-203	418	5	e[l(1)2	e[l(1)2	ADJ
ma-203	418	6	]	]	X
ma-203	418	7	2γ(2h	2γ(2h	NUM
ma-203	418	8	+	+	SYM
ma-203	418	9	1	1	NUM
ma-203	418	10	)	)	PUNCT
ma-203	418	11	sin(πh	sin(πh	NOUN
ma-203	418	12	)	)	PUNCT
ma-203	419	1	[	[	X
ma-203	419	2	|t|2h	|t|2h	ADJ
ma-203	419	3	+	+	CCONJ
ma-203	419	4	|s|2h	|s|2h	ADJ
ma-203	419	5	−	−	PROPN
ma-203	419	6	|t	|t	NOUN
ma-203	419	7	−	−	PROPN
ma-203	419	8	s|2h	s|2h	ADJ
ma-203	419	9	]	]	PUNCT
ma-203	419	10	.	.	PUNCT
ma-203	420	1	2	2	X
ma-203	420	2	)	)	PUNCT
ma-203	420	3	sh	sh	NOUN
ma-203	420	4	is	be	AUX
ma-203	420	5	not	not	PART
ma-203	420	6	a	a	DET
ma-203	420	7	martingale	martingale	NOUN
ma-203	420	8	.	.	PUNCT
ma-203	421	1	for	for	ADP
ma-203	421	2	a	a	DET
ma-203	421	3	large	large	ADJ
ma-203	421	4	class	class	NOUN
ma-203	421	5	of	of	ADP
ma-203	421	6	levy	levy	NOUN
ma-203	421	7	processes	process	NOUN
ma-203	421	8	,	,	PUNCT
ma-203	421	9	sh	sh	PROPN
ma-203	421	10	is	be	AUX
ma-203	421	11	neither	neither	CCONJ
ma-203	421	12	a	a	DET
ma-203	421	13	semimartingalenor	semimartingalenor	NOUN
ma-203	421	14	a	a	DET
ma-203	421	15	markov	markov	NOUN
ma-203	421	16	process	process	NOUN
ma-203	421	17	.	.	PUNCT
ma-203	422	1	3	3	X
ma-203	422	2	)	)	PUNCT
ma-203	422	3	sh	sh	PROPN
ma-203	422	4	is	be	AUX
ma-203	422	5	hölder	hölder	NOUN
ma-203	422	6	continuous	continuous	ADJ
ma-203	422	7	of	of	ADP
ma-203	422	8	any	any	DET
ma-203	422	9	order	order	NOUN
ma-203	422	10	β	β	X
ma-203	422	11	less	less	ADJ
ma-203	422	12	than	than	ADP
ma-203	422	13	h	h	NOUN
ma-203	422	14	−	−	NOUN
ma-203	422	15	1	1	NUM
ma-203	422	16	2	2	NUM
ma-203	422	17	.	.	PUNCT
ma-203	423	1	4	4	X
ma-203	423	2	)	)	PUNCT
ma-203	423	3	sh	sh	PROPN
ma-203	423	4	hasnonstationary	hasnonstationary	ADJ
ma-203	423	5	increments	increment	NOUN
ma-203	423	6	.	.	PUNCT
ma-203	424	1	5	5	X
ma-203	424	2	)	)	PUNCT
ma-203	424	3	sh	sh	PROPN
ma-203	424	4	is	be	AUX
ma-203	424	5	symmetric	symmetric	ADJ
ma-203	424	6	.	.	PUNCT
ma-203	425	1	6	6	X
ma-203	425	2	)	)	PUNCT
ma-203	425	3	sh	sh	PROPN
ma-203	425	4	is	be	AUX
ma-203	425	5	self	self	NOUN
ma-203	425	6	similar	similar	ADJ
ma-203	425	7	.	.	PUNCT
ma-203	426	1	7	7	X
ma-203	426	2	)	)	PUNCT
ma-203	426	3	sh	sh	NOUN
ma-203	426	4	has	have	AUX
ma-203	426	5	infinite	infinite	VERB
ma-203	426	6	totalvariation	totalvariation	NOUN
ma-203	426	7	on	on	ADP
ma-203	426	8	compacts	compact	NOUN
ma-203	426	9	.	.	PUNCT
ma-203	427	1	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	427	2	eur	eur	PROPN
ma-203	427	3	.	.	PUNCT
ma-203	428	1	j.	j.	PROPN
ma-203	428	2	math	math	PROPN
ma-203	428	3	.	.	PUNCT
ma-203	429	1	anal	anal	PROPN
ma-203	429	2	.	.	PUNCT
ma-203	430	1	10.28924	10.28924	NUM
ma-203	430	2	/	/	SYM
ma-203	430	3	ada	ada	PROPN
ma-203	430	4	/	/	SYM
ma-203	430	5	ma.4.12	ma.4.12	PROPN
ma-203	430	6	16it	16it	NOUN
ma-203	430	7	would	would	AUX
ma-203	430	8	be	be	AUX
ma-203	430	9	interesting	interesting	ADJ
ma-203	430	10	to	to	PART
ma-203	430	11	investigate	investigate	VERB
ma-203	430	12	estimation	estimation	NOUN
ma-203	430	13	in	in	ADP
ma-203	430	14	spde	spde	NOUN
ma-203	430	15	driven	drive	VERB
ma-203	430	16	by	by	ADP
ma-203	430	17	subfractional	subfractional	ADJ
ma-203	430	18	levy	levy	NOUN
ma-203	430	19	processeswhich	processeswhich	NOUN
ma-203	430	20	incorporate	incorporate	VERB
ma-203	430	21	both	both	PRON
ma-203	430	22	jumps	jump	VERB
ma-203	430	23	and	and	CCONJ
ma-203	430	24	long	long	ADJ
ma-203	430	25	memory	memory	NOUN
ma-203	430	26	apart	apart	ADV
ma-203	430	27	from	from	ADP
ma-203	430	28	nonstationarity	nonstationarity	NOUN
ma-203	430	29	.	.	PUNCT
ma-203	431	1	references	reference	NOUN
ma-203	431	2	[	[	X
ma-203	431	3	1	1	NUM
ma-203	431	4	]	]	X
ma-203	431	5	d.	d.	PROPN
ma-203	431	6	applebaum	applebaum	PROPN
ma-203	431	7	,	,	PUNCT
ma-203	431	8	levy	levy	NOUN
ma-203	431	9	processes	process	NOUN
ma-203	431	10	and	and	CCONJ
ma-203	431	11	stochastic	stochastic	ADJ
ma-203	431	12	calculus	calculus	NOUN
ma-203	431	13	,	,	PUNCT
ma-203	431	14	second	second	ADJ
ma-203	431	15	edition	edition	NOUN
ma-203	431	16	,	,	PUNCT
ma-203	431	17	cambridge	cambridge	PROPN
ma-203	431	18	university	university	PROPN
ma-203	431	19	press	press	NOUN
ma-203	431	20	,	,	PUNCT
ma-203	431	21	new	new	ADJ
ma-203	431	22	york,(2009).[2	york,(2009).[2	NOUN
ma-203	431	23	]	]	PUNCT
ma-203	431	24	o.	o.	PROPN
ma-203	431	25	bencheikh	bencheikh	PROPN
ma-203	431	26	,	,	PUNCT
ma-203	431	27	b.	b.	PROPN
ma-203	431	28	jourdain	jourdain	PROPN
ma-203	431	29	,	,	PUNCT
ma-203	431	30	bias	bias	NOUN
ma-203	431	31	beahavior	beahavior	NOUN
ma-203	431	32	and	and	CCONJ
ma-203	431	33	antithetic	antithetic	ADJ
ma-203	431	34	sampling	sampling	NOUN
ma-203	431	35	in	in	ADP
ma-203	431	36	mean	mean	ADJ
ma-203	431	37	-	-	PUNCT
ma-203	431	38	field	field	NOUN
ma-203	431	39	particle	particle	NOUN
ma-203	431	40	approximations	approximation	NOUN
ma-203	431	41	of	of	ADP
ma-203	431	42	sdesnonlinear	sdesnonlinear	NOUN
ma-203	431	43	in	in	ADP
ma-203	431	44	the	the	DET
ma-203	431	45	sense	sense	NOUN
ma-203	431	46	of	of	ADP
ma-203	431	47	mckean	mckean	PROPN
ma-203	431	48	,	,	PUNCT
ma-203	431	49	esaim	esaim	NOUN
ma-203	431	50	:	:	PUNCT
ma-203	431	51	proc	proc	NOUN
ma-203	431	52	.	.	PUNCT
ma-203	432	1	surv	surv	NOUN
ma-203	432	2	.	.	PUNCT
ma-203	433	1	65	65	NUM
ma-203	433	2	(	(	PUNCT
ma-203	433	3	2019	2019	NUM
ma-203	433	4	)	)	PUNCT
ma-203	433	5	219	219	NUM
ma-203	433	6	-	-	SYM
ma-203	433	7	235.[3	235.[3	NUM
ma-203	433	8	]	]	X
ma-203	433	9	b.m	b.m	PROPN
ma-203	433	10	.	.	PROPN
ma-203	433	11	bibby	bibby	PROPN
ma-203	433	12	,	,	PUNCT
ma-203	433	13	m.	m.	NOUN
ma-203	433	14	srensen	srensen	PROPN
ma-203	433	15	,	,	PUNCT
ma-203	433	16	martingale	martingale	ADJ
ma-203	433	17	estimation	estimation	NOUN
ma-203	433	18	functions	function	NOUN
ma-203	433	19	for	for	ADP
ma-203	433	20	discretely	discretely	ADV
ma-203	433	21	observed	observe	VERB
ma-203	433	22	diffusion	diffusion	NOUN
ma-203	433	23	processes	process	NOUN
ma-203	433	24	,	,	PUNCT
ma-203	433	25	bernoulli	bernoulli	NOUN
ma-203	433	26	1(1995	1(1995	NUM
ma-203	433	27	)	)	PUNCT
ma-203	433	28	17	17	NUM
ma-203	433	29	-	-	SYM
ma-203	433	30	39.[4	39.[4	NUM
ma-203	433	31	]	]	PUNCT
ma-203	433	32	j.p.n	j.p.n	PROPN
ma-203	433	33	.	.	PROPN
ma-203	433	34	bishwal	bishwal	PROPN
ma-203	433	35	,	,	PUNCT
ma-203	433	36	bayes	bayes	PROPN
ma-203	433	37	and	and	CCONJ
ma-203	433	38	sequential	sequential	ADJ
ma-203	433	39	estimation	estimation	NOUN
ma-203	433	40	in	in	ADP
ma-203	433	41	hilbert	hilbert	NOUN
ma-203	433	42	space	space	NOUN
ma-203	433	43	valued	value	VERB
ma-203	433	44	stochastic	stochastic	ADJ
ma-203	433	45	differential	differential	ADJ
ma-203	433	46	equations	equation	NOUN
ma-203	433	47	,	,	PUNCT
ma-203	433	48	j.	j.	PROPN
ma-203	433	49	koreanstat	koreanstat	PROPN
ma-203	433	50	.	.	PUNCT
ma-203	434	1	soc	soc	PROPN
ma-203	434	2	.	.	PUNCT
ma-203	435	1	28	28	NUM
ma-203	435	2	(	(	PUNCT
ma-203	435	3	1999	1999	NUM
ma-203	435	4	)	)	PUNCT
ma-203	435	5	93	93	NUM
ma-203	435	6	-	-	SYM
ma-203	435	7	106.[5	106.[5	NUM
ma-203	435	8	]	]	PUNCT
ma-203	435	9	j.p.n	j.p.n	PROPN
ma-203	435	10	.	.	PROPN
ma-203	435	11	bishwal	bishwal	NOUN
ma-203	435	12	,	,	PUNCT
ma-203	435	13	rates	rate	NOUN
ma-203	435	14	of	of	ADP
ma-203	435	15	convergence	convergence	NOUN
ma-203	435	16	of	of	ADP
ma-203	435	17	the	the	DET
ma-203	435	18	posterior	posterior	ADJ
ma-203	435	19	distributions	distribution	NOUN
ma-203	435	20	and	and	CCONJ
ma-203	435	21	the	the	DET
ma-203	435	22	bayes	bayes	NOUN
ma-203	435	23	estimators	estimator	NOUN
ma-203	435	24	in	in	ADP
ma-203	435	25	the	the	DET
ma-203	435	26	ornstein	ornstein	PROPN
ma-203	435	27	-	-	PUNCT
ma-203	435	28	uhlenbeck	uhlenbeck	PROPN
ma-203	435	29	process	process	NOUN
ma-203	435	30	,	,	PUNCT
ma-203	435	31	rand	rand	NOUN
ma-203	435	32	.	.	PUNCT
ma-203	436	1	oper	oper	PROPN
ma-203	436	2	.	.	PROPN
ma-203	436	3	stoch	stoch	PROPN
ma-203	436	4	.	.	PUNCT
ma-203	437	1	equ	equ	PROPN
ma-203	437	2	.	.	PROPN
ma-203	437	3	8	8	NUM
ma-203	437	4	(	(	PUNCT
ma-203	437	5	2000	2000	NUM
ma-203	437	6	)	)	PUNCT
ma-203	437	7	51	51	NUM
ma-203	437	8	-	-	SYM
ma-203	437	9	70.[6	70.[6	PROPN
ma-203	437	10	]	]	PUNCT
ma-203	437	11	j.p.n	j.p.n	PROPN
ma-203	437	12	.	.	PROPN
ma-203	437	13	bishwal	bishwal	PROPN
ma-203	437	14	,	,	PUNCT
ma-203	437	15	the	the	DET
ma-203	437	16	bernstein	bernstein	PROPN
ma-203	437	17	-	-	PUNCT
ma-203	437	18	von	von	PROPN
ma-203	437	19	mises	mises	PROPN
ma-203	437	20	theorem	theorem	VERB
ma-203	437	21	and	and	CCONJ
ma-203	437	22	spectral	spectral	ADJ
ma-203	437	23	asymptotics	asymptotic	NOUN
ma-203	437	24	of	of	ADP
ma-203	437	25	bayes	bayes	NOUN
ma-203	437	26	estimators	estimator	NOUN
ma-203	437	27	for	for	ADP
ma-203	437	28	parabolic	parabolic	ADJ
ma-203	437	29	spdes	spde	NOUN
ma-203	437	30	,	,	PUNCT
ma-203	437	31	j.	j.	PROPN
ma-203	437	32	aust	aust	PROPN
ma-203	437	33	.	.	PUNCT
ma-203	438	1	math	math	PROPN
ma-203	438	2	.	.	PUNCT
ma-203	439	1	soc	soc	PROPN
ma-203	439	2	.	.	PUNCT
ma-203	440	1	72	72	NUM
ma-203	440	2	(	(	PUNCT
ma-203	440	3	2001	2001	NUM
ma-203	440	4	)	)	PUNCT
ma-203	440	5	289	289	NUM
ma-203	440	6	-	-	SYM
ma-203	440	7	300.[7	300.[7	NUM
ma-203	440	8	]	]	PUNCT
ma-203	440	9	j.p.n	j.p.n	PROPN
ma-203	440	10	.	.	PROPN
ma-203	440	11	bishwal	bishwal	PROPN
ma-203	440	12	,	,	PUNCT
ma-203	440	13	a	a	DET
ma-203	440	14	new	new	ADJ
ma-203	440	15	estimating	estimating	NOUN
ma-203	440	16	function	function	NOUN
ma-203	440	17	for	for	ADP
ma-203	440	18	discretely	discretely	ADV
ma-203	440	19	sampled	sample	VERB
ma-203	440	20	diffusions	diffusion	NOUN
ma-203	440	21	,	,	PUNCT
ma-203	440	22	rand	rand	NOUN
ma-203	440	23	.	.	PUNCT
ma-203	441	1	oper	oper	PROPN
ma-203	441	2	.	.	PROPN
ma-203	441	3	stoch	stoch	PROPN
ma-203	441	4	.	.	PUNCT
ma-203	442	1	equ	equ	PROPN
ma-203	442	2	.	.	PROPN
ma-203	442	3	15	15	NUM
ma-203	442	4	(	(	PUNCT
ma-203	442	5	2007)65	2007)65	NUM
ma-203	442	6	-	-	SYM
ma-203	442	7	88.[8	88.[8	NUM
ma-203	442	8	]	]	PUNCT
ma-203	442	9	j.p.n	j.p.n	PROPN
ma-203	442	10	.	.	PROPN
ma-203	442	11	bishwal	bishwal	PROPN
ma-203	442	12	,	,	PUNCT
ma-203	442	13	parameter	parameter	NOUN
ma-203	442	14	estimation	estimation	NOUN
ma-203	442	15	in	in	ADP
ma-203	442	16	stochastic	stochastic	ADJ
ma-203	442	17	differential	differential	ADJ
ma-203	442	18	equations	equation	NOUN
ma-203	442	19	,	,	PUNCT
ma-203	442	20	lecture	lecture	NOUN
ma-203	442	21	notes	note	NOUN
ma-203	442	22	in	in	ADP
ma-203	442	23	mathematics	mathematic	NOUN
ma-203	442	24	,	,	PUNCT
ma-203	442	25	1923,springer	1923,springer	NUM
ma-203	442	26	-	-	PUNCT
ma-203	442	27	verlag	verlag	NOUN
ma-203	442	28	,	,	PUNCT
ma-203	442	29	(	(	PUNCT
ma-203	442	30	2008).[9	2008).[9	NOUN
ma-203	442	31	]	]	X
ma-203	442	32	j.p.n	j.p.n	PROPN
ma-203	442	33	.	.	PROPN
ma-203	442	34	bishwal	bishwal	PROPN
ma-203	442	35	,	,	PUNCT
ma-203	442	36	maximum	maximum	ADJ
ma-203	442	37	quasi	quasi	ADJ
ma-203	442	38	-	-	ADJ
ma-203	442	39	likelihood	likelihood	ADJ
ma-203	442	40	estimation	estimation	NOUN
ma-203	442	41	in	in	ADP
ma-203	442	42	fractional	fractional	ADJ
ma-203	442	43	levy	levy	NOUN
ma-203	442	44	stochastic	stochastic	ADJ
ma-203	442	45	volatility	volatility	NOUN
ma-203	442	46	model	model	NOUN
ma-203	442	47	,	,	PUNCT
ma-203	442	48	j.	j.	PROPN
ma-203	442	49	math	math	PROPN
ma-203	442	50	.	.	PUNCT
ma-203	443	1	finance1	finance1	X
ma-203	444	1	(	(	PUNCT
ma-203	444	2	2011	2011	NUM
ma-203	444	3	)	)	PUNCT
ma-203	444	4	12	12	NUM
ma-203	444	5	-	-	SYM
ma-203	444	6	15.[10	15.[10	NUM
ma-203	444	7	]	]	PUNCT
ma-203	444	8	j.p.n	j.p.n	PROPN
ma-203	444	9	.	.	PROPN
ma-203	444	10	bishwal	bishwal	PROPN
ma-203	444	11	,	,	PUNCT
ma-203	444	12	hypothesis	hypothesis	NOUN
ma-203	444	13	testing	testing	NOUN
ma-203	444	14	for	for	ADP
ma-203	444	15	fractional	fractional	ADJ
ma-203	444	16	stochastic	stochastic	ADJ
ma-203	444	17	partial	partial	ADJ
ma-203	444	18	differential	differential	NOUN
ma-203	444	19	equations	equation	NOUN
ma-203	444	20	with	with	ADP
ma-203	444	21	applications	application	NOUN
ma-203	444	22	to	to	ADP
ma-203	444	23	neu	neu	NOUN
ma-203	444	24	-	-	PUNCT
ma-203	444	25	rophysiology	rophysiology	NOUN
ma-203	444	26	and	and	CCONJ
ma-203	444	27	finance	finance	NOUN
ma-203	444	28	,	,	PUNCT
ma-203	444	29	asian	asian	ADJ
ma-203	444	30	res	re	NOUN
ma-203	444	31	.	.	PUNCT
ma-203	445	1	j.	j.	PROPN
ma-203	445	2	math	math	PROPN
ma-203	445	3	.	.	PUNCT
ma-203	446	1	4	4	NUM
ma-203	446	2	(	(	PUNCT
ma-203	446	3	2017	2017	NUM
ma-203	446	4	)	)	PUNCT
ma-203	446	5	1	1	NUM
ma-203	446	6	-	-	SYM
ma-203	446	7	24.[11	24.[11	NUM
ma-203	446	8	]	]	PUNCT
ma-203	446	9	j.p.n	j.p.n	PROPN
ma-203	446	10	.	.	PROPN
ma-203	446	11	bishwal	bishwal	PROPN
ma-203	446	12	,	,	PUNCT
ma-203	446	13	benstein	benstein	PROPN
ma-203	446	14	-	-	PUNCT
ma-203	446	15	von	von	PROPN
ma-203	446	16	mises	mises	PROPN
ma-203	446	17	theorem	theorem	VERB
ma-203	446	18	and	and	CCONJ
ma-203	446	19	small	small	ADJ
ma-203	446	20	noise	noise	NOUN
ma-203	446	21	bayesian	bayesian	NOUN
ma-203	446	22	asymptotics	asymptotic	NOUN
ma-203	446	23	for	for	ADP
ma-203	446	24	parabolic	parabolic	ADJ
ma-203	446	25	stochastic	stochastic	ADJ
ma-203	446	26	partialdifferential	partialdifferential	ADJ
ma-203	446	27	equations	equation	NOUN
ma-203	446	28	,	,	PUNCT
ma-203	446	29	theory	theory	NOUN
ma-203	446	30	stoch	stoch	NOUN
ma-203	446	31	.	.	PUNCT
ma-203	447	1	processes	process	VERB
ma-203	447	2	23	23	NUM
ma-203	447	3	(	(	PUNCT
ma-203	447	4	2018	2018	NUM
ma-203	447	5	)	)	PUNCT
ma-203	447	6	6	6	NUM
ma-203	447	7	-	-	SYM
ma-203	447	8	17.[12	17.[12	NUM
ma-203	447	9	]	]	PUNCT
ma-203	447	10	j.p.n	j.p.n	PROPN
ma-203	447	11	.	.	PROPN
ma-203	447	12	bishwal	bishwal	PROPN
ma-203	447	13	,	,	PUNCT
ma-203	447	14	parameter	parameter	NOUN
ma-203	447	15	estimation	estimation	NOUN
ma-203	447	16	in	in	ADP
ma-203	447	17	stochastic	stochastic	ADJ
ma-203	447	18	volatility	volatility	NOUN
ma-203	447	19	models	model	NOUN
ma-203	447	20	,	,	PUNCT
ma-203	447	21	springer	springer	NOUN
ma-203	447	22	nature	nature	NOUN
ma-203	447	23	,	,	PUNCT
ma-203	447	24	cham	cham	PROPN
ma-203	447	25	.	.	PUNCT
ma-203	448	1	(	(	PUNCT
ma-203	448	2	2022).[13	2022).[13	NOUN
ma-203	448	3	]	]	X
ma-203	448	4	j.p.n	j.p.n	PROPN
ma-203	448	5	.	.	PROPN
ma-203	448	6	bishwal	bishwal	PROPN
ma-203	448	7	,	,	PUNCT
ma-203	448	8	parameter	parameter	NOUN
ma-203	448	9	estimation	estimation	NOUN
ma-203	448	10	for	for	ADP
ma-203	448	11	spdes	spde	NOUN
ma-203	448	12	driven	drive	VERB
ma-203	448	13	by	by	ADP
ma-203	448	14	cylindrical	cylindrical	ADJ
ma-203	448	15	stable	stable	ADJ
ma-203	448	16	processes	process	NOUN
ma-203	448	17	,	,	PUNCT
ma-203	448	18	eur	eur	PROPN
ma-203	448	19	.	.	PUNCT
ma-203	449	1	j.	j.	PROPN
ma-203	449	2	math	math	PROPN
ma-203	449	3	.	.	PUNCT
ma-203	450	1	anal	anal	ADJ
ma-203	450	2	.	.	PUNCT
ma-203	451	1	3	3	NUM
ma-203	451	2	(	(	PUNCT
ma-203	451	3	2023)4.[14	2023)4.[14	PROPN
ma-203	451	4	]	]	X
ma-203	451	5	t.	t.	PROPN
ma-203	451	6	bojdecki	bojdecki	PROPN
ma-203	451	7	,	,	PUNCT
ma-203	451	8	l.g	l.g	PROPN
ma-203	451	9	.	.	PROPN
ma-203	451	10	gorostiza	gorostiza	PROPN
ma-203	451	11	,	,	PUNCT
ma-203	451	12	a.	a.	NOUN
ma-203	451	13	talarczyk	talarczyk	NOUN
ma-203	451	14	,	,	PUNCT
ma-203	451	15	sub	sub	ADJ
ma-203	451	16	-	-	ADJ
ma-203	451	17	fractional	fractional	ADJ
ma-203	451	18	brownian	brownian	ADJ
ma-203	451	19	motion	motion	NOUN
ma-203	451	20	and	and	CCONJ
ma-203	451	21	its	its	PRON
ma-203	451	22	relation	relation	NOUN
ma-203	451	23	to	to	ADP
ma-203	451	24	occupation	occupation	PROPN
ma-203	451	25	times	time	NOUN
ma-203	451	26	,	,	PUNCT
ma-203	451	27	stat.prob	stat.prob	PROPN
ma-203	451	28	.	.	PUNCT
ma-203	452	1	lett	lett	PROPN
ma-203	452	2	.	.	PUNCT
ma-203	453	1	69	69	NUM
ma-203	453	2	(	(	PUNCT
ma-203	453	3	2004	2004	NUM
ma-203	453	4	)	)	PUNCT
ma-203	453	5	405	405	NUM
ma-203	453	6	-	-	SYM
ma-203	453	7	419.[15	419.[15	PROPN
ma-203	453	8	]	]	PUNCT
ma-203	453	9	b.	b.	PROPN
ma-203	453	10	buchmann	buchmann	PROPN
ma-203	453	11	,	,	PUNCT
ma-203	453	12	c.	c.	PROPN
ma-203	453	13	kluppelberg	kluppelberg	PROPN
ma-203	453	14	,	,	PUNCT
ma-203	453	15	fractional	fractional	ADJ
ma-203	453	16	integral	integral	ADJ
ma-203	453	17	equations	equation	NOUN
ma-203	453	18	and	and	CCONJ
ma-203	453	19	state	state	NOUN
ma-203	453	20	space	space	NOUN
ma-203	453	21	transform	transform	NOUN
ma-203	453	22	,	,	PUNCT
ma-203	453	23	bernoulli	bernoulli	PROPN
ma-203	453	24	12	12	NUM
ma-203	453	25	(	(	PUNCT
ma-203	453	26	2006	2006	NUM
ma-203	453	27	)	)	PUNCT
ma-203	453	28	431	431	NUM
ma-203	453	29	-	-	SYM
ma-203	453	30	456.[16	456.[16	NUM
ma-203	453	31	]	]	PUNCT
ma-203	453	32	p.	p.	PROPN
ma-203	453	33	carr	carr	PROPN
ma-203	453	34	,	,	PUNCT
ma-203	453	35	h.	h.	PROPN
ma-203	453	36	geman	geman	PROPN
ma-203	453	37	,	,	PUNCT
ma-203	453	38	d.	d.	PROPN
ma-203	453	39	madan	madan	PROPN
ma-203	453	40	,	,	PUNCT
ma-203	453	41	m.	m.	NOUN
ma-203	453	42	yor	yor	PROPN
ma-203	453	43	,	,	PUNCT
ma-203	453	44	the	the	DET
ma-203	453	45	fine	fine	ADJ
ma-203	453	46	structure	structure	NOUN
ma-203	453	47	of	of	ADP
ma-203	453	48	asset	asset	NOUN
ma-203	453	49	returns	return	NOUN
ma-203	453	50	:	:	PUNCT
ma-203	453	51	an	an	DET
ma-203	453	52	empirical	empirical	ADJ
ma-203	453	53	investigation	investigation	NOUN
ma-203	453	54	,	,	PUNCT
ma-203	453	55	j.	j.	PROPN
ma-203	453	56	bus	bus	PROPN
ma-203	453	57	.	.	PUNCT
ma-203	454	1	75(2002	75(2002	NUM
ma-203	454	2	)	)	PUNCT
ma-203	454	3	305	305	NUM
ma-203	454	4	-	-	SYM
ma-203	454	5	332.[17	332.[17	PROPN
ma-203	454	6	]	]	PUNCT
ma-203	454	7	i.	i.	PROPN
ma-203	454	8	cialenko	cialenko	PROPN
ma-203	454	9	,	,	PUNCT
ma-203	454	10	parameter	parameter	NOUN
ma-203	454	11	estimations	estimation	NOUN
ma-203	454	12	for	for	ADP
ma-203	454	13	spdes	spde	NOUN
ma-203	454	14	with	with	ADP
ma-203	454	15	multiplicative	multiplicative	ADJ
ma-203	454	16	fractional	fractional	ADJ
ma-203	454	17	noise	noise	NOUN
ma-203	454	18	,	,	PUNCT
ma-203	454	19	stoch	stoch	NOUN
ma-203	454	20	.	.	PUNCT
ma-203	455	1	dyn	dyn	PROPN
ma-203	455	2	.	.	PUNCT
ma-203	456	1	10	10	NUM
ma-203	456	2	(	(	PUNCT
ma-203	456	3	2010	2010	NUM
ma-203	456	4	)	)	PUNCT
ma-203	456	5	561	561	NUM
ma-203	456	6	-	-	SYM
ma-203	456	7	576.[18	576.[18	NUM
ma-203	456	8	]	]	PUNCT
ma-203	456	9	g.	g.	PROPN
ma-203	456	10	da	da	PROPN
ma-203	456	11	prato	prato	PROPN
ma-203	456	12	,	,	PUNCT
ma-203	456	13	j.	j.	PROPN
ma-203	456	14	zabczyk	zabczyk	PROPN
ma-203	456	15	,	,	PUNCT
ma-203	456	16	stochastic	stochastic	ADJ
ma-203	456	17	equations	equation	NOUN
ma-203	456	18	in	in	ADP
ma-203	456	19	infinite	infinite	ADJ
ma-203	456	20	dimensions	dimension	NOUN
ma-203	456	21	,	,	PUNCT
ma-203	456	22	second	second	ADJ
ma-203	456	23	ed	ed	NOUN
ma-203	456	24	.	.	PROPN
ma-203	456	25	,	,	PUNCT
ma-203	456	26	cambridge	cambridge	PROPN
ma-203	456	27	university	university	PROPN
ma-203	456	28	press,(2014).[19	press,(2014).[19	PROPN
ma-203	456	29	]	]	X
ma-203	456	30	d.	d.	PROPN
ma-203	456	31	dawson	dawson	PROPN
ma-203	456	32	,	,	PUNCT
ma-203	456	33	critical	critical	ADJ
ma-203	456	34	dynamics	dynamic	NOUN
ma-203	456	35	and	and	CCONJ
ma-203	456	36	fluctuations	fluctuation	NOUN
ma-203	456	37	for	for	ADP
ma-203	456	38	a	a	DET
ma-203	456	39	mean	mean	ADJ
ma-203	456	40	-	-	PUNCT
ma-203	456	41	field	field	NOUN
ma-203	456	42	model	model	NOUN
ma-203	456	43	of	of	ADP
ma-203	456	44	cooperative	cooperative	ADJ
ma-203	456	45	behavior	behavior	NOUN
ma-203	456	46	,	,	PUNCT
ma-203	456	47	j.	j.	PROPN
ma-203	456	48	stat	stat	PROPN
ma-203	456	49	.	.	PUNCT
ma-203	457	1	phys	phy	NOUN
ma-203	457	2	.	.	PUNCT
ma-203	458	1	31(1983	31(1983	NUM
ma-203	458	2	)	)	PUNCT
ma-203	458	3	29	29	NUM
ma-203	458	4	-	-	SYM
ma-203	458	5	85.[20	85.[20	NUM
ma-203	458	6	]	]	PUNCT
ma-203	458	7	z.	z.	PROPN
ma-203	458	8	fu	fu	PROPN
ma-203	458	9	,	,	PUNCT
ma-203	458	10	z.	z.	PROPN
ma-203	458	11	li	li	PROPN
ma-203	458	12	,	,	PUNCT
ma-203	458	13	stochastic	stochastic	ADJ
ma-203	458	14	equations	equation	NOUN
ma-203	458	15	of	of	ADP
ma-203	458	16	non	non	ADJ
ma-203	458	17	-	-	ADJ
ma-203	458	18	negative	negative	ADJ
ma-203	458	19	processes	process	NOUN
ma-203	458	20	with	with	ADP
ma-203	458	21	jumps	jump	NOUN
ma-203	458	22	,	,	PUNCT
ma-203	458	23	stoch	stoch	NOUN
ma-203	458	24	.	.	PUNCT
ma-203	459	1	proc	proc	PROPN
ma-203	459	2	.	.	PUNCT
ma-203	460	1	appl	appl	PROPN
ma-203	460	2	.	.	PUNCT
ma-203	461	1	120	120	NUM
ma-203	461	2	(	(	PUNCT
ma-203	461	3	2010	2010	NUM
ma-203	461	4	)	)	PUNCT
ma-203	461	5	306	306	NUM
ma-203	461	6	-	-	SYM
ma-203	461	7	330.[21	330.[21	NUM
ma-203	461	8	]	]	PUNCT
ma-203	461	9	h.	h.	PROPN
ma-203	461	10	he	he	PROPN
ma-203	461	11	,	,	PUNCT
ma-203	461	12	z.	z.	PROPN
ma-203	461	13	li	li	PROPN
ma-203	461	14	,	,	PUNCT
ma-203	461	15	x.	x.	PROPN
ma-203	461	16	yang	yang	PROPN
ma-203	461	17	,	,	PUNCT
ma-203	461	18	stochastic	stochastic	ADJ
ma-203	461	19	equations	equation	NOUN
ma-203	461	20	of	of	ADP
ma-203	461	21	super	super	ADJ
ma-203	461	22	-	-	ADJ
ma-203	461	23	levy	levy	ADJ
ma-203	461	24	processes	process	NOUN
ma-203	461	25	with	with	ADP
ma-203	461	26	genaral	genaral	ADJ
ma-203	461	27	branching	branch	VERB
ma-203	461	28	mechanism	mechanism	NOUN
ma-203	461	29	,	,	PUNCT
ma-203	461	30	stoch.process	stoch.process	NOUN
ma-203	461	31	.	.	PUNCT
ma-203	462	1	appl	appl	PROPN
ma-203	462	2	.	.	PROPN
ma-203	463	1	124	124	NUM
ma-203	463	2	(	(	PUNCT
ma-203	463	3	2014	2014	NUM
ma-203	463	4	)	)	PUNCT
ma-203	463	5	1519	1519	NUM
ma-203	463	6	-	-	SYM
ma-203	463	7	1565.[22	1565.[22	NUM
ma-203	463	8	]	]	X
ma-203	463	9	y.	y.	PROPN
ma-203	463	10	hu	hu	PROPN
ma-203	463	11	,	,	PUNCT
ma-203	463	12	h.	h.	PROPN
ma-203	463	13	long	long	PROPN
ma-203	463	14	,	,	PUNCT
ma-203	463	15	parameter	parameter	NOUN
ma-203	463	16	estimation	estimation	NOUN
ma-203	463	17	for	for	ADP
ma-203	463	18	ornstein	ornstein	PROPN
ma-203	463	19	-	-	PUNCT
ma-203	463	20	uhlenbeck	uhlenbeck	PROPN
ma-203	463	21	processes	process	NOUN
ma-203	463	22	driven	drive	VERB
ma-203	463	23	by	by	ADP
ma-203	463	24	α	α	VERB
ma-203	463	25	-	-	ADJ
ma-203	463	26	stable	stable	ADJ
ma-203	463	27	levy	levy	NOUN
ma-203	463	28	motions	motion	NOUN
ma-203	463	29	,	,	PUNCT
ma-203	463	30	comm.stoch	comm.stoch	PROPN
ma-203	463	31	.	.	PUNCT
ma-203	464	1	anal	anal	PROPN
ma-203	464	2	.	.	PUNCT
ma-203	465	1	1	1	NUM
ma-203	465	2	(	(	PUNCT
ma-203	465	3	2007	2007	NUM
ma-203	465	4	)	)	PUNCT
ma-203	465	5	175	175	NUM
ma-203	465	6	-	-	SYM
ma-203	465	7	192	192	NUM
ma-203	465	8	.	.	PUNCT
ma-203	466	1	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	PROPN
ma-203	466	2	eur	eur	PROPN
ma-203	466	3	.	.	PUNCT
ma-203	467	1	j.	j.	PROPN
ma-203	467	2	math	math	PROPN
ma-203	467	3	.	.	PUNCT
ma-203	468	1	anal	anal	PROPN
ma-203	468	2	.	.	PUNCT
ma-203	469	1	10.28924	10.28924	NUM
ma-203	469	2	/	/	SYM
ma-203	469	3	ada	ada	PROPN
ma-203	469	4	/	/	SYM
ma-203	469	5	ma.4.12	ma.4.12	NOUN
ma-203	469	6	17	17	NUM
ma-203	470	1	[	[	X
ma-203	470	2	23	23	NUM
ma-203	470	3	]	]	X
ma-203	470	4	y.	y.	PROPN
ma-203	470	5	hu	hu	PROPN
ma-203	470	6	,	,	PUNCT
ma-203	470	7	h.	h.	PROPN
ma-203	470	8	long	long	ADV
ma-203	470	9	,	,	PUNCT
ma-203	470	10	least	least	ADJ
ma-203	470	11	squares	square	NOUN
ma-203	470	12	estimator	estimator	NOUN
ma-203	470	13	for	for	ADP
ma-203	470	14	ornstein	ornstein	PROPN
ma-203	470	15	-	-	PUNCT
ma-203	470	16	uhlenbeck	uhlenbeck	PROPN
ma-203	470	17	processes	process	NOUN
ma-203	470	18	driven	drive	VERB
ma-203	470	19	by	by	ADP
ma-203	470	20	α	α	VERB
ma-203	470	21	-	-	ADJ
ma-203	470	22	stable	stable	ADJ
ma-203	470	23	levy	levy	NOUN
ma-203	470	24	motions	motion	NOUN
ma-203	470	25	,	,	PUNCT
ma-203	470	26	stoch.process	stoch.process	NOUN
ma-203	470	27	.	.	PUNCT
ma-203	471	1	appl	appl	PROPN
ma-203	471	2	.	.	PUNCT
ma-203	472	1	119	119	NUM
ma-203	472	2	(	(	PUNCT
ma-203	472	3	2009	2009	NUM
ma-203	472	4	)	)	PUNCT
ma-203	472	5	2465	2465	NUM
ma-203	472	6	-	-	SYM
ma-203	472	7	2480.[24	2480.[24	NUM
ma-203	472	8	]	]	X
ma-203	472	9	r.a	r.a	PROPN
ma-203	472	10	.	.	PROPN
ma-203	472	11	kasonga	kasonga	PROPN
ma-203	472	12	,	,	PUNCT
ma-203	472	13	maximum	maximum	ADJ
ma-203	472	14	likelihood	likelihood	NOUN
ma-203	472	15	theory	theory	NOUN
ma-203	472	16	for	for	ADP
ma-203	472	17	large	large	ADJ
ma-203	472	18	interacting	interact	VERB
ma-203	472	19	systems	system	NOUN
ma-203	472	20	,	,	PUNCT
ma-203	472	21	siam	siam	PROPN
ma-203	472	22	j.	j.	PROPN
ma-203	472	23	appl	appl	PROPN
ma-203	472	24	.	.	PROPN
ma-203	472	25	math	math	PROPN
ma-203	472	26	.	.	PUNCT
ma-203	473	1	50	50	NUM
ma-203	473	2	(	(	PUNCT
ma-203	473	3	1990	1990	NUM
ma-203	473	4	)	)	PUNCT
ma-203	473	5	865	865	NUM
ma-203	473	6	-	-	SYM
ma-203	473	7	875.[25	875.[25	NUM
ma-203	473	8	]	]	X
ma-203	473	9	y.s	y.s	PROPN
ma-203	473	10	.	.	PROPN
ma-203	473	11	kim	kim	PROPN
ma-203	473	12	,	,	PUNCT
ma-203	473	13	s.t	s.t	PROPN
ma-203	473	14	.	.	PROPN
ma-203	473	15	rachev	rachev	PROPN
ma-203	473	16	,	,	PUNCT
ma-203	473	17	d.m	d.m	PROPN
ma-203	473	18	.	.	PROPN
ma-203	473	19	chung	chung	PROPN
ma-203	473	20	,	,	PUNCT
ma-203	473	21	m.l	m.l	PROPN
ma-203	473	22	.	.	PROPN
ma-203	473	23	bianichi	bianichi	PROPN
ma-203	473	24	,	,	PUNCT
ma-203	473	25	a	a	DET
ma-203	473	26	modified	modify	VERB
ma-203	473	27	tempered	temper	VERB
ma-203	473	28	stable	stable	ADJ
ma-203	473	29	distribution	distribution	NOUN
ma-203	473	30	with	with	ADP
ma-203	473	31	volatility	volatility	NOUN
ma-203	473	32	cluster	cluster	NOUN
ma-203	473	33	-	-	PUNCT
ma-203	473	34	ing	ing	NOUN
ma-203	473	35	,	,	PUNCT
ma-203	473	36	in	in	ADP
ma-203	473	37	:	:	PUNCT
ma-203	473	38	j.o	j.o	PROPN
ma-203	473	39	.	.	PROPN
ma-203	473	40	soares	soares	PROPN
ma-203	473	41	,	,	PUNCT
ma-203	473	42	j.	j.	PROPN
ma-203	473	43	pina	pina	PROPN
ma-203	473	44	,	,	PUNCT
ma-203	473	45	m.	m.	NOUN
ma-203	473	46	catalao	catalao	PROPN
ma-203	473	47	-	-	PUNCT
ma-203	473	48	lopes	lope	NOUN
ma-203	473	49	,	,	PUNCT
ma-203	473	50	new	new	ADJ
ma-203	473	51	developments	development	NOUN
ma-203	473	52	in	in	ADP
ma-203	473	53	financial	financial	ADJ
ma-203	473	54	modelling	modelling	NOUN
ma-203	473	55	,	,	PUNCT
ma-203	473	56	cambridge	cambridge	PROPN
ma-203	473	57	scholarspublishing	scholarspublishing	PROPN
ma-203	473	58	,	,	PUNCT
ma-203	473	59	newcastle	newcastle	PROPN
ma-203	473	60	upon	upon	SCONJ
ma-203	473	61	tyne	tyne	PROPN
ma-203	473	62	,	,	PUNCT
ma-203	473	63	uk	uk	PROPN
ma-203	473	64	,	,	PUNCT
ma-203	473	65	(	(	PUNCT
ma-203	473	66	2008).[26	2008).[26	X
ma-203	473	67	]	]	X
ma-203	473	68	n.	n.	NOUN
ma-203	473	69	konno	konno	NOUN
ma-203	473	70	,	,	PUNCT
ma-203	473	71	t.	t.	PROPN
ma-203	473	72	shiga	shiga	PROPN
ma-203	473	73	,	,	PUNCT
ma-203	473	74	stochatic	stochatic	ADJ
ma-203	473	75	partial	partial	ADJ
ma-203	473	76	differential	differential	ADJ
ma-203	473	77	equations	equation	NOUN
ma-203	473	78	for	for	ADP
ma-203	473	79	measure	measure	NOUN
ma-203	473	80	-	-	PUNCT
ma-203	473	81	valued	value	VERB
ma-203	473	82	diffusions	diffusion	NOUN
ma-203	473	83	,	,	PUNCT
ma-203	473	84	prob	prob	PROPN
ma-203	473	85	.	.	PROPN
ma-203	473	86	theory	theory	NOUN
ma-203	473	87	relatedfields	relatedfield	VERB
ma-203	473	88	79	79	NUM
ma-203	473	89	(	(	PUNCT
ma-203	473	90	1988	1988	NUM
ma-203	473	91	)	)	PUNCT
ma-203	473	92	201	201	NUM
ma-203	473	93	-	-	SYM
ma-203	473	94	225.[27	225.[27	NUM
ma-203	473	95	]	]	PUNCT
ma-203	473	96	a.	a.	NOUN
ma-203	473	97	janicki	janicki	PROPN
ma-203	473	98	,	,	PUNCT
ma-203	473	99	a.	a.	NOUN
ma-203	473	100	weron	weron	PROPN
ma-203	473	101	,	,	PUNCT
ma-203	473	102	simulation	simulation	NOUN
ma-203	473	103	and	and	CCONJ
ma-203	473	104	chaotic	chaotic	ADJ
ma-203	473	105	behavior	behavior	NOUN
ma-203	473	106	of	of	ADP
ma-203	473	107	α	α	NOUN
ma-203	473	108	-	-	ADJ
ma-203	473	109	stable	stable	ADJ
ma-203	473	110	stochastic	stochastic	NOUN
ma-203	473	111	processes	process	NOUN
ma-203	473	112	,	,	PUNCT
ma-203	473	113	marcel	marcel	PROPN
ma-203	473	114	dekker	dekker	PROPN
ma-203	473	115	,	,	PUNCT
ma-203	473	116	new	new	ADJ
ma-203	473	117	york,(1994).[28	york,(1994).[28	PROPN
ma-203	473	118	]	]	PUNCT
ma-203	473	119	z.	z.	PROPN
ma-203	473	120	li	li	PROPN
ma-203	473	121	,	,	PUNCT
ma-203	473	122	c.	c.	PROPN
ma-203	473	123	ma	ma	PROPN
ma-203	473	124	,	,	PUNCT
ma-203	473	125	asymptotic	asymptotic	ADJ
ma-203	473	126	properties	property	NOUN
ma-203	473	127	of	of	ADP
ma-203	473	128	estimators	estimator	NOUN
ma-203	473	129	in	in	ADP
ma-203	473	130	a	a	DET
ma-203	473	131	stable	stable	ADJ
ma-203	473	132	cox	cox	PROPN
ma-203	473	133	-	-	PUNCT
ma-203	473	134	ingersoll	ingersoll	PROPN
ma-203	473	135	-	-	PUNCT
ma-203	473	136	ross	ross	PROPN
ma-203	473	137	model	model	PROPN
ma-203	473	138	,	,	PUNCT
ma-203	473	139	stoch	stoch	PROPN
ma-203	473	140	.	.	PUNCT
ma-203	474	1	proc	proc	PROPN
ma-203	474	2	.	.	PUNCT
ma-203	475	1	appl	appl	PROPN
ma-203	475	2	.	.	PROPN
ma-203	476	1	125	125	NUM
ma-203	476	2	(	(	PUNCT
ma-203	476	3	2015)3196	2015)3196	NUM
ma-203	476	4	-	-	SYM
ma-203	476	5	3233.[29	3233.[29	NUM
ma-203	476	6	]	]	PUNCT
ma-203	476	7	k.	k.	PROPN
ma-203	476	8	oelschlager	oelschlager	PROPN
ma-203	476	9	,	,	PUNCT
ma-203	476	10	a	a	DET
ma-203	476	11	martingale	martingale	ADJ
ma-203	476	12	approach	approach	NOUN
ma-203	476	13	to	to	ADP
ma-203	476	14	the	the	DET
ma-203	476	15	law	law	NOUN
ma-203	476	16	of	of	ADP
ma-203	476	17	large	large	ADJ
ma-203	476	18	numbers	number	NOUN
ma-203	476	19	for	for	ADP
ma-203	476	20	weakly	weakly	ADJ
ma-203	476	21	interacting	interact	VERB
ma-203	476	22	particle	particle	NOUN
ma-203	476	23	stochasticprocesses	stochasticprocesse	NOUN
ma-203	476	24	,	,	PUNCT
ma-203	476	25	ann	ann	PROPN
ma-203	476	26	.	.	PROPN
ma-203	476	27	prob	prob	PROPN
ma-203	476	28	.	.	PROPN
ma-203	477	1	12	12	NUM
ma-203	477	2	(	(	PUNCT
ma-203	477	3	1984	1984	NUM
ma-203	477	4	)	)	PUNCT
ma-203	477	5	458	458	NUM
ma-203	477	6	-	-	SYM
ma-203	477	7	479.[30	479.[30	PROPN
ma-203	477	8	]	]	X
ma-203	477	9	g.a	g.a	PROPN
ma-203	477	10	.	.	PROPN
ma-203	477	11	pavliotis	pavliotis	PROPN
ma-203	477	12	,	,	PUNCT
ma-203	477	13	a.	a.	NOUN
ma-203	477	14	zanoni	zanoni	PROPN
ma-203	477	15	,	,	PUNCT
ma-203	477	16	eigenfunction	eigenfunction	NOUN
ma-203	477	17	martingale	martingale	ADJ
ma-203	477	18	estimators	estimator	NOUN
ma-203	477	19	for	for	ADP
ma-203	477	20	interacting	interact	VERB
ma-203	477	21	particle	particle	NOUN
ma-203	477	22	systems	system	NOUN
ma-203	477	23	and	and	CCONJ
ma-203	477	24	their	their	PRON
ma-203	477	25	mean	mean	ADJ
ma-203	477	26	fieldlimit	fieldlimit	NOUN
ma-203	477	27	,	,	PUNCT
ma-203	477	28	arxiv:2112.04870	arxiv:2112.04870	NOUN
ma-203	477	29	,	,	PUNCT
ma-203	477	30	(	(	PUNCT
ma-203	477	31	2022).[31	2022).[31	NUM
ma-203	477	32	]	]	X
ma-203	477	33	s.	s.	PROPN
ma-203	477	34	peszat	peszat	PROPN
ma-203	477	35	,	,	PUNCT
ma-203	477	36	j.	j.	PROPN
ma-203	477	37	zabczyk	zabczyk	PROPN
ma-203	477	38	,	,	PUNCT
ma-203	477	39	stochastic	stochastic	ADJ
ma-203	477	40	partial	partial	ADJ
ma-203	477	41	differential	differential	ADJ
ma-203	477	42	equations	equation	NOUN
ma-203	477	43	with	with	ADP
ma-203	477	44	levy	levy	NOUN
ma-203	477	45	noise	noise	NOUN
ma-203	477	46	:	:	PUNCT
ma-203	477	47	evolution	evolution	NOUN
ma-203	477	48	equations	equation	NOUN
ma-203	477	49	approach	approach	PROPN
ma-203	477	50	,	,	PUNCT
ma-203	477	51	cambridge	cambridge	PROPN
ma-203	477	52	university	university	PROPN
ma-203	477	53	press	press	PROPN
ma-203	477	54	,	,	PUNCT
ma-203	477	55	cambridge	cambridge	PROPN
ma-203	477	56	,	,	PUNCT
ma-203	477	57	england	england	PROPN
ma-203	477	58	,	,	PUNCT
ma-203	477	59	(	(	PUNCT
ma-203	477	60	2007).[32	2007).[32	PROPN
ma-203	477	61	]	]	X
ma-203	477	62	e.	e.	PROPN
ma-203	477	63	priola	priola	PROPN
ma-203	477	64	,	,	PUNCT
ma-203	477	65	a.	a.	PROPN
ma-203	477	66	shirikyan	shirikyan	PROPN
ma-203	477	67	,	,	PUNCT
ma-203	477	68	l.	l.	PROPN
ma-203	477	69	xu	xu	PROPN
ma-203	477	70	,	,	PUNCT
ma-203	477	71	j.	j.	PROPN
ma-203	477	72	zabczyk	zabczyk	PROPN
ma-203	477	73	,	,	PUNCT
ma-203	477	74	exponential	exponential	ADJ
ma-203	477	75	ergodicity	ergodicity	NOUN
ma-203	477	76	and	and	CCONJ
ma-203	477	77	regularity	regularity	NOUN
ma-203	477	78	for	for	ADP
ma-203	477	79	equations	equation	NOUN
ma-203	477	80	with	with	ADP
ma-203	477	81	levy	levy	NOUN
ma-203	477	82	noise	noise	NOUN
ma-203	477	83	,	,	PUNCT
ma-203	477	84	stoch.proc	stoch.proc	PROPN
ma-203	477	85	.	.	PUNCT
ma-203	477	86	appl	appl	PROPN
ma-203	477	87	.	.	PUNCT
ma-203	478	1	122	122	NUM
ma-203	478	2	(	(	PUNCT
ma-203	478	3	2012	2012	NUM
ma-203	478	4	)	)	PUNCT
ma-203	478	5	106	106	NUM
ma-203	478	6	-	-	SYM
ma-203	478	7	133.[33	133.[33	NUM
ma-203	478	8	]	]	X
ma-203	478	9	e.	e.	PROPN
ma-203	478	10	priola	priola	PROPN
ma-203	478	11	,	,	PUNCT
ma-203	478	12	j.	j.	PROPN
ma-203	478	13	zabczyk	zabczyk	PROPN
ma-203	478	14	,	,	PUNCT
ma-203	478	15	structural	structural	ADJ
ma-203	478	16	properties	property	NOUN
ma-203	478	17	of	of	ADP
ma-203	478	18	semilinear	semilinear	ADJ
ma-203	478	19	spdes	spde	NOUN
ma-203	478	20	driven	drive	VERB
ma-203	478	21	by	by	ADP
ma-203	478	22	cylindrical	cylindrical	ADJ
ma-203	478	23	stable	stable	ADJ
ma-203	478	24	processes	process	NOUN
ma-203	478	25	,	,	PUNCT
ma-203	478	26	prob	prob	PROPN
ma-203	478	27	.	.	PROPN
ma-203	478	28	theoryrelated	theoryrelate	VERB
ma-203	478	29	fields	field	NOUN
ma-203	478	30	149	149	NUM
ma-203	478	31	(	(	PUNCT
ma-203	478	32	2011	2011	NUM
ma-203	478	33	)	)	PUNCT
ma-203	478	34	97	97	NUM
ma-203	478	35	-	-	SYM
ma-203	478	36	137.[34	137.[34	NUM
ma-203	478	37	]	]	X
ma-203	478	38	r.	r.	PROPN
ma-203	478	39	rebolledo	rebolledo	PROPN
ma-203	478	40	,	,	PUNCT
ma-203	478	41	central	central	ADJ
ma-203	478	42	limit	limit	NOUN
ma-203	478	43	theorems	theorem	NOUN
ma-203	478	44	for	for	ADP
ma-203	478	45	local	local	ADJ
ma-203	478	46	martingales	martingale	NOUN
ma-203	478	47	,	,	PUNCT
ma-203	478	48	zeit	zeit	PROPN
ma-203	478	49	.	.	PUNCT
ma-203	479	1	wahr	wahr	PROPN
ma-203	479	2	.	.	PUNCT
ma-203	480	1	verw	verw	PROPN
ma-203	480	2	.	.	PUNCT
ma-203	481	1	gebiete	gebiete	PROPN
ma-203	481	2	51	51	NUM
ma-203	481	3	(	(	PUNCT
ma-203	481	4	1980	1980	NUM
ma-203	481	5	)	)	PUNCT
ma-203	481	6	269	269	NUM
ma-203	481	7	-	-	PUNCT
ma-203	481	8	286.[35	286.[35	PROPN
ma-203	481	9	]	]	X
ma-203	481	10	l.	l.	PROPN
ma-203	481	11	sharrock	sharrock	PROPN
ma-203	481	12	,	,	PUNCT
ma-203	481	13	n.	n.	NOUN
ma-203	481	14	kantas	kanta	NOUN
ma-203	481	15	,	,	PUNCT
ma-203	481	16	p.	p.	NOUN
ma-203	481	17	parpas	parpas	PROPN
ma-203	481	18	,	,	PUNCT
ma-203	481	19	g.a	g.a	PROPN
ma-203	481	20	.	.	PROPN
ma-203	481	21	pavliotis	pavliotis	PROPN
ma-203	481	22	,	,	PUNCT
ma-203	481	23	parameter	parameter	NOUN
ma-203	481	24	estimation	estimation	NOUN
ma-203	481	25	for	for	ADP
ma-203	481	26	the	the	DET
ma-203	481	27	mckean	mckean	ADJ
ma-203	481	28	-	-	PUNCT
ma-203	481	29	vlasov	vlasov	PROPN
ma-203	481	30	stochastic	stochastic	ADJ
ma-203	481	31	differentialequation	differentialequation	NOUN
ma-203	481	32	,	,	PUNCT
ma-203	481	33	arxiv:2106.13751	arxiv:2106.13751	NOUN
ma-203	481	34	,	,	PUNCT
ma-203	481	35	(	(	PUNCT
ma-203	481	36	2021).[36	2021).[36	NUM
ma-203	481	37	]	]	PUNCT
ma-203	481	38	k.	k.	PROPN
ma-203	481	39	sato	sato	PROPN
ma-203	481	40	,	,	PUNCT
ma-203	481	41	levy	levy	NOUN
ma-203	481	42	processes	process	NOUN
ma-203	481	43	and	and	CCONJ
ma-203	481	44	infinitely	infinitely	ADV
ma-203	481	45	divisible	divisible	ADJ
ma-203	481	46	distributions	distribution	NOUN
ma-203	481	47	,	,	PUNCT
ma-203	481	48	cambridge	cambridge	PROPN
ma-203	481	49	university	university	PROPN
ma-203	481	50	press	press	PROPN
ma-203	481	51	,	,	PUNCT
ma-203	481	52	cambridge	cambridge	PROPN
ma-203	481	53	,	,	PUNCT
ma-203	481	54	(	(	PUNCT
ma-203	481	55	1999).[37	1999).[37	X
ma-203	481	56	]	]	X
ma-203	481	57	d.	d.	PROPN
ma-203	481	58	talay	talay	PROPN
ma-203	481	59	,	,	PUNCT
ma-203	481	60	l.	l.	PROPN
ma-203	481	61	tubaro	tubaro	NOUN
ma-203	481	62	,	,	PUNCT
ma-203	481	63	expansion	expansion	NOUN
ma-203	481	64	of	of	ADP
ma-203	481	65	the	the	DET
ma-203	481	66	global	global	ADJ
ma-203	481	67	error	error	NOUN
ma-203	481	68	for	for	ADP
ma-203	481	69	numerical	numerical	ADJ
ma-203	481	70	schemes	scheme	NOUN
ma-203	481	71	solving	solve	VERB
ma-203	481	72	stochastic	stochastic	ADJ
ma-203	481	73	differential	differential	ADJ
ma-203	481	74	equations	equation	NOUN
ma-203	481	75	,	,	PUNCT
ma-203	481	76	stoch	stoch	NOUN
ma-203	481	77	.	.	PUNCT
ma-203	482	1	anal	anal	PROPN
ma-203	482	2	.	.	PUNCT
ma-203	483	1	appl	appl	PROPN
ma-203	483	2	.	.	PROPN
ma-203	484	1	8	8	NUM
ma-203	484	2	(	(	PUNCT
ma-203	484	3	1990	1990	NUM
ma-203	484	4	)	)	PUNCT
ma-203	484	5	483	483	NUM
ma-203	484	6	-	-	SYM
ma-203	484	7	509.[38	509.[38	PROPN
ma-203	484	8	]	]	X
ma-203	484	9	a.w	a.w	PROPN
ma-203	484	10	.	.	PROPN
ma-203	484	11	van	van	PROPN
ma-203	484	12	der	der	PROPN
ma-203	484	13	vaart	vaart	PROPN
ma-203	484	14	,	,	PUNCT
ma-203	484	15	asymptotic	asymptotic	ADJ
ma-203	484	16	statistics	statistic	NOUN
ma-203	484	17	,	,	PUNCT
ma-203	484	18	cambridge	cambridge	PROPN
ma-203	484	19	university	university	PROPN
ma-203	484	20	press	press	PROPN
ma-203	484	21	,	,	PUNCT
ma-203	484	22	cambridge	cambridge	PROPN
ma-203	484	23	,	,	PUNCT
ma-203	484	24	(	(	PUNCT
ma-203	484	25	2000).[39	2000).[39	X
ma-203	484	26	]	]	PUNCT
ma-203	484	27	l.	l.	PROPN
ma-203	484	28	wang	wang	PROPN
ma-203	484	29	,	,	PUNCT
ma-203	484	30	x.	x.	PROPN
ma-203	484	31	yang	yang	PROPN
ma-203	484	32	,	,	PUNCT
ma-203	484	33	x.	x.	PROPN
ma-203	484	34	zhou	zhou	PROPN
ma-203	484	35	,	,	PUNCT
ma-203	484	36	a	a	DET
ma-203	484	37	distribution	distribution	NOUN
ma-203	484	38	function	function	NOUN
ma-203	484	39	valued	value	VERB
ma-203	484	40	spde	spde	NOUN
ma-203	484	41	and	and	CCONJ
ma-203	484	42	its	its	PRON
ma-203	484	43	applications	application	NOUN
ma-203	484	44	,	,	PUNCT
ma-203	484	45	j.	j.	PROPN
ma-203	484	46	diff	diff	PROPN
ma-203	484	47	.	.	PUNCT
ma-203	485	1	equ	equ	PROPN
ma-203	485	2	.	.	PROPN
ma-203	486	1	262	262	NUM
ma-203	486	2	(	(	PUNCT
ma-203	486	3	2017)1085	2017)1085	NOUN
ma-203	486	4	-	-	SYM
ma-203	486	5	1118.[40	1118.[40	NUM
ma-203	486	6	]	]	X
ma-203	486	7	j.	j.	PROPN
ma-203	486	8	xiong	xiong	PROPN
ma-203	486	9	,	,	PUNCT
ma-203	486	10	super	super	ADJ
ma-203	486	11	-	-	ADJ
ma-203	486	12	brownian	brownian	ADJ
ma-203	486	13	motion	motion	NOUN
ma-203	486	14	as	as	ADP
ma-203	486	15	the	the	DET
ma-203	486	16	unique	unique	ADJ
ma-203	486	17	strong	strong	ADJ
ma-203	486	18	solution	solution	NOUN
ma-203	486	19	to	to	ADP
ma-203	486	20	an	an	DET
ma-203	486	21	spde	spde	NOUN
ma-203	486	22	,	,	PUNCT
ma-203	486	23	ann	ann	PROPN
ma-203	486	24	.	.	PROPN
ma-203	486	25	prob	prob	PROPN
ma-203	486	26	.	.	PROPN
ma-203	487	1	41	41	NUM
ma-203	487	2	(	(	PUNCT
ma-203	487	3	2013	2013	NUM
ma-203	487	4	)	)	PUNCT
ma-203	487	5	1030	1030	NUM
ma-203	487	6	-	-	SYM
ma-203	487	7	1054.[41	1054.[41	NUM
ma-203	487	8	]	]	X
ma-203	487	9	j.	j.	PROPN
ma-203	487	10	xiong	xiong	PROPN
ma-203	487	11	,	,	PUNCT
ma-203	487	12	x.	x.	PROPN
ma-203	487	13	yang	yang	PROPN
ma-203	487	14	,	,	PUNCT
ma-203	487	15	existence	existence	NOUN
ma-203	487	16	and	and	CCONJ
ma-203	487	17	pathwise	pathwise	NOUN
ma-203	487	18	uniqueness	uniqueness	NOUN
ma-203	487	19	to	to	ADP
ma-203	487	20	an	an	DET
ma-203	487	21	spde	spde	NOUN
ma-203	487	22	driven	drive	VERB
ma-203	487	23	by	by	ADP
ma-203	487	24	α	α	VERB
ma-203	487	25	-	-	ADJ
ma-203	487	26	stable	stable	ADJ
ma-203	487	27	colored	colored	ADJ
ma-203	487	28	noise	noise	NOUN
ma-203	487	29	,	,	PUNCT
ma-203	487	30	stoch	stoch	NOUN
ma-203	487	31	.	.	PUNCT
ma-203	488	1	process.appl	process.appl	NOUN
ma-203	488	2	.	.	PUNCT
ma-203	489	1	129	129	NUM
ma-203	489	2	(	(	PUNCT
ma-203	489	3	2019	2019	NUM
ma-203	489	4	)	)	PUNCT
ma-203	489	5	2681	2681	NUM
ma-203	489	6	-	-	SYM
ma-203	489	7	2772.[42	2772.[42	NUM
ma-203	489	8	]	]	X
ma-203	489	9	x.	x.	NOUN
ma-203	489	10	yang	yang	PROPN
ma-203	489	11	,	,	PUNCT
ma-203	489	12	x.	x.	PROPN
ma-203	489	13	zhou	zhou	PROPN
ma-203	489	14	,	,	PUNCT
ma-203	489	15	pathwise	pathwise	NOUN
ma-203	489	16	uniqueness	uniqueness	NOUN
ma-203	489	17	for	for	ADP
ma-203	489	18	an	an	DET
ma-203	489	19	spde	spde	NOUN
ma-203	489	20	with	with	ADP
ma-203	489	21	hölder	hölder	PROPN
ma-203	489	22	continuous	continuous	ADJ
ma-203	489	23	coefficient	coefficient	NOUN
ma-203	489	24	driven	drive	VERB
ma-203	489	25	by	by	ADP
ma-203	489	26	α	α	NOUN
ma-203	489	27	-	-	ADJ
ma-203	489	28	stable	stable	ADJ
ma-203	489	29	noise	noise	NOUN
ma-203	489	30	,	,	PUNCT
ma-203	489	31	elec	elec	PROPN
ma-203	489	32	.	.	PUNCT
ma-203	490	1	j.	j.	PROPN
ma-203	490	2	prob	prob	PROPN
ma-203	490	3	.	.	PROPN
ma-203	491	1	22	22	NUM
ma-203	491	2	(	(	PUNCT
ma-203	491	3	2017	2017	NUM
ma-203	491	4	)	)	PUNCT
ma-203	491	5	1	1	NUM
ma-203	491	6	-	-	SYM
ma-203	491	7	48.[43	48.[43	NUM
ma-203	491	8	]	]	PUNCT
ma-203	491	9	m.	m.	PROPN
ma-203	491	10	yoshida	yoshida	PROPN
ma-203	491	11	,	,	PUNCT
ma-203	491	12	malliavin	malliavin	PROPN
ma-203	491	13	calculus	calculus	NOUN
ma-203	491	14	and	and	CCONJ
ma-203	491	15	asymptotic	asymptotic	ADJ
ma-203	491	16	expansion	expansion	NOUN
ma-203	491	17	for	for	ADP
ma-203	491	18	martingales	martingale	NOUN
ma-203	491	19	,	,	PUNCT
ma-203	491	20	prob	prob	NOUN
ma-203	491	21	.	.	PROPN
ma-203	491	22	theory	theory	PROPN
ma-203	491	23	relat	relat	NOUN
ma-203	491	24	.	.	PUNCT
ma-203	492	1	fields	field	NOUN
ma-203	492	2	109	109	NUM
ma-203	492	3	(	(	PUNCT
ma-203	492	4	1997)301	1997)301	PROPN
ma-203	492	5	-	-	PUNCT
ma-203	492	6	342.[44	342.[44	PROPN
ma-203	492	7	]	]	X
ma-203	492	8	n.	n.	PROPN
ma-203	492	9	yoshida	yoshida	PROPN
ma-203	492	10	,	,	PUNCT
ma-203	492	11	malliavin	malliavin	PROPN
ma-203	492	12	calculus	calculus	NOUN
ma-203	492	13	and	and	CCONJ
ma-203	492	14	martingale	martingale	ADJ
ma-203	492	15	expansion	expansion	NOUN
ma-203	492	16	,	,	PUNCT
ma-203	492	17	bull	bull	NOUN
ma-203	492	18	.	.	PUNCT
ma-203	493	1	sci	sci	PROPN
ma-203	493	2	.	.	PUNCT
ma-203	493	3	math	math	PROPN
ma-203	493	4	.	.	PUNCT
ma-203	494	1	125	125	NUM
ma-203	494	2	(	(	PUNCT
ma-203	494	3	2001	2001	NUM
ma-203	494	4	)	)	PUNCT
ma-203	494	5	431	431	NUM
ma-203	494	6	-	-	SYM
ma-203	494	7	456.[45	456.[45	NUM
ma-203	494	8	]	]	X
ma-203	494	9	n.	n.	PROPN
ma-203	494	10	yoshida	yoshida	PROPN
ma-203	494	11	,	,	PUNCT
ma-203	494	12	asymptotic	asymptotic	ADJ
ma-203	494	13	expansions	expansion	NOUN
ma-203	494	14	for	for	ADP
ma-203	494	15	stochastic	stochastic	ADJ
ma-203	494	16	processes	process	NOUN
ma-203	494	17	,	,	PUNCT
ma-203	494	18	in	in	ADP
ma-203	494	19	:	:	PUNCT
ma-203	494	20	rabi	rabi	PROPN
ma-203	494	21	n.	n.	PROPN
ma-203	494	22	bhattacharya	bhattacharya	PROPN
ma-203	494	23	selected	select	VERB
ma-203	494	24	papers	paper	NOUN
ma-203	494	25	,	,	PUNCT
ma-203	494	26	(	(	PUNCT
ma-203	494	27	eds.)denker	eds.)denker	NOUN
ma-203	494	28	,	,	PUNCT
ma-203	494	29	m.	m.	NOUN
ma-203	494	30	,	,	PUNCT
ma-203	494	31	waymire	waymire	ADJ
ma-203	494	32	,	,	PUNCT
ma-203	494	33	e.c	e.c	PROPN
ma-203	494	34	.	.	PROPN
ma-203	494	35	,	,	PUNCT
ma-203	494	36	springer	springer	PROPN
ma-203	494	37	international	international	PROPN
ma-203	494	38	publising	publising	PROPN
ma-203	494	39	,	,	PUNCT
ma-203	494	40	switzerland	switzerland	PROPN
ma-203	494	41	,	,	PUNCT
ma-203	494	42	(	(	PUNCT
ma-203	494	43	2016	2016	NUM
ma-203	494	44	)	)	PUNCT
ma-203	494	45	,	,	PUNCT
ma-203	494	46	15	15	NUM
ma-203	494	47	-	-	SYM
ma-203	494	48	32.[46	32.[46	PROPN
ma-203	494	49	]	]	X
ma-203	494	50	n.	n.	PROPN
ma-203	494	51	yoshida	yoshida	PROPN
ma-203	494	52	,	,	PUNCT
ma-203	494	53	polynomial	polynomial	ADJ
ma-203	494	54	type	type	NOUN
ma-203	494	55	large	large	ADJ
ma-203	494	56	deviation	deviation	NOUN
ma-203	494	57	inequalities	inequality	NOUN
ma-203	494	58	and	and	CCONJ
ma-203	494	59	quasi	quasi	ADJ
ma-203	494	60	-	-	ADJ
ma-203	494	61	likelihood	likelihood	ADJ
ma-203	494	62	analysis	analysis	NOUN
ma-203	494	63	for	for	ADP
ma-203	494	64	stochastic	stochastic	ADJ
ma-203	494	65	differentialequations	differentialequation	NOUN
ma-203	494	66	,	,	PUNCT
ma-203	494	67	ann	ann	PROPN
ma-203	494	68	.	.	PROPN
ma-203	494	69	inst	inst	PROPN
ma-203	494	70	.	.	PUNCT
ma-203	495	1	stat	stat	PROPN
ma-203	495	2	.	.	PUNCT
ma-203	496	1	math	math	NOUN
ma-203	496	2	.	.	PUNCT
ma-203	497	1	63	63	NUM
ma-203	497	2	(	(	PUNCT
ma-203	497	3	2011	2011	NUM
ma-203	497	4	)	)	PUNCT
ma-203	497	5	431	431	NUM
ma-203	497	6	-	-	SYM
ma-203	497	7	479	479	NUM
ma-203	497	8	.	.	PUNCT
ma-203	498	1	https://doi.org/10.28924/ada/ma.4.12	https://doi.org/10.28924/ada/ma.4.12	NOUN
ma-203	498	2	references	reference	NOUN