id	sid	tid	token	lemma	pos
ma-179	1	1	2023	2023	NUM
ma-179	1	2	ada	ada	PROPN
ma-179	1	3	academica	academica	PROPN
ma-179	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-179	1	5	.	.	PUNCT
ma-179	2	1	j.	j.	PROPN
ma-179	2	2	math	math	PROPN
ma-179	2	3	.	.	PUNCT
ma-179	3	1	anal	anal	ADJ
ma-179	3	2	.	.	PUNCT
ma-179	4	1	3	3	NUM
ma-179	4	2	(	(	PUNCT
ma-179	4	3	2023	2023	NUM
ma-179	4	4	)	)	PUNCT
ma-179	4	5	25doi	25doi	NOUN
ma-179	4	6	:	:	PUNCT
ma-179	4	7	10.28924	10.28924	NUM
ma-179	4	8	/	/	SYM
ma-179	4	9	ada	ada	PROPN
ma-179	4	10	/	/	SYM
ma-179	4	11	ma.3.25	ma.3.25	NOUN
ma-179	4	12	on	on	ADP
ma-179	4	13	the	the	DET
ma-179	4	14	kolmogorov	kolmogorov	ADJ
ma-179	4	15	distance	distance	NOUN
ma-179	4	16	for	for	ADP
ma-179	4	17	the	the	DET
ma-179	4	18	maximum	maximum	ADJ
ma-179	4	19	likelihood	likelihood	NOUN
ma-179	4	20	estimator	estimator	NOUN
ma-179	4	21	in	in	ADP
ma-179	4	22	the	the	DET
ma-179	4	23	explosive	explosive	ADJ
ma-179	4	24	ornstein	ornstein	PROPN
ma-179	4	25	-	-	PUNCT
ma-179	4	26	uhlenbeck	uhlenbeck	PROPN
ma-179	4	27	process	process	PROPN
ma-179	4	28	jaya	jaya	PROPN
ma-179	4	29	p.	p.	PROPN
ma-179	4	30	n.	n.	PROPN
ma-179	4	31	bishwal	bishwal	PROPN
ma-179	4	32	department	department	PROPN
ma-179	4	33	of	of	ADP
ma-179	4	34	mathematics	mathematics	PROPN
ma-179	4	35	and	and	CCONJ
ma-179	4	36	statistics	statistic	NOUN
ma-179	4	37	,	,	PUNCT
ma-179	4	38	university	university	PROPN
ma-179	4	39	of	of	ADP
ma-179	4	40	north	north	PROPN
ma-179	4	41	carolina	carolina	PROPN
ma-179	4	42	at	at	ADP
ma-179	4	43	charlotte	charlotte	PROPN
ma-179	4	44	,	,	PUNCT
ma-179	4	45	376	376	NUM
ma-179	4	46	fretwell	fretwell	NOUN
ma-179	4	47	bldg,9201	bldg,9201	NOUN
ma-179	4	48	university	university	NOUN
ma-179	4	49	city	city	NOUN
ma-179	4	50	blvd	blvd	PROPN
ma-179	4	51	.	.	PUNCT
ma-179	5	1	charlotte	charlotte	PROPN
ma-179	5	2	,	,	PUNCT
ma-179	5	3	nc	nc	PROPN
ma-179	5	4	28223	28223	NUM
ma-179	5	5	-	-	PUNCT
ma-179	5	6	0001	0001	NUM
ma-179	5	7	,	,	PUNCT
ma-179	5	8	usacorrespondence	usacorrespondence	NOUN
ma-179	5	9	:	:	PUNCT
ma-179	5	10	j.bishwal@uncc.edu	j.bishwal@uncc.edu	PROPN
ma-179	5	11	abstract	abstract	ADJ
ma-179	5	12	.	.	PUNCT
ma-179	6	1	the	the	DET
ma-179	6	2	paper	paper	NOUN
ma-179	6	3	estimates	estimate	VERB
ma-179	6	4	the	the	DET
ma-179	6	5	kolmogorov	kolmogorov	ADJ
ma-179	6	6	distance	distance	NOUN
ma-179	6	7	between	between	ADP
ma-179	6	8	the	the	DET
ma-179	6	9	distribution	distribution	NOUN
ma-179	6	10	of	of	ADP
ma-179	6	11	the	the	DET
ma-179	6	12	normalizedmaximum	normalizedmaximum	ADJ
ma-179	6	13	likelihood	likelihood	NOUN
ma-179	6	14	estimator	estimator	NOUN
ma-179	6	15	of	of	ADP
ma-179	6	16	the	the	DET
ma-179	6	17	positive	positive	ADJ
ma-179	6	18	drift	drift	NOUN
ma-179	6	19	parameter	parameter	NOUN
ma-179	6	20	in	in	ADP
ma-179	6	21	the	the	DET
ma-179	6	22	nonergodic	nonergodic	ADJ
ma-179	6	23	ornstein	ornstein	NOUN
ma-179	6	24	-	-	PUNCT
ma-179	6	25	uhlenbeckprocess	uhlenbeckprocess	NOUN
ma-179	6	26	and	and	CCONJ
ma-179	6	27	the	the	DET
ma-179	6	28	standard	standard	ADJ
ma-179	6	29	cauchy	cauchy	ADJ
ma-179	6	30	distribution	distribution	NOUN
ma-179	6	31	and	and	CCONJ
ma-179	6	32	shows	show	VERB
ma-179	6	33	exponential	exponential	ADJ
ma-179	6	34	error	error	NOUN
ma-179	6	35	rate	rate	NOUN
ma-179	6	36	for	for	ADP
ma-179	6	37	large	large	ADJ
ma-179	6	38	time	time	NOUN
ma-179	6	39	limit	limit	NOUN
ma-179	6	40	.	.	PUNCT
ma-179	7	1	1	1	X
ma-179	7	2	.	.	X
ma-179	7	3	introduction	introduction	NOUN
ma-179	7	4	estimating	estimate	VERB
ma-179	7	5	the	the	DET
ma-179	7	6	rate	rate	NOUN
ma-179	7	7	in	in	ADP
ma-179	7	8	the	the	DET
ma-179	7	9	kolmogorov	kolmogorov	ADJ
ma-179	7	10	distance	distance	NOUN
ma-179	7	11	between	between	ADP
ma-179	7	12	two	two	NUM
ma-179	7	13	distributions	distribution	NOUN
ma-179	7	14	has	have	VERB
ma-179	7	15	a	a	DET
ma-179	7	16	long	long	ADJ
ma-179	7	17	history	history	NOUN
ma-179	7	18	inprobability	inprobability	NOUN
ma-179	7	19	and	and	CCONJ
ma-179	7	20	statistics	statistic	NOUN
ma-179	7	21	.	.	PUNCT
ma-179	8	1	the	the	DET
ma-179	8	2	estimate	estimate	NOUN
ma-179	8	3	could	could	AUX
ma-179	8	4	be	be	AUX
ma-179	8	5	useful	useful	ADJ
ma-179	8	6	in	in	ADP
ma-179	8	7	finding	find	VERB
ma-179	8	8	confidence	confidence	NOUN
ma-179	8	9	interval	interval	NOUN
ma-179	8	10	and	and	CCONJ
ma-179	8	11	inhypothesis	inhypothesis	NOUN
ma-179	8	12	testing	testing	NOUN
ma-179	8	13	,	,	PUNCT
ma-179	8	14	see	see	VERB
ma-179	8	15	bishwal	bishwal	NOUN
ma-179	8	16	[	[	X
ma-179	8	17	8	8	NUM
ma-179	8	18	,	,	PUNCT
ma-179	8	19	11	11	NUM
ma-179	8	20	]	]	PUNCT
ma-179	8	21	.	.	PUNCT
ma-179	9	1	in	in	ADP
ma-179	9	2	the	the	DET
ma-179	9	3	i.i.d	i.i.d	PROPN
ma-179	9	4	.	.	PROPN
ma-179	9	5	case	case	NOUN
ma-179	9	6	,	,	PUNCT
ma-179	9	7	the	the	DET
ma-179	9	8	berry	berry	NOUN
ma-179	9	9	-	-	PUNCT
ma-179	9	10	esseen	esseen	PROPN
ma-179	9	11	bound	bind	VERB
ma-179	9	12	for	for	ADP
ma-179	9	13	minimumcontrast	minimumcontrast	ADJ
ma-179	9	14	estimators	estimator	NOUN
ma-179	9	15	was	be	AUX
ma-179	9	16	obtained	obtain	VERB
ma-179	9	17	in	in	ADP
ma-179	9	18	pfanzagl	pfanzagl	NOUN
ma-179	9	19	[	[	X
ma-179	9	20	28	28	NUM
ma-179	9	21	]	]	PUNCT
ma-179	9	22	improving	improve	VERB
ma-179	9	23	that	that	PRON
ma-179	9	24	from	from	ADP
ma-179	9	25	michel	michel	PROPN
ma-179	9	26	and	and	CCONJ
ma-179	9	27	pfanzagl	pfanzagl	NOUN
ma-179	10	1	[	[	X
ma-179	10	2	24].borokov	24].borokov	PROPN
ma-179	10	3	[	[	X
ma-179	10	4	14	14	NUM
ma-179	10	5	]	]	PUNCT
ma-179	10	6	obtained	obtain	VERB
ma-179	10	7	the	the	DET
ma-179	10	8	rate	rate	NOUN
ma-179	10	9	of	of	ADP
ma-179	10	10	convergence	convergence	NOUN
ma-179	10	11	for	for	ADP
ma-179	10	12	the	the	DET
ma-179	10	13	invariance	invariance	NOUN
ma-179	10	14	principle	principle	NOUN
ma-179	10	15	in	in	ADP
ma-179	10	16	the	the	DET
ma-179	10	17	i.i.d	i.i.d	PROPN
ma-179	10	18	.	.	PROPN
ma-179	10	19	case	case	NOUN
ma-179	10	20	.	.	PUNCT
ma-179	11	1	hall	hall	PROPN
ma-179	11	2	andheyde	andheyde	PROPN
ma-179	12	1	[	[	X
ma-179	12	2	20	20	NUM
ma-179	12	3	]	]	PUNCT
ma-179	12	4	obtained	obtain	VERB
ma-179	12	5	rate	rate	NOUN
ma-179	12	6	of	of	ADP
ma-179	12	7	convergence	convergence	NOUN
ma-179	12	8	in	in	ADP
ma-179	12	9	the	the	DET
ma-179	12	10	central	central	ADJ
ma-179	12	11	limit	limit	NOUN
ma-179	12	12	theorem	theorem	VERB
ma-179	12	13	for	for	ADP
ma-179	12	14	martingales	martingale	NOUN
ma-179	12	15	using	use	VERB
ma-179	12	16	skorohodembedding	skorohodembedde	VERB
ma-179	12	17	.	.	PUNCT
ma-179	13	1	uniform	uniform	ADJ
ma-179	13	2	rate	rate	NOUN
ma-179	13	3	of	of	ADP
ma-179	13	4	weak	weak	ADJ
ma-179	13	5	convergence	convergence	NOUN
ma-179	13	6	for	for	ADP
ma-179	13	7	the	the	DET
ma-179	13	8	minimum	minimum	ADJ
ma-179	13	9	contrast	contrast	NOUN
ma-179	13	10	estimator	estimator	NOUN
ma-179	13	11	in	in	ADP
ma-179	13	12	the	the	DET
ma-179	13	13	ornstein	ornstein	NOUN
ma-179	13	14	-	-	PUNCT
ma-179	13	15	uhlenbeck	uhlenbeck	PROPN
ma-179	13	16	(	(	PUNCT
ma-179	13	17	o	o	NOUN
ma-179	13	18	-	-	NOUN
ma-179	13	19	u	u	NOUN
ma-179	13	20	)	)	PUNCT
ma-179	13	21	process	process	NOUN
ma-179	13	22	was	be	AUX
ma-179	13	23	studied	study	VERB
ma-179	13	24	in	in	ADP
ma-179	13	25	bishwal	bishwal	NOUN
ma-179	13	26	[	[	X
ma-179	13	27	5	5	NUM
ma-179	13	28	]	]	PUNCT
ma-179	13	29	.	.	PUNCT
ma-179	14	1	the	the	DET
ma-179	14	2	rates	rate	NOUN
ma-179	14	3	of	of	ADP
ma-179	14	4	convergence	convergence	NOUN
ma-179	14	5	of	of	ADP
ma-179	14	6	the	the	DET
ma-179	14	7	conditionalleast	conditionalleast	ADJ
ma-179	14	8	squares	square	NOUN
ma-179	14	9	estimator	estimator	NOUN
ma-179	14	10	and	and	CCONJ
ma-179	14	11	an	an	DET
ma-179	14	12	approximate	approximate	ADJ
ma-179	14	13	maximum	maximum	ADJ
ma-179	14	14	likelihood	likelihood	NOUN
ma-179	14	15	estimator	estimator	NOUN
ma-179	14	16	when	when	SCONJ
ma-179	14	17	the	the	DET
ma-179	14	18	o	o	NOUN
ma-179	14	19	-	-	NOUN
ma-179	14	20	u	u	ADJ
ma-179	14	21	processis	processis	NOUN
ma-179	14	22	observed	observe	VERB
ma-179	14	23	at	at	ADP
ma-179	14	24	discrete	discrete	ADJ
ma-179	14	25	time	time	NOUN
ma-179	14	26	points	point	NOUN
ma-179	14	27	in	in	ADP
ma-179	14	28	[	[	X
ma-179	14	29	0	0	NUM
ma-179	14	30	,	,	PUNCT
ma-179	14	31	t	t	PROPN
ma-179	14	32	]	]	PUNCT
ma-179	14	33	has	have	AUX
ma-179	14	34	been	be	AUX
ma-179	14	35	studied	study	VERB
ma-179	14	36	in	in	ADP
ma-179	14	37	bishwal	bishwal	NOUN
ma-179	14	38	and	and	CCONJ
ma-179	14	39	bose	bose	NOUN
ma-179	15	1	[	[	X
ma-179	15	2	13](2001	13](2001	NUM
ma-179	15	3	)	)	PUNCT
ma-179	15	4	inthe	inthe	PRON
ma-179	15	5	ergodic	ergodic	ADJ
ma-179	15	6	case	case	NOUN
ma-179	15	7	.	.	PUNCT
ma-179	16	1	in	in	ADP
ma-179	16	2	a	a	DET
ma-179	16	3	bayesian	bayesian	NOUN
ma-179	16	4	framework	framework	NOUN
ma-179	16	5	,	,	PUNCT
ma-179	16	6	the	the	DET
ma-179	16	7	rates	rate	NOUN
ma-179	16	8	of	of	ADP
ma-179	16	9	convergence	convergence	NOUN
ma-179	16	10	of	of	ADP
ma-179	16	11	the	the	DET
ma-179	16	12	posterior	posterior	ADJ
ma-179	16	13	distributionsand	distributionsand	NOUN
ma-179	16	14	the	the	DET
ma-179	16	15	bayes	bayes	NOUN
ma-179	16	16	estimators	estimator	NOUN
ma-179	16	17	has	have	AUX
ma-179	16	18	been	be	AUX
ma-179	16	19	studied	study	VERB
ma-179	16	20	in	in	ADP
ma-179	16	21	bishwal	bishwal	NOUN
ma-179	16	22	[	[	X
ma-179	16	23	6	6	NUM
ma-179	16	24	]	]	PUNCT
ma-179	16	25	and	and	CCONJ
ma-179	16	26	bishwal	bishwal	NOUN
ma-179	16	27	[	[	X
ma-179	16	28	10	10	NUM
ma-179	16	29	]	]	PUNCT
ma-179	16	30	for	for	ADP
ma-179	16	31	the	the	DET
ma-179	16	32	continuousobservation	continuousobservation	NOUN
ma-179	16	33	and	and	CCONJ
ma-179	16	34	discrete	discrete	ADJ
ma-179	16	35	observations	observation	NOUN
ma-179	16	36	respectively	respectively	ADV
ma-179	16	37	in	in	ADP
ma-179	16	38	the	the	DET
ma-179	16	39	ergodic	ergodic	ADJ
ma-179	16	40	case	case	NOUN
ma-179	16	41	.	.	PUNCT
ma-179	17	1	in	in	ADP
ma-179	17	2	finance	finance	NOUN
ma-179	17	3	,	,	PUNCT
ma-179	17	4	asset	asset	NOUN
ma-179	17	5	price	price	NOUN
ma-179	17	6	maybehave	maybehave	NOUN
ma-179	17	7	in	in	ADP
ma-179	17	8	nonergodic	nonergodic	ADJ
ma-179	17	9	manner	manner	NOUN
ma-179	17	10	,	,	PUNCT
ma-179	17	11	i.e.	i.e.	X
ma-179	17	12	,	,	PUNCT
ma-179	17	13	efficient	efficient	ADJ
ma-179	17	14	market	market	NOUN
ma-179	17	15	hypotheses	hypothesis	NOUN
ma-179	17	16	may	may	AUX
ma-179	17	17	not	not	PART
ma-179	17	18	hold	hold	VERB
ma-179	17	19	,	,	PUNCT
ma-179	17	20	possibly	possibly	ADV
ma-179	17	21	be	be	AUX
ma-179	17	22	due	due	ADJ
ma-179	17	23	tosocial	tosocial	ADJ
ma-179	17	24	interaction	interaction	NOUN
ma-179	17	25	among	among	ADP
ma-179	17	26	consumers	consumer	NOUN
ma-179	17	27	among	among	ADP
ma-179	17	28	other	other	ADJ
ma-179	17	29	reasons	reason	NOUN
ma-179	17	30	,	,	PUNCT
ma-179	17	31	see	see	VERB
ma-179	17	32	horst	horst	PROPN
ma-179	17	33	and	and	CCONJ
ma-179	17	34	wenzelburger	wenzelburger	NOUN
ma-179	18	1	[	[	X
ma-179	18	2	21	21	NUM
ma-179	18	3	]	]	PUNCT
ma-179	18	4	.	.	PUNCT
ma-179	19	1	westudy	westudy	VERB
ma-179	19	2	the	the	DET
ma-179	19	3	nonergodic	nonergodic	PROPN
ma-179	19	4	ornstein	ornstein	PROPN
ma-179	19	5	-	-	PUNCT
ma-179	19	6	uhlenbeck	uhlenbeck	PROPN
ma-179	19	7	process	process	NOUN
ma-179	19	8	in	in	ADP
ma-179	19	9	this	this	DET
ma-179	19	10	paper	paper	NOUN
ma-179	19	11	and	and	CCONJ
ma-179	19	12	focus	focus	VERB
ma-179	19	13	on	on	ADP
ma-179	19	14	the	the	DET
ma-179	19	15	rate	rate	NOUN
ma-179	19	16	of	of	ADP
ma-179	19	17	convergenceof	convergenceof	NOUN
ma-179	19	18	the	the	DET
ma-179	19	19	kolmogorov	kolmogorov	PROPN
ma-179	19	20	distance	distance	NOUN
ma-179	19	21	.	.	PUNCT
ma-179	20	1	received	receive	VERB
ma-179	20	2	:	:	PUNCT
ma-179	20	3	5	5	NUM
ma-179	20	4	jul	jul	PROPN
ma-179	20	5	2023	2023	NUM
ma-179	20	6	.	.	PUNCT
ma-179	21	1	key	key	ADJ
ma-179	21	2	words	word	NOUN
ma-179	21	3	and	and	CCONJ
ma-179	21	4	phrases	phrase	NOUN
ma-179	21	5	.	.	PUNCT
ma-179	22	1	itô	itô	ADP
ma-179	22	2	stochastic	stochastic	ADJ
ma-179	22	3	differential	differential	NOUN
ma-179	22	4	equation	equation	NOUN
ma-179	22	5	,	,	PUNCT
ma-179	22	6	explosive	explosive	ADJ
ma-179	22	7	ornstein	ornstein	PROPN
ma-179	22	8	-	-	PUNCT
ma-179	22	9	uhlenbeck	uhlenbeck	PROPN
ma-179	22	10	process	process	NOUN
ma-179	22	11	,	,	PUNCT
ma-179	22	12	maximum	maximum	ADJ
ma-179	22	13	likeli	likeli	ADJ
ma-179	22	14	-	-	PUNCT
ma-179	22	15	hood	hood	NOUN
ma-179	22	16	estimator	estimator	NOUN
ma-179	22	17	,	,	PUNCT
ma-179	22	18	kolmogorov	kolmogorov	ADJ
ma-179	22	19	distance	distance	NOUN
ma-179	22	20	,	,	PUNCT
ma-179	22	21	inefficient	inefficient	ADJ
ma-179	22	22	market	market	NOUN
ma-179	22	23	.	.	PUNCT
ma-179	23	1	1	1	NUM
ma-179	23	2	https://adac.ee	https://adac.ee	PROPN
ma-179	23	3	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	PROPN
ma-179	23	4	eur	eur	PROPN
ma-179	23	5	.	.	PUNCT
ma-179	24	1	j.	j.	PROPN
ma-179	24	2	math	math	PROPN
ma-179	24	3	.	.	PUNCT
ma-179	25	1	anal	anal	PROPN
ma-179	25	2	.	.	PUNCT
ma-179	26	1	10.28924	10.28924	NUM
ma-179	26	2	/	/	SYM
ma-179	26	3	ada	ada	PROPN
ma-179	26	4	/	/	PROPN
ma-179	26	5	ma.3.25	ma.3.25	PROPN
ma-179	26	6	2let	2let	NUM
ma-179	26	7	(	(	PUNCT
ma-179	26	8	ω	ω	PROPN
ma-179	26	9	,	,	PUNCT
ma-179	26	10	f	f	PROPN
ma-179	26	11	,	,	PUNCT
ma-179	26	12	{	{	PUNCT
ma-179	26	13	ft}t≥0	ft}t≥0	NOUN
ma-179	26	14	,	,	PUNCT
ma-179	26	15	p	p	NOUN
ma-179	26	16	)	)	PUNCT
ma-179	26	17	be	be	AUX
ma-179	26	18	a	a	DET
ma-179	26	19	stochastic	stochastic	ADJ
ma-179	26	20	basis	basis	NOUN
ma-179	26	21	on	on	ADP
ma-179	26	22	which	which	PRON
ma-179	26	23	is	be	AUX
ma-179	26	24	defined	define	VERB
ma-179	26	25	the	the	DET
ma-179	26	26	ornstein	ornstein	PROPN
ma-179	26	27	-	-	PUNCT
ma-179	26	28	uhlenbeck	uhlenbeck	PROPN
ma-179	26	29	process	process	NOUN
ma-179	26	30	{	{	PUNCT
ma-179	26	31	xt	xt	ADP
ma-179	26	32	}	}	PUNCT
ma-179	26	33	satisfying	satisfy	VERB
ma-179	26	34	the	the	DET
ma-179	26	35	itô	itô	PROPN
ma-179	26	36	stochastic	stochastic	ADJ
ma-179	26	37	differential	differential	NOUN
ma-179	26	38	equation	equation	NOUN
ma-179	27	1	dxt	dxt	PROPN
ma-179	27	2	=	=	PUNCT
ma-179	27	3	θxtdt	θxtdt	PROPN
ma-179	27	4	+	+	CCONJ
ma-179	27	5	dwt	dwt	PROPN
ma-179	27	6	,	,	PUNCT
ma-179	27	7	t	t	PROPN
ma-179	27	8	≥	≥	PROPN
ma-179	27	9	0	0	NUM
ma-179	27	10	,	,	PUNCT
ma-179	27	11	x0	x0	PROPN
ma-179	27	12	=	=	SYM
ma-179	27	13	0	0	PUNCT
ma-179	27	14	(	(	PUNCT
ma-179	27	15	1.1	1.1	NUM
ma-179	27	16	)	)	PUNCT
ma-179	27	17	where	where	SCONJ
ma-179	27	18	{	{	PUNCT
ma-179	27	19	wt}t≥0	wt}t≥0	NOUN
ma-179	27	20	is	be	AUX
ma-179	27	21	a	a	DET
ma-179	27	22	standard	standard	ADJ
ma-179	27	23	wiener	wiener	NOUN
ma-179	27	24	process	process	NOUN
ma-179	27	25	with	with	ADP
ma-179	27	26	respect	respect	NOUN
ma-179	27	27	to	to	ADP
ma-179	27	28	the	the	DET
ma-179	27	29	filtration	filtration	NOUN
ma-179	27	30	{	{	PUNCT
ma-179	27	31	ft}t≥0	ft}t≥0	NOUN
ma-179	27	32	and	and	CCONJ
ma-179	27	33	θ	θ	PROPN
ma-179	27	34	>	>	X
ma-179	28	1	0is	0is	NOUN
ma-179	28	2	the	the	DET
ma-179	28	3	unknown	unknown	ADJ
ma-179	28	4	parameter	parameter	NOUN
ma-179	28	5	to	to	PART
ma-179	28	6	be	be	AUX
ma-179	28	7	estimated	estimate	VERB
ma-179	28	8	on	on	ADP
ma-179	28	9	the	the	DET
ma-179	28	10	basis	basis	NOUN
ma-179	28	11	of	of	ADP
ma-179	28	12	continuous	continuous	ADJ
ma-179	28	13	observation	observation	NOUN
ma-179	28	14	of	of	ADP
ma-179	28	15	the	the	DET
ma-179	28	16	process	process	NOUN
ma-179	28	17	{	{	PUNCT
ma-179	28	18	xt}t≥0	xt}t≥0	PROPN
ma-179	28	19	on	on	ADP
ma-179	28	20	the	the	DET
ma-179	28	21	time	time	NOUN
ma-179	28	22	interval	interval	NOUN
ma-179	29	1	[	[	X
ma-179	29	2	0	0	NUM
ma-179	29	3	,	,	PUNCT
ma-179	29	4	t	t	X
ma-179	29	5	]	]	PUNCT
ma-179	29	6	.let	.let	PUNCT
ma-179	30	1	us	we	PRON
ma-179	30	2	denote	denote	VERB
ma-179	30	3	the	the	DET
ma-179	30	4	realization	realization	NOUN
ma-179	30	5	{	{	PUNCT
ma-179	30	6	xt	xt	PROPN
ma-179	30	7	,	,	PUNCT
ma-179	30	8	0	0	NUM
ma-179	30	9	≤	≤	NUM
ma-179	30	10	t	t	PROPN
ma-179	30	11	≤	≤	X
ma-179	30	12	t	t	PROPN
ma-179	30	13	}	}	PUNCT
ma-179	30	14	by	by	ADP
ma-179	30	15	xt0	xt0	PROPN
ma-179	30	16	.	.	PUNCT
ma-179	31	1	let	let	VERB
ma-179	31	2	p	p	PRON
ma-179	31	3	tθ	tθ	VERB
ma-179	31	4	be	be	AUX
ma-179	31	5	the	the	DET
ma-179	31	6	measure	measure	NOUN
ma-179	31	7	generated	generate	VERB
ma-179	31	8	on	on	ADP
ma-179	31	9	thespace	thespace	NOUN
ma-179	31	10	(	(	PUNCT
ma-179	31	11	ct	ct	INTJ
ma-179	31	12	,	,	PUNCT
ma-179	31	13	bt	bt	PROPN
ma-179	31	14	)	)	PUNCT
ma-179	31	15	of	of	ADP
ma-179	31	16	continuous	continuous	ADJ
ma-179	31	17	functions	function	NOUN
ma-179	31	18	on	on	ADP
ma-179	31	19	[	[	X
ma-179	31	20	0	0	NUM
ma-179	31	21	,	,	PUNCT
ma-179	31	22	t	t	X
ma-179	31	23	]	]	PUNCT
ma-179	31	24	with	with	SCONJ
ma-179	31	25	the	the	DET
ma-179	31	26	associated	associated	PROPN
ma-179	31	27	borel	borel	PROPN
ma-179	31	28	σ	σ	PROPN
ma-179	31	29	-	-	PROPN
ma-179	31	30	algebra	algebra	NOUN
ma-179	31	31	bt	bt	NOUN
ma-179	31	32	generatedunder	generatedunder	NOUN
ma-179	31	33	the	the	DET
ma-179	31	34	supremum	supremum	ADJ
ma-179	31	35	norm	norm	NOUN
ma-179	31	36	by	by	ADP
ma-179	31	37	the	the	DET
ma-179	31	38	process	process	NOUN
ma-179	31	39	xt0	xt0	PROPN
ma-179	31	40	and	and	CCONJ
ma-179	31	41	p	p	PROPN
ma-179	31	42	t0	t0	PROPN
ma-179	31	43	be	be	AUX
ma-179	31	44	the	the	DET
ma-179	31	45	standard	standard	ADJ
ma-179	31	46	wiener	wiener	NOUN
ma-179	31	47	measure	measure	NOUN
ma-179	31	48	.	.	PUNCT
ma-179	32	1	it	it	PRON
ma-179	32	2	is	be	AUX
ma-179	32	3	wellknown	wellknown	ADJ
ma-179	32	4	that	that	SCONJ
ma-179	32	5	when	when	SCONJ
ma-179	32	6	θ	θ	PROPN
ma-179	32	7	is	be	AUX
ma-179	32	8	the	the	DET
ma-179	32	9	true	true	ADJ
ma-179	32	10	value	value	NOUN
ma-179	32	11	of	of	ADP
ma-179	32	12	the	the	DET
ma-179	32	13	parameter	parameter	NOUN
ma-179	32	14	p	p	PROPN
ma-179	32	15	tθ	tθ	PROPN
ma-179	32	16	is	be	AUX
ma-179	32	17	absolutely	absolutely	ADV
ma-179	32	18	continuous	continuous	ADJ
ma-179	32	19	with	with	ADP
ma-179	32	20	respect	respect	NOUN
ma-179	32	21	to	to	ADP
ma-179	32	22	p	p	PROPN
ma-179	32	23	t0	t0	PROPN
ma-179	32	24	and	and	CCONJ
ma-179	32	25	the	the	DET
ma-179	32	26	radon	radon	PROPN
ma-179	32	27	-	-	PUNCT
ma-179	32	28	nikodym	nikodym	PROPN
ma-179	32	29	derivative	derivative	NOUN
ma-179	32	30	(	(	PUNCT
ma-179	32	31	likelihood	likelihood	NOUN
ma-179	32	32	)	)	PUNCT
ma-179	32	33	of	of	ADP
ma-179	32	34	p	p	NOUN
ma-179	32	35	tθ	tθ	NOUN
ma-179	32	36	with	with	ADP
ma-179	32	37	respect	respect	NOUN
ma-179	32	38	to	to	ADP
ma-179	32	39	p	p	PROPN
ma-179	32	40	t0	t0	PROPN
ma-179	32	41	based	base	VERB
ma-179	32	42	on	on	ADP
ma-179	32	43	xt0	xt0	PROPN
ma-179	32	44	is	be	AUX
ma-179	32	45	givenby	givenby	PROPN
ma-179	32	46	lt	lt	PROPN
ma-179	32	47	(	(	PUNCT
ma-179	32	48	θ	θ	NOUN
ma-179	32	49	)	)	PUNCT
ma-179	32	50	:	:	PUNCT
ma-179	33	1	=	=	PUNCT
ma-179	33	2	dp	dp	NOUN
ma-179	33	3	tθ	tθ	NOUN
ma-179	33	4	dp	dp	NOUN
ma-179	33	5	t0	t0	PROPN
ma-179	33	6	(	(	PUNCT
ma-179	33	7	xt0	xt0	PROPN
ma-179	33	8	)	)	PUNCT
ma-179	34	1	=	=	NOUN
ma-179	34	2	exp	exp	NOUN
ma-179	34	3	{	{	PUNCT
ma-179	34	4	θ	θ	PROPN
ma-179	34	5	∫	∫	PROPN
ma-179	34	6	t	t	PROPN
ma-179	34	7	0	0	NUM
ma-179	35	1	xtdxt	xtdxt	PROPN
ma-179	35	2	−	−	PROPN
ma-179	35	3	θ2	θ2	PROPN
ma-179	35	4	2	2	NUM
ma-179	35	5	∫	∫	NOUN
ma-179	35	6	t	t	PROPN
ma-179	35	7	0	0	NUM
ma-179	36	1	x2	x2	PROPN
ma-179	36	2	t	t	NOUN
ma-179	36	3	dt	dt	X
ma-179	36	4	}	}	PUNCT
ma-179	36	5	.	.	PUNCT
ma-179	37	1	(	(	PUNCT
ma-179	37	2	1.2	1.2	X
ma-179	37	3	)	)	PUNCT
ma-179	37	4	maximizing	maximize	VERB
ma-179	37	5	the	the	DET
ma-179	37	6	log	log	NOUN
ma-179	37	7	-	-	PUNCT
ma-179	37	8	likelihood	likelihood	NOUN
ma-179	37	9	with	with	ADP
ma-179	37	10	respect	respect	NOUN
ma-179	37	11	to	to	ADP
ma-179	37	12	θ	θ	PROPN
ma-179	37	13	provides	provide	VERB
ma-179	37	14	the	the	DET
ma-179	37	15	maximum	maximum	ADJ
ma-179	37	16	likelihood	likelihood	NOUN
ma-179	37	17	estimate	estimate	NOUN
ma-179	37	18	(	(	PUNCT
ma-179	37	19	mle	mle	PROPN
ma-179	37	20	)	)	PUNCT
ma-179	37	21	θt	θt	NOUN
ma-179	37	22	:	:	PUNCT
ma-179	38	1	=	=	SYM
ma-179	38	2	∫	∫	PROPN
ma-179	38	3	t	t	PROPN
ma-179	38	4	0	0	NUM
ma-179	38	5	xtdxt∫	xtdxt∫	PROPN
ma-179	38	6	t	t	PROPN
ma-179	38	7	0	0	NUM
ma-179	39	1	x2	x2	PROPN
ma-179	39	2	t	t	PROPN
ma-179	39	3	dt	dt	X
ma-179	39	4	.	.	PUNCT
ma-179	40	1	(	(	PUNCT
ma-179	40	2	1.3	1.3	NUM
ma-179	40	3	)	)	PUNCT
ma-179	40	4	in	in	ADP
ma-179	40	5	this	this	DET
ma-179	40	6	transient	transient	ADJ
ma-179	40	7	case	case	NOUN
ma-179	40	8	,	,	PUNCT
ma-179	40	9	we	we	PRON
ma-179	40	10	show	show	VERB
ma-179	40	11	that	that	SCONJ
ma-179	40	12	this	this	DET
ma-179	40	13	estimator	estimator	NOUN
ma-179	40	14	converges	converge	VERB
ma-179	40	15	to	to	ADP
ma-179	40	16	the	the	DET
ma-179	40	17	cauchy	cauchy	ADJ
ma-179	40	18	distribution	distribution	NOUN
ma-179	40	19	withan	withan	VERB
ma-179	40	20	error	error	NOUN
ma-179	40	21	rate	rate	NOUN
ma-179	40	22	o(e−θt	o(e−θt	NOUN
ma-179	40	23	)	)	PUNCT
ma-179	40	24	.	.	PUNCT
ma-179	41	1	note	note	VERB
ma-179	41	2	that	that	SCONJ
ma-179	41	3	in	in	ADP
ma-179	41	4	the	the	DET
ma-179	41	5	transient	transient	ADJ
ma-179	41	6	case	case	NOUN
ma-179	41	7	,	,	PUNCT
ma-179	41	8	with	with	ADP
ma-179	41	9	random	random	ADJ
ma-179	41	10	norming	norming	NOUN
ma-179	41	11	,	,	PUNCT
ma-179	41	12	specifically	specifically	ADV
ma-179	41	13	if	if	SCONJ
ma-179	41	14	onenormalizes	onenormalize	VERB
ma-179	41	15	the	the	DET
ma-179	41	16	mle	mle	NOUN
ma-179	41	17	by	by	ADP
ma-179	41	18	the	the	DET
ma-179	41	19	square	square	ADJ
ma-179	41	20	root	root	NOUN
ma-179	41	21	of	of	ADP
ma-179	41	22	the	the	DET
ma-179	41	23	observed	observe	VERB
ma-179	41	24	fisher	fisher	PROPN
ma-179	41	25	information	information	NOUN
ma-179	41	26	,	,	PUNCT
ma-179	41	27	then	then	ADV
ma-179	41	28	the	the	DET
ma-179	41	29	mle	mle	PROPN
ma-179	41	30	convergesto	convergesto	PROPN
ma-179	41	31	the	the	DET
ma-179	41	32	normal	normal	ADJ
ma-179	41	33	distribution	distribution	NOUN
ma-179	41	34	,	,	PUNCT
ma-179	41	35	see	see	VERB
ma-179	41	36	feigin	feigin	NOUN
ma-179	41	37	[	[	X
ma-179	41	38	16	16	NUM
ma-179	41	39	]	]	PUNCT
ma-179	41	40	.	.	PUNCT
ma-179	42	1	maximum	maximum	ADJ
ma-179	42	2	likelihood	likelihood	NOUN
ma-179	42	3	estimation	estimation	NOUN
ma-179	42	4	in	in	ADP
ma-179	42	5	non	non	ADJ
ma-179	42	6	-	-	ADJ
ma-179	42	7	recurrent	recurrent	ADJ
ma-179	42	8	casewas	casewas	NOUN
ma-179	42	9	studied	study	VERB
ma-179	42	10	in	in	ADP
ma-179	42	11	dietz	dietz	PROPN
ma-179	42	12	and	and	CCONJ
ma-179	42	13	kutoyants	kutoyant	NOUN
ma-179	43	1	[	[	X
ma-179	43	2	15	15	NUM
ma-179	43	3	]	]	PUNCT
ma-179	43	4	.	.	PUNCT
ma-179	44	1	local	local	ADJ
ma-179	44	2	asymptotic	asymptotic	ADJ
ma-179	44	3	mixed	mixed	ADJ
ma-179	44	4	normality	normality	NOUN
ma-179	44	5	for	for	ADP
ma-179	44	6	discretely	discretely	ADV
ma-179	44	7	observednon	observednon	ADJ
ma-179	44	8	-	-	PUNCT
ma-179	44	9	recurrent	recurrent	NOUN
ma-179	44	10	ornstein	ornstein	PROPN
ma-179	44	11	-	-	PUNCT
ma-179	44	12	uhlenbeck	uhlenbeck	PROPN
ma-179	44	13	processes	process	NOUN
ma-179	44	14	was	be	AUX
ma-179	44	15	studied	study	VERB
ma-179	44	16	in	in	ADP
ma-179	44	17	shimizu	shimizu	PROPN
ma-179	44	18	[	[	X
ma-179	44	19	30	30	NUM
ma-179	44	20	]	]	PUNCT
ma-179	44	21	.	.	PUNCT
ma-179	45	1	θt	θt	VERB
ma-179	45	2	−	−	NUM
ma-179	45	3	θ	θ	NOUN
ma-179	45	4	:	:	PUNCT
ma-179	46	1	=	=	SYM
ma-179	46	2	∫	∫	PROPN
ma-179	46	3	t	t	PROPN
ma-179	46	4	0	0	NUM
ma-179	46	5	xtdwt∫	xtdwt∫	PROPN
ma-179	47	1	t	t	NOUN
ma-179	47	2	0	0	NUM
ma-179	48	1	x2	x2	PROPN
ma-179	48	2	t	t	NOUN
ma-179	48	3	dt	dt	NOUN
ma-179	49	1	=	=	SYM
ma-179	49	2	zt	zt	PROPN
ma-179	49	3	it	it	PRON
ma-179	49	4	(	(	PUNCT
ma-179	49	5	1.4	1.4	NUM
ma-179	49	6	)	)	PUNCT
ma-179	50	1	where	where	SCONJ
ma-179	50	2	zt	zt	PROPN
ma-179	50	3	:	:	PUNCT
ma-179	50	4	=	=	SYM
ma-179	50	5	∫	∫	PROPN
ma-179	50	6	t	t	PROPN
ma-179	50	7	0	0	NUM
ma-179	50	8	xtdwt	xtdwt	PROPN
ma-179	50	9	and	and	CCONJ
ma-179	50	10	it	it	PRON
ma-179	50	11	:	:	PUNCT
ma-179	51	1	=	=	SYM
ma-179	51	2	∫	∫	PROPN
ma-179	51	3	t	t	PROPN
ma-179	51	4	0	0	NUM
ma-179	51	5	x2	x2	PROPN
ma-179	51	6	t	t	PROPN
ma-179	51	7	dt	dt	PROPN
ma-179	51	8	.	.	PUNCT
ma-179	52	1	(	(	PUNCT
ma-179	52	2	1.5	1.5	NUM
ma-179	52	3	)	)	PUNCT
ma-179	52	4	hence	hence	ADV
ma-179	52	5	eθt	eθt	VERB
ma-179	52	6	2θ	2θ	NUM
ma-179	52	7	(	(	PUNCT
ma-179	52	8	θt	θt	PROPN
ma-179	52	9	−	−	PROPN
ma-179	52	10	θ	θ	NOUN
ma-179	52	11	)	)	PUNCT
ma-179	52	12	=	=	SYM
ma-179	52	13	e−θt	e−θt	NOUN
ma-179	52	14	2θzt	2θzt	PROPN
ma-179	52	15	e−2θt	e−2θt	VERB
ma-179	52	16	4θ2it	4θ2it	NUM
ma-179	53	1	=	=	SYM
ma-179	54	1	(	(	PUNCT
ma-179	54	2	e−2θt	e−2θt	PROPN
ma-179	54	3	4θ2	4θ2	NUM
ma-179	54	4	)	)	PUNCT
ma-179	54	5	1/2	1/2	NUM
ma-179	55	1	zt	zt	PROPN
ma-179	55	2	e−2θt	e−2θt	ADJ
ma-179	55	3	4θ2it	4θ2it	NUM
ma-179	55	4	(	(	PUNCT
ma-179	55	5	1.6)in	1.6)in	NUM
ma-179	55	6	(	(	PUNCT
ma-179	55	7	1.6	1.6	NUM
ma-179	55	8	)	)	PUNCT
ma-179	55	9	,	,	PUNCT
ma-179	55	10	the	the	DET
ma-179	55	11	numerator	numerator	NOUN
ma-179	55	12	of	of	ADP
ma-179	55	13	the	the	DET
ma-179	55	14	normalized	normalize	VERB
ma-179	55	15	mle	mle	PROPN
ma-179	55	16	is	be	AUX
ma-179	55	17	a	a	DET
ma-179	55	18	normalized	normalize	VERB
ma-179	55	19	martingale	martingale	NOUN
ma-179	55	20	which	which	PRON
ma-179	55	21	converges	converge	VERB
ma-179	55	22	tothe	tothe	PRON
ma-179	55	23	standard	standard	ADJ
ma-179	55	24	normal	normal	ADJ
ma-179	55	25	variable	variable	NOUN
ma-179	55	26	and	and	CCONJ
ma-179	55	27	the	the	DET
ma-179	55	28	denominator	denominator	NOUN
ma-179	55	29	is	be	AUX
ma-179	55	30	its	its	PRON
ma-179	55	31	corresponding	correspond	VERB
ma-179	55	32	increasing	increase	VERB
ma-179	55	33	process	process	NOUN
ma-179	55	34	whichconverges	whichconverge	NOUN
ma-179	55	35	to	to	ADP
ma-179	55	36	a	a	DET
ma-179	55	37	chi	chi	ADJ
ma-179	55	38	-	-	PUNCT
ma-179	55	39	square	square	ADJ
ma-179	55	40	random	random	ADJ
ma-179	55	41	variable	variable	NOUN
ma-179	55	42	as	as	ADP
ma-179	55	43	t	t	PROPN
ma-179	55	44	→	→	SYM
ma-179	55	45	∞	∞	PROPN
ma-179	55	46	which	which	PRON
ma-179	55	47	is	be	AUX
ma-179	55	48	independent	independent	ADJ
ma-179	55	49	of	of	ADP
ma-179	55	50	the	the	DET
ma-179	55	51	numerator.hence	numerator.hence	PROPN
ma-179	55	52	the	the	DET
ma-179	55	53	ratio	ratio	NOUN
ma-179	55	54	converges	converge	VERB
ma-179	55	55	to	to	ADP
ma-179	55	56	a	a	DET
ma-179	55	57	cauchy	cauchy	ADJ
ma-179	55	58	distribution	distribution	NOUN
ma-179	55	59	with	with	ADP
ma-179	55	60	parameters	parameter	NOUN
ma-179	55	61	(	(	PUNCT
ma-179	55	62	0	0	NUM
ma-179	55	63	,	,	PUNCT
ma-179	55	64	1).let	1).let	NUM
ma-179	55	65	us	we	PRON
ma-179	55	66	introduce	introduce	VERB
ma-179	55	67	two	two	NUM
ma-179	55	68	wiener	wiener	NOUN
ma-179	55	69	integrals	integral	NOUN
ma-179	55	70	:	:	PUNCT
ma-179	55	71	ξt	ξt	X
ma-179	55	72	:	:	PUNCT
ma-179	55	73	=	=	SYM
ma-179	55	74	∫	∫	PROPN
ma-179	55	75	t	t	PROPN
ma-179	55	76	0	0	NUM
ma-179	55	77	e−θsdws	e−θsdws	PROPN
ma-179	55	78	,	,	PUNCT
ma-179	55	79	and	and	CCONJ
ma-179	55	80	ηt	ηt	ADP
ma-179	55	81	:	:	PUNCT
ma-179	55	82	=	=	SYM
ma-179	55	83	∫	∫	PROPN
ma-179	55	84	t	t	PROPN
ma-179	55	85	0	0	NUM
ma-179	55	86	eθsdws	eθsdws	NOUN
ma-179	55	87	,	,	PUNCT
ma-179	55	88	t	t	PROPN
ma-179	55	89	≥	≥	PROPN
ma-179	55	90	0	0	NUM
ma-179	55	91	.	.	PUNCT
ma-179	56	1	(	(	PUNCT
ma-179	56	2	1.7	1.7	NUM
ma-179	56	3	)	)	PUNCT
ma-179	56	4	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	NOUN
ma-179	56	5	eur	eur	PROPN
ma-179	56	6	.	.	PUNCT
ma-179	57	1	j.	j.	PROPN
ma-179	57	2	math	math	PROPN
ma-179	57	3	.	.	PUNCT
ma-179	58	1	anal	anal	PROPN
ma-179	58	2	.	.	PUNCT
ma-179	59	1	10.28924	10.28924	NUM
ma-179	59	2	/	/	SYM
ma-179	59	3	ada	ada	PROPN
ma-179	59	4	/	/	SYM
ma-179	59	5	ma.3.25	ma.3.25	NOUN
ma-179	59	6	3	3	NUM
ma-179	59	7	and	and	CCONJ
ma-179	59	8	the	the	DET
ma-179	59	9	respective	respective	ADJ
ma-179	59	10	limits	limit	NOUN
ma-179	60	1	ξ	ξ	PROPN
ma-179	60	2	=	=	SYM
ma-179	60	3	limt→∞	limt→∞	PROPN
ma-179	60	4	∫	∫	PROPN
ma-179	60	5	t	t	PROPN
ma-179	60	6	0	0	NUM
ma-179	60	7	e−θsdws	e−θsdws	PROPN
ma-179	60	8	:	:	PUNCT
ma-179	60	9	=	=	SYM
ma-179	60	10	∫∞	∫∞	NOUN
ma-179	60	11	0	0	NUM
ma-179	60	12	e−θsdws	e−θsdws	PROPN
ma-179	60	13	which	which	PRON
ma-179	60	14	has	have	VERB
ma-179	60	15	n	n	NUM
ma-179	60	16	(	(	PUNCT
ma-179	60	17	0	0	NUM
ma-179	60	18	,	,	PUNCT
ma-179	60	19	1	1	NUM
ma-179	60	20	2θ	2θ	NUM
ma-179	60	21	)	)	PUNCT
ma-179	60	22	distribu	distribu	NOUN
ma-179	60	23	-	-	PUNCT
ma-179	60	24	tion	tion	NOUN
ma-179	60	25	and	and	CCONJ
ma-179	60	26	η	η	PROPN
ma-179	60	27	:	:	PUNCT
ma-179	61	1	=	=	SYM
ma-179	61	2	limt→∞	limt→∞	NOUN
ma-179	61	3	e	e	X
ma-179	61	4	−θtηt	−θtηt	ADV
ma-179	61	5	=	=	PUNCT
ma-179	61	6	limt→∞	limt→∞	PROPN
ma-179	61	7	e	e	X
ma-179	61	8	−θt	−θt	PROPN
ma-179	61	9	∫	∫	PROPN
ma-179	61	10	t	t	PROPN
ma-179	61	11	0	0	NUM
ma-179	61	12	eθsdws	eθsdws	NOUN
ma-179	61	13	=	=	NOUN
ma-179	61	14	∫∞	∫∞	NOUN
ma-179	61	15	0	0	NUM
ma-179	61	16	e−θsdws	e−θsdws	PROPN
ma-179	61	17	which	which	PRON
ma-179	61	18	has	have	VERB
ma-179	61	19	n	n	NUM
ma-179	61	20	(	(	PUNCT
ma-179	61	21	0	0	NUM
ma-179	61	22	,	,	PUNCT
ma-179	61	23	1	1	NUM
ma-179	61	24	2θ	2θ	NUM
ma-179	61	25	)	)	PUNCT
ma-179	62	1	distribution.with	distribution.with	ADP
ma-179	62	2	these	these	DET
ma-179	62	3	notations	notation	NOUN
ma-179	62	4	zt	zt	X
ma-179	62	5	:	:	PUNCT
ma-179	62	6	=	=	SYM
ma-179	62	7	∫	∫	PROPN
ma-179	62	8	t	t	PROPN
ma-179	62	9	0	0	NUM
ma-179	63	1	xtdwt	xtdwt	PROPN
ma-179	63	2	=	=	SYM
ma-179	64	1	∫	∫	PROPN
ma-179	64	2	t	t	NOUN
ma-179	64	3	0	0	NUM
ma-179	64	4	eθtξtdwt	eθtξtdwt	NOUN
ma-179	64	5	and	and	CCONJ
ma-179	64	6	it	it	PRON
ma-179	64	7	:	:	PUNCT
ma-179	65	1	=	=	SYM
ma-179	65	2	∫	∫	PROPN
ma-179	65	3	t	t	PROPN
ma-179	65	4	0	0	NUM
ma-179	66	1	x2	x2	PROPN
ma-179	66	2	t	t	NOUN
ma-179	66	3	dt	dt	NOUN
ma-179	67	1	=	=	SYM
ma-179	67	2	∫	∫	PROPN
ma-179	67	3	t	t	PROPN
ma-179	67	4	0	0	NUM
ma-179	68	1	e2θtξ2	e2θtξ2	PROPN
ma-179	68	2	t	t	PROPN
ma-179	68	3	dt	dt	PROPN
ma-179	68	4	,	,	PUNCT
ma-179	68	5	θt	θt	PROPN
ma-179	68	6	−	−	PROPN
ma-179	68	7	θ	θ	PROPN
ma-179	68	8	=	=	SYM
ma-179	68	9	∫	∫	PROPN
ma-179	69	1	t	t	PROPN
ma-179	69	2	0	0	NUM
ma-179	69	3	eθtξtdwt∫	eθtξtdwt∫	VERB
ma-179	70	1	t	t	PROPN
ma-179	70	2	0	0	NUM
ma-179	70	3	e2θtξ2	e2θtξ2	PROPN
ma-179	70	4	t	t	PROPN
ma-179	71	1	dt	dt	X
ma-179	71	2	,	,	PUNCT
ma-179	71	3	(	(	PUNCT
ma-179	71	4	1.8	1.8	NUM
ma-179	71	5	)	)	PUNCT
ma-179	71	6	eθt	eθt	NOUN
ma-179	71	7	2θ	2θ	NUM
ma-179	71	8	(	(	PUNCT
ma-179	71	9	θt	θt	PROPN
ma-179	71	10	−	−	PROPN
ma-179	71	11	θ	θ	NOUN
ma-179	71	12	)	)	PUNCT
ma-179	71	13	=	=	NOUN
ma-179	71	14	(	(	PUNCT
ma-179	71	15	e−2θt	e−2θt	PROPN
ma-179	71	16	4θ2	4θ2	NUM
ma-179	71	17	)	)	PUNCT
ma-179	71	18	1/2	1/2	NUM
ma-179	71	19	∫	∫	NOUN
ma-179	71	20	t	t	NOUN
ma-179	71	21	0	0	NUM
ma-179	71	22	eθtξtdwt	eθtξtdwt	NOUN
ma-179	71	23	e−2θt	e−2θt	ADJ
ma-179	71	24	4θ2	4θ2	NUM
ma-179	72	1	∫	∫	PROPN
ma-179	72	2	t	t	PROPN
ma-179	72	3	0	0	NUM
ma-179	73	1	e2θtξ2	e2θtξ2	PROPN
ma-179	73	2	t	t	NOUN
ma-179	73	3	dt	dt	NOUN
ma-179	74	1	=	=	PUNCT
ma-179	74	2	(	(	PUNCT
ma-179	74	3	e−2θt	e−2θt	PROPN
ma-179	74	4	4θ2	4θ2	NUM
ma-179	74	5	)	)	PUNCT
ma-179	74	6	1/2	1/2	NUM
ma-179	74	7	∫	∫	PROPN
ma-179	74	8	t	t	PROPN
ma-179	74	9	0	0	NUM
ma-179	74	10	eθt	eθt	PROPN
ma-179	74	11	(	(	PUNCT
ma-179	74	12	∫	∫	PROPN
ma-179	74	13	t	t	PROPN
ma-179	74	14	0	0	NUM
ma-179	74	15	e	e	NOUN
ma-179	74	16	−θsdws)dwt	−θsdws)dwt	PROPN
ma-179	74	17	e−2θt	e−2θt	ADJ
ma-179	74	18	4θ2	4θ2	NUM
ma-179	74	19	∫	∫	PROPN
ma-179	74	20	t	t	PROPN
ma-179	74	21	0	0	NUM
ma-179	74	22	e2θt	e2θt	NUM
ma-179	74	23	(	(	PUNCT
ma-179	74	24	∫	∫	PROPN
ma-179	74	25	t	t	PROPN
ma-179	74	26	0	0	NUM
ma-179	74	27	e	e	X
ma-179	74	28	−θsdws)2dt	−θsdws)2dt	NOUN
ma-179	74	29	=	=	SYM
ma-179	74	30	ξt	ξt	X
ma-179	74	31	ξ	ξ	X
ma-179	74	32	2θe−2θt	2θe−2θt	NUM
ma-179	74	33	∫	∫	PROPN
ma-179	74	34	t	t	PROPN
ma-179	74	35	0	0	NUM
ma-179	74	36	e2θtξ2	e2θtξ2	PROPN
ma-179	75	1	t	t	PROPN
ma-179	75	2	dt	dt	X
ma-179	75	3	×	×	PROPN
ma-179	75	4	e−θt	e−θt	PROPN
ma-179	75	5	∫	∫	PROPN
ma-179	75	6	t	t	PROPN
ma-179	75	7	0	0	NUM
ma-179	75	8	eθtdwt	eθtdwt	NOUN
ma-179	75	9	ξ	ξ	X
ma-179	76	1	=	=	SYM
ma-179	76	2	ξt	ξt	X
ma-179	76	3	ξ	ξ	SYM
ma-179	76	4	2θe−2θt	2θe−2θt	NUM
ma-179	76	5	it	it	PRON
ma-179	76	6	×	×	NOUN
ma-179	76	7	e−θtηt	e−θtηt	X
ma-179	76	8	ξ	ξ	X
ma-179	76	9	=	=	NOUN
ma-179	76	10	:	:	PUNCT
ma-179	76	11	aθt	aθt	X
ma-179	76	12	×	×	PROPN
ma-179	76	13	bθt	bθt	NOUN
ma-179	76	14	.	.	PUNCT
ma-179	77	1	(	(	PUNCT
ma-179	77	2	1.9	1.9	NUM
ma-179	77	3	)	)	PUNCT
ma-179	77	4	we	we	PRON
ma-179	77	5	have	have	VERB
ma-179	77	6	aθt	aθt	VERB
ma-179	77	7	→	→	SYM
ma-179	77	8	1	1	NUM
ma-179	77	9	almost	almost	ADV
ma-179	77	10	surely	surely	ADV
ma-179	77	11	as	as	ADP
ma-179	77	12	t	t	PROPN
ma-179	77	13	→∞	→∞	PROPN
ma-179	77	14	,	,	PUNCT
ma-179	77	15	(	(	PUNCT
ma-179	77	16	1.10	1.10	NUM
ma-179	77	17	)	)	PUNCT
ma-179	77	18	bθt	bθt	NOUN
ma-179	77	19	d→	d→	VERB
ma-179	77	20	n√	n√	PROPN
ma-179	77	21	2θξ	2θξ	NOUN
ma-179	77	22	as	as	ADP
ma-179	77	23	t	t	PROPN
ma-179	77	24	→∞	→∞	PROPN
ma-179	77	25	(	(	PUNCT
ma-179	77	26	1.11	1.11	NUM
ma-179	77	27	)	)	PUNCT
ma-179	77	28	where	where	SCONJ
ma-179	77	29	√2θξ	√2θξ	NOUN
ma-179	77	30	=	=	SYM
ma-179	77	31	n1	n1	NOUN
ma-179	77	32	,	,	PUNCT
ma-179	77	33	and	and	CCONJ
ma-179	77	34	n1	n1	NOUN
ma-179	77	35	and	and	CCONJ
ma-179	77	36	n	n	PRON
ma-179	77	37	are	be	AUX
ma-179	77	38	independent	independent	ADJ
ma-179	77	39	standard	standard	ADJ
ma-179	77	40	normal	normal	ADJ
ma-179	77	41	random	random	ADJ
ma-179	77	42	variables	variable	NOUN
ma-179	77	43	.	.	PUNCT
ma-179	78	1	since	since	SCONJ
ma-179	78	2	n√	n√	PROPN
ma-179	78	3	2θξ	2θξ	NOUN
ma-179	78	4	d	d	X
ma-179	78	5	=	=	PUNCT
ma-179	78	6	c(1	c(1	NOUN
ma-179	78	7	)	)	PUNCT
ma-179	78	8	as	as	ADP
ma-179	78	9	t	t	PROPN
ma-179	78	10	→∞	→∞	PROPN
ma-179	78	11	(	(	PUNCT
ma-179	78	12	1.12	1.12	NUM
ma-179	78	13	)	)	PUNCT
ma-179	78	14	where	where	SCONJ
ma-179	78	15	c(1	c(1	NOUN
ma-179	78	16	)	)	PUNCT
ma-179	78	17	is	be	AUX
ma-179	78	18	the	the	DET
ma-179	78	19	standard	standard	ADJ
ma-179	78	20	cauchy	cauchy	ADJ
ma-179	78	21	distribution	distribution	NOUN
ma-179	78	22	,	,	PUNCT
ma-179	78	23	by	by	ADP
ma-179	78	24	slutsky	slutsky	PROPN
ma-179	78	25	’s	’s	PART
ma-179	78	26	theorem	theorem	PROPN
ma-179	78	27	,	,	PUNCT
ma-179	78	28	we	we	PRON
ma-179	78	29	have	have	AUX
ma-179	78	30	aθt	aθt	VERB
ma-179	78	31	×	×	PROPN
ma-179	78	32	bθt	bθt	ADJ
ma-179	78	33	d→c(1	d→c(1	NOUN
ma-179	78	34	)	)	PUNCT
ma-179	78	35	as	as	ADP
ma-179	78	36	t	t	PROPN
ma-179	78	37	→∞.	→∞.	PROPN
ma-179	78	38	(	(	PUNCT
ma-179	78	39	1.13	1.13	NUM
ma-179	78	40	)	)	PUNCT
ma-179	78	41	note	note	VERB
ma-179	78	42	that	that	SCONJ
ma-179	78	43	ξt	ξt	X
ma-179	78	44	d→	d→	ADJ
ma-179	78	45	ξ	ξ	PROPN
ma-179	78	46	as	as	ADP
ma-179	78	47	t	t	PROPN
ma-179	78	48	→∞.	→∞.	PROPN
ma-179	78	49	(	(	PUNCT
ma-179	78	50	1.14)using	1.14)using	NUM
ma-179	78	51	borel	borel	PROPN
ma-179	78	52	-	-	PUNCT
ma-179	78	53	cantelli	cantelli	PROPN
ma-179	78	54	lemma	lemma	PROPN
ma-179	78	55	and	and	CCONJ
ma-179	78	56	stochastic	stochastic	ADJ
ma-179	78	57	fubini	fubini	ADJ
ma-179	78	58	theorem	theorem	NOUN
ma-179	78	59	,	,	PUNCT
ma-179	78	60	it	it	PRON
ma-179	78	61	can	can	AUX
ma-179	78	62	be	be	AUX
ma-179	78	63	shown	show	VERB
ma-179	78	64	that	that	SCONJ
ma-179	78	65	ξt	ξt	X
ma-179	78	66	→	→	SYM
ma-179	78	67	ξ	ξ	X
ma-179	78	68	almostsurely	almostsurely	ADV
ma-179	78	69	and	and	CCONJ
ma-179	78	70	in	in	ADP
ma-179	78	71	l2(ω	l2(ω	PROPN
ma-179	78	72	)	)	PUNCT
ma-179	78	73	as	as	ADP
ma-179	78	74	t	t	PROPN
ma-179	78	75	→∞.	→∞.	PUNCT
ma-179	78	76	by	by	ADP
ma-179	78	77	integration	integration	NOUN
ma-179	78	78	by	by	ADP
ma-179	78	79	parts	part	NOUN
ma-179	78	80	we	we	PRON
ma-179	78	81	have	have	AUX
ma-179	78	82	e−2θt	e−2θt	VERB
ma-179	78	83	it	it	PRON
ma-179	78	84	=	=	PUNCT
ma-179	79	1	e−2θt	e−2θt	PROPN
ma-179	79	2	∫	∫	PROPN
ma-179	80	1	t	t	PROPN
ma-179	80	2	0	0	NUM
ma-179	81	1	x2	x2	PROPN
ma-179	81	2	s	s	VERB
ma-179	81	3	ds	ds	NOUN
ma-179	81	4	=	=	PUNCT
ma-179	81	5	e−2θt	e−2θt	ADJ
ma-179	81	6	∫	∫	PROPN
ma-179	81	7	t	t	PROPN
ma-179	81	8	0	0	NUM
ma-179	81	9	e2θsξ2	e2θsξ2	NOUN
ma-179	81	10	s	s	X
ma-179	81	11	ds	ds	ADJ
ma-179	81	12	=	=	SYM
ma-179	81	13	ξ2	ξ2	NOUN
ma-179	81	14	t	t	NOUN
ma-179	81	15	2θ	2θ	NUM
ma-179	81	16	−	−	ADP
ma-179	82	1	e−2θt	e−2θt	ADJ
ma-179	82	2	θ	θ	X
ma-179	82	3	∫	∫	PROPN
ma-179	82	4	t	t	PROPN
ma-179	82	5	0	0	NUM
ma-179	82	6	e2θsξsdξs	e2θsξsdξs	PROPN
ma-179	82	7	−	−	PROPN
ma-179	82	8	te−2θt	te−2θt	NUM
ma-179	82	9	θ	θ	NOUN
ma-179	82	10	=	=	SYM
ma-179	82	11	ξ2	ξ2	PROPN
ma-179	82	12	t	t	NOUN
ma-179	82	13	2θ	2θ	NUM
ma-179	82	14	−	−	ADP
ma-179	83	1	e−2θt	e−2θt	ADJ
ma-179	83	2	θ	θ	PROPN
ma-179	83	3	∫	∫	PROPN
ma-179	83	4	t	t	PROPN
ma-179	83	5	0	0	NUM
ma-179	83	6	eθsξsdws	eθsξsdws	PROPN
ma-179	83	7	−	−	PROPN
ma-179	83	8	te−2θt	te−2θt	NUM
ma-179	83	9	θ	θ	NOUN
ma-179	83	10	.	.	PUNCT
ma-179	84	1	(	(	PUNCT
ma-179	84	2	1.15	1.15	NUM
ma-179	84	3	)	)	PUNCT
ma-179	84	4	this	this	DET
ma-179	84	5	equality	equality	NOUN
ma-179	84	6	together	together	ADV
ma-179	84	7	with	with	ADP
ma-179	84	8	e	e	PROPN
ma-179	84	9	(	(	PUNCT
ma-179	84	10	∫	∫	PROPN
ma-179	84	11	t	t	PROPN
ma-179	84	12	0	0	NUM
ma-179	84	13	eθsξsdws	eθsξsdws	PROPN
ma-179	84	14	)	)	PUNCT
ma-179	85	1	2	2	NUM
ma-179	85	2	=	=	SYM
ma-179	85	3	∫	∫	PROPN
ma-179	85	4	t	t	NOUN
ma-179	85	5	0	0	NUM
ma-179	86	1	e2θse(ξ2	e2θse(ξ2	PROPN
ma-179	86	2	s	s	PART
ma-179	86	3	)	)	PUNCT
ma-179	86	4	ds	ds	ADJ
ma-179	86	5	=	=	SYM
ma-179	86	6	1	1	NUM
ma-179	86	7	2θ	2θ	NUM
ma-179	86	8	∫	∫	PROPN
ma-179	86	9	t	t	NOUN
ma-179	86	10	0	0	NUM
ma-179	86	11	e2θs(1−	e2θs(1−	PROPN
ma-179	86	12	e−2θs)ds	e−2θs)ds	PROPN
ma-179	86	13	=	=	PUNCT
ma-179	86	14	e2θt	e2θt	PUNCT
ma-179	86	15	−	−	PROPN
ma-179	86	16	1−	1−	NUM
ma-179	86	17	2θt	2θt	ADJ
ma-179	86	18	4θ2	4θ2	NUM
ma-179	86	19	(	(	PUNCT
ma-179	86	20	1.16	1.16	NUM
ma-179	86	21	)	)	PUNCT
ma-179	86	22	by	by	ADP
ma-179	86	23	the	the	DET
ma-179	86	24	clt	clt	NOUN
ma-179	86	25	for	for	ADP
ma-179	86	26	stochastic	stochastic	ADJ
ma-179	86	27	integrals	integral	NOUN
ma-179	86	28	provides	provide	VERB
ma-179	86	29	e−2θt	e−2θt	ADJ
ma-179	86	30	∫	∫	PROPN
ma-179	86	31	t	t	PROPN
ma-179	86	32	0	0	NUM
ma-179	87	1	x2	x2	PROPN
ma-179	87	2	s	s	PART
ma-179	87	3	ds	ds	PROPN
ma-179	87	4	d→	d→	NUM
ma-179	87	5	ξ2	ξ2	NUM
ma-179	87	6	2θ	2θ	NUM
ma-179	87	7	as	as	ADP
ma-179	87	8	t	t	PROPN
ma-179	87	9	→∞	→∞	PROPN
ma-179	87	10	(	(	PUNCT
ma-179	87	11	1.17	1.17	NUM
ma-179	87	12	)	)	PUNCT
ma-179	87	13	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	NOUN
ma-179	87	14	eur	eur	PROPN
ma-179	87	15	.	.	PUNCT
ma-179	88	1	j.	j.	PROPN
ma-179	88	2	math	math	PROPN
ma-179	88	3	.	.	PUNCT
ma-179	89	1	anal	anal	PROPN
ma-179	89	2	.	.	PUNCT
ma-179	90	1	10.28924	10.28924	NUM
ma-179	90	2	/	/	SYM
ma-179	90	3	ada	ada	PROPN
ma-179	90	4	/	/	SYM
ma-179	90	5	ma.3.25	ma.3.25	VERB
ma-179	90	6	4	4	NUM
ma-179	90	7	i.e.	i.e.	X
ma-179	90	8	,	,	PUNCT
ma-179	90	9	e−2θt	e−2θt	VERB
ma-179	90	10	it	it	PRON
ma-179	90	11	d→	d→	VERB
ma-179	90	12	ξ2	ξ2	ADJ
ma-179	90	13	2θ	2θ	NUM
ma-179	90	14	as	as	SCONJ
ma-179	90	15	t	t	PROPN
ma-179	90	16	→∞.it	→∞.it	PROPN
ma-179	90	17	can	can	AUX
ma-179	90	18	be	be	AUX
ma-179	90	19	shown	show	VERB
ma-179	90	20	that	that	SCONJ
ma-179	90	21	e−2θt	e−2θt	VERB
ma-179	90	22	it	it	PRON
ma-179	90	23	→	→	SYM
ma-179	90	24	ξ2	ξ2	ADJ
ma-179	90	25	2θ	2θ	NUM
ma-179	90	26	almost	almost	ADV
ma-179	90	27	surely	surely	ADV
ma-179	90	28	as	as	SCONJ
ma-179	90	29	t	t	PROPN
ma-179	90	30	→∞.	→∞.	PUNCT
ma-179	90	31	(	(	PUNCT
ma-179	90	32	1.18)by	1.18)by	NUM
ma-179	90	33	itô	itô	PROPN
ma-179	90	34	formula	formula	NOUN
ma-179	90	35	,	,	PUNCT
ma-179	90	36	we	we	PRON
ma-179	90	37	have	have	VERB
ma-179	91	1	zt	zt	PROPN
ma-179	91	2	=	=	SYM
ma-179	91	3	∫	∫	PROPN
ma-179	91	4	t	t	PROPN
ma-179	91	5	0	0	NUM
ma-179	91	6	xsdws	xsdws	PROPN
ma-179	92	1	=	=	SYM
ma-179	92	2	∫	∫	PROPN
ma-179	92	3	t	t	PROPN
ma-179	92	4	0	0	NUM
ma-179	93	1	eθsξsdws	eθsξsdws	PROPN
ma-179	93	2	=	=	X
ma-179	93	3	∫	∫	PROPN
ma-179	93	4	t	t	PROPN
ma-179	93	5	0	0	NUM
ma-179	93	6	ξsdηs	ξsdηs	PROPN
ma-179	93	7	=	=	SYM
ma-179	93	8	ξtηt	ξtηt	PROPN
ma-179	93	9	−	−	PROPN
ma-179	93	10	t	t	PROPN
ma-179	93	11	−	−	PROPN
ma-179	93	12	∫	∫	PROPN
ma-179	93	13	t	t	PROPN
ma-179	93	14	0	0	NUM
ma-179	93	15	ηsdξs	ηsdξs	NOUN
ma-179	93	16	=	=	PROPN
ma-179	93	17	ξtηt	ξtηt	PROPN
ma-179	93	18	−	−	PROPN
ma-179	93	19	t	t	PROPN
ma-179	94	1	−	−	PROPN
ma-179	94	2	∫	∫	PROPN
ma-179	94	3	t	t	PROPN
ma-179	94	4	0	0	NUM
ma-179	95	1	ηse	ηse	PROPN
ma-179	95	2	−θsdws	−θsdws	PUNCT
ma-179	95	3	.	.	PUNCT
ma-179	96	1	(	(	PUNCT
ma-179	96	2	1.19	1.19	NUM
ma-179	96	3	)	)	PUNCT
ma-179	96	4	hence	hence	ADV
ma-179	96	5	e−θtzt	e−θtzt	PUNCT
ma-179	97	1	=	=	SYM
ma-179	97	2	e−θt	e−θt	NOUN
ma-179	97	3	ξtηt	ξtηt	NOUN
ma-179	97	4	−	−	PROPN
ma-179	97	5	e−θtt	e−θtt	NOUN
ma-179	97	6	−	−	PROPN
ma-179	97	7	e−θt	e−θt	PROPN
ma-179	98	1	∫	∫	PROPN
ma-179	98	2	t	t	PROPN
ma-179	98	3	0	0	NUM
ma-179	98	4	ηse	ηse	PROPN
ma-179	98	5	−θsdws	−θsdws	PUNCT
ma-179	98	6	.	.	PUNCT
ma-179	99	1	(	(	PUNCT
ma-179	99	2	1.20	1.20	NUM
ma-179	99	3	)	)	PUNCT
ma-179	99	4	direct	direct	ADJ
ma-179	99	5	calculation	calculation	NOUN
ma-179	99	6	gives	give	VERB
ma-179	99	7	e−θtηt	e−θtηt	ADP
ma-179	99	8	d→	d→	VERB
ma-179	99	9	η	η	NOUN
ma-179	99	10	∼	∼	NOUN
ma-179	99	11	n	n	CCONJ
ma-179	99	12	(	(	PUNCT
ma-179	99	13	0	0	NUM
ma-179	99	14	,	,	PUNCT
ma-179	99	15	1	1	NUM
ma-179	99	16	2θ	2θ	NUM
ma-179	99	17	)	)	PUNCT
ma-179	99	18	as	as	ADP
ma-179	99	19	t	t	PROPN
ma-179	99	20	→∞	→∞	PROPN
ma-179	99	21	(	(	PUNCT
ma-179	99	22	1.21	1.21	NUM
ma-179	99	23	)	)	PUNCT
ma-179	99	24	and	and	CCONJ
ma-179	99	25	e(ξη	e(ξη	NOUN
ma-179	99	26	)	)	PUNCT
ma-179	100	1	=	=	VERB
ma-179	100	2	lim	lim	PROPN
ma-179	100	3	t→∞	t→∞	X
ma-179	100	4	e(ξtηt	e(ξtηt	NOUN
ma-179	100	5	e	e	X
ma-179	100	6	−θt	−θt	X
ma-179	100	7	)	)	PUNCT
ma-179	101	1	=	=	SYM
ma-179	101	2	lim	lim	PROPN
ma-179	101	3	t→∞	t→∞	ADP
ma-179	101	4	te−θt	te−θt	NOUN
ma-179	102	1	=	=	NOUN
ma-179	102	2	0	0	X
ma-179	102	3	.	.	PUNCT
ma-179	103	1	(	(	PUNCT
ma-179	103	2	1.22)hence	1.22)hence	NUM
ma-179	103	3	e−θtzt	e−θtzt	PROPN
ma-179	103	4	d→	d→	VERB
ma-179	103	5	ξη	ξη	PRON
ma-179	103	6	as	as	ADP
ma-179	103	7	t	t	PROPN
ma-179	103	8	→∞.	→∞.	PROPN
ma-179	103	9	(	(	PUNCT
ma-179	103	10	1.23)hence	1.23)hence	NUM
ma-179	103	11	the	the	DET
ma-179	103	12	limit	limit	NOUN
ma-179	103	13	distribution	distribution	NOUN
ma-179	103	14	of	of	ADP
ma-179	103	15	the	the	DET
ma-179	103	16	pair	pair	NOUN
ma-179	103	17	(	(	PUNCT
ma-179	103	18	ξt	ξt	INTJ
ma-179	103	19	,	,	PUNCT
ma-179	103	20	e	e	NOUN
ma-179	103	21	−θtηt	−θtηt	ADV
ma-179	103	22	)	)	PUNCT
ma-179	103	23	is	be	AUX
ma-179	103	24	a	a	DET
ma-179	103	25	gaussian	gaussian	ADJ
ma-179	103	26	distribution	distribution	NOUN
ma-179	103	27	of	of	ADP
ma-179	103	28	two	two	NUM
ma-179	103	29	indepen	indepen	ADJ
ma-179	103	30	-	-	PUNCT
ma-179	103	31	dent	dent	NOUN
ma-179	103	32	variables	variable	NOUN
ma-179	103	33	.	.	PUNCT
ma-179	104	1	thus	thus	ADV
ma-179	104	2	eθt	eθt	VERB
ma-179	104	3	ξt	ξt	X
ma-179	104	4	ηt	ηt	ADP
ma-179	104	5	d→	d→	X
ma-179	104	6	ζ	ζ	NOUN
ma-179	104	7	as	as	ADP
ma-179	104	8	t	t	PROPN
ma-179	104	9	→∞	→∞	PROPN
ma-179	104	10	(	(	PUNCT
ma-179	104	11	1.24	1.24	NUM
ma-179	104	12	)	)	PUNCT
ma-179	104	13	where	where	SCONJ
ma-179	104	14	ζ	ζ	NOUN
ma-179	104	15	is	be	AUX
ma-179	104	16	the	the	DET
ma-179	104	17	standard	standard	ADJ
ma-179	104	18	cauchy	cauchy	ADJ
ma-179	104	19	variable	variable	NOUN
ma-179	104	20	with	with	ADP
ma-179	104	21	probability	probability	NOUN
ma-179	104	22	density	density	NOUN
ma-179	104	23	function	function	NOUN
ma-179	104	24	f	f	PROPN
ma-179	104	25	(	(	PUNCT
ma-179	104	26	x	x	X
ma-179	104	27	)	)	PUNCT
ma-179	104	28	=	=	SYM
ma-179	104	29	1	1	NUM
ma-179	104	30	π(1	π(1	NOUN
ma-179	104	31	+	+	CCONJ
ma-179	104	32	x2	x2	NOUN
ma-179	104	33	)	)	PUNCT
ma-179	104	34	,	,	PUNCT
ma-179	104	35	x	x	PROPN
ma-179	104	36	∈	∈	PROPN
ma-179	104	37	r.	r.	PROPN
ma-179	104	38	(	(	PUNCT
ma-179	104	39	1.25	1.25	NUM
ma-179	104	40	)	)	PUNCT
ma-179	104	41	and	and	CCONJ
ma-179	104	42	cdf	cdf	PROPN
ma-179	104	43	c(x	c(x	NOUN
ma-179	104	44	)	)	PUNCT
ma-179	104	45	=	=	SYM
ma-179	104	46	1	1	NUM
ma-179	104	47	2	2	NUM
ma-179	104	48	+	+	SYM
ma-179	104	49	1	1	NUM
ma-179	104	50	π	π	PROPN
ma-179	104	51	arctan	arctan	PROPN
ma-179	104	52	x	x	PROPN
ma-179	104	53	,	,	PUNCT
ma-179	104	54	x	x	SYM
ma-179	104	55	∈	∈	NOUN
ma-179	104	56	r	r	NOUN
ma-179	104	57	(	(	PUNCT
ma-179	104	58	1.26)and	1.26)and	NUM
ma-179	104	59	characteristic	characteristic	ADJ
ma-179	104	60	function	function	NOUN
ma-179	104	61	∫	∫	PROPN
ma-179	104	62	∞	∞	PROPN
ma-179	104	63	−∞	−∞	ADP
ma-179	104	64	e	e	PROPN
ma-179	104	65	iλxdc(x	iλxdc(x	PROPN
ma-179	104	66	)	)	PUNCT
ma-179	104	67	=	=	SYM
ma-179	104	68	e−|λ|	e−|λ|	NOUN
ma-179	104	69	.	.	PUNCT
ma-179	105	1	(	(	PUNCT
ma-179	105	2	1.27	1.27	NUM
ma-179	105	3	)	)	PUNCT
ma-179	105	4	hence	hence	ADV
ma-179	105	5	eθt	eθt	VERB
ma-179	105	6	2θ	2θ	NUM
ma-179	105	7	(	(	PUNCT
ma-179	105	8	θt	θt	PROPN
ma-179	105	9	−	−	PROPN
ma-179	105	10	θ	θ	PROPN
ma-179	105	11	)	)	PUNCT
ma-179	105	12	d→	d→	VERB
ma-179	105	13	ζ	ζ	NOUN
ma-179	105	14	.	.	PUNCT
ma-179	106	1	(	(	PUNCT
ma-179	106	2	1.28)we	1.28)we	NUM
ma-179	106	3	estimate	estimate	VERB
ma-179	106	4	the	the	DET
ma-179	106	5	rate	rate	NOUN
ma-179	106	6	of	of	ADP
ma-179	106	7	convergence	convergence	NOUN
ma-179	106	8	in	in	ADP
ma-179	106	9	this	this	DET
ma-179	106	10	phenomenon	phenomenon	NOUN
ma-179	106	11	.	.	PUNCT
ma-179	107	1	we	we	PRON
ma-179	107	2	need	need	VERB
ma-179	107	3	the	the	DET
ma-179	107	4	following	follow	VERB
ma-179	107	5	lemma	lemma	PROPN
ma-179	107	6	in	in	ADP
ma-179	107	7	thesequel	thesequel	PROPN
ma-179	107	8	.	.	PUNCT
ma-179	108	1	lemma	lemma	PROPN
ma-179	108	2	1.1	1.1	NUM
ma-179	108	3	(	(	PUNCT
ma-179	108	4	esseen	esseen	AUX
ma-179	108	5	’s	’s	AUX
ma-179	108	6	smoothing	smooth	VERB
ma-179	108	7	lemma	lemma	PROPN
ma-179	108	8	)	)	PUNCT
ma-179	108	9	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	PROPN
ma-179	108	10	eur	eur	PROPN
ma-179	108	11	.	.	PUNCT
ma-179	109	1	j.	j.	PROPN
ma-179	109	2	math	math	PROPN
ma-179	109	3	.	.	PUNCT
ma-179	110	1	anal	anal	PROPN
ma-179	110	2	.	.	PUNCT
ma-179	111	1	10.28924	10.28924	NUM
ma-179	111	2	/	/	SYM
ma-179	111	3	ada	ada	PROPN
ma-179	111	4	/	/	SYM
ma-179	111	5	ma.3.25	ma.3.25	VERB
ma-179	111	6	5let	5let	NOUN
ma-179	111	7	f	f	AUX
ma-179	111	8	be	be	AUX
ma-179	111	9	a	a	DET
ma-179	111	10	non	non	ADJ
ma-179	111	11	-	-	ADJ
ma-179	111	12	decreasing	decrease	VERB
ma-179	111	13	function	function	NOUN
ma-179	111	14	and	and	CCONJ
ma-179	111	15	h	h	NOUN
ma-179	111	16	be	be	AUX
ma-179	111	17	a	a	DET
ma-179	111	18	differentiable	differentiable	ADJ
ma-179	111	19	function	function	NOUN
ma-179	111	20	of	of	ADP
ma-179	111	21	bounded	bounded	ADJ
ma-179	111	22	variation	variation	NOUN
ma-179	111	23	on	on	ADP
ma-179	111	24	thereal	thereal	ADJ
ma-179	111	25	line	line	NOUN
ma-179	111	26	with	with	ADP
ma-179	111	27	f	f	PROPN
ma-179	111	28	(	(	PUNCT
ma-179	111	29	±∞	±∞	PROPN
ma-179	111	30	)	)	PUNCT
ma-179	111	31	=	=	SYM
ma-179	111	32	g(±∞	g(±∞	NOUN
ma-179	111	33	)	)	PUNCT
ma-179	111	34	.	.	PUNCT
ma-179	112	1	denote	denote	VERB
ma-179	112	2	the	the	DET
ma-179	112	3	corresponding	corresponding	ADJ
ma-179	112	4	fourier	fourier	NOUN
ma-179	112	5	-	-	PUNCT
ma-179	112	6	stieltjes	stieltjes	NOUN
ma-179	112	7	transforms	transform	VERB
ma-179	112	8	by	by	ADP
ma-179	112	9	f̂	f̂	NUM
ma-179	112	10	and	and	CCONJ
ma-179	112	11	ĝ	ĝ	NOUN
ma-179	112	12	,	,	PUNCT
ma-179	112	13	respectively	respectively	ADV
ma-179	112	14	.	.	PUNCT
ma-179	113	1	then	then	ADV
ma-179	113	2	for	for	ADP
ma-179	113	3	all	all	DET
ma-179	113	4	λ	λ	PROPN
ma-179	113	5	>	>	X
ma-179	113	6	0	0	NUM
ma-179	113	7	,	,	PUNCT
ma-179	113	8	sup	sup	NOUN
ma-179	113	9	x∈r	x∈r	PROPN
ma-179	113	10	|f	|f	PROPN
ma-179	113	11	(	(	PUNCT
ma-179	113	12	x)−	x)−	PROPN
ma-179	113	13	g(x)|	g(x)|	VERB
ma-179	113	14	≤	≤	NUM
ma-179	113	15	1	1	NUM
ma-179	113	16	π	π	NOUN
ma-179	113	17	∫	∫	PROPN
ma-179	113	18	λ	λ	PROPN
ma-179	113	19	−λ	−λ	PROPN
ma-179	113	20	∣∣∣f̂	∣∣∣f̂	PROPN
ma-179	113	21	(	(	PUNCT
ma-179	113	22	λ)−	λ)−	X
ma-179	113	23	ĝ(λ	ĝ(λ	NOUN
ma-179	113	24	)	)	PUNCT
ma-179	113	25	∣∣∣	∣∣∣	NOUN
ma-179	113	26	|λ|	|λ|	PROPN
ma-179	113	27	dλ+	dλ+	NOUN
ma-179	113	28	24	24	NUM
ma-179	113	29	πλ	πλ	NOUN
ma-179	113	30	sup	sup	PROPN
ma-179	113	31	x∈r	x∈r	PROPN
ma-179	113	32	|g′(x)|	|g′(x)|	ADP
ma-179	113	33	.	.	PUNCT
ma-179	114	1	proof	proof	NOUN
ma-179	114	2	:	:	PUNCT
ma-179	114	3	see	see	VERB
ma-179	114	4	petrov	petrov	PROPN
ma-179	115	1	[	[	X
ma-179	115	2	27	27	NUM
ma-179	115	3	]	]	PUNCT
ma-179	115	4	or	or	CCONJ
ma-179	115	5	feller	feller	NOUN
ma-179	116	1	[	[	X
ma-179	116	2	18	18	NUM
ma-179	116	3	]	]	PUNCT
ma-179	116	4	.	.	PUNCT
ma-179	117	1	let	let	VERB
ma-179	117	2	φ	φ	NUM
ma-179	117	3	(	(	PUNCT
ma-179	117	4	·	·	PUNCT
ma-179	117	5	)	)	PUNCT
ma-179	117	6	denote	denote	VERB
ma-179	118	1	the	the	DET
ma-179	118	2	standard	standard	ADJ
ma-179	118	3	normal	normal	ADJ
ma-179	118	4	distribution	distribution	NOUN
ma-179	118	5	function	function	NOUN
ma-179	118	6	and	and	CCONJ
ma-179	118	7	c	c	X
ma-179	118	8	(	(	PUNCT
ma-179	118	9	·	·	PUNCT
ma-179	118	10	)	)	PUNCT
ma-179	118	11	denotes	denote	VERB
ma-179	118	12	the	the	DET
ma-179	118	13	standard	standard	ADJ
ma-179	118	14	cauchydistribution	cauchydistribution	NOUN
ma-179	118	15	function	function	NOUN
ma-179	118	16	.	.	PUNCT
ma-179	119	1	throughout	throughout	ADP
ma-179	119	2	the	the	DET
ma-179	119	3	paper	paper	NOUN
ma-179	119	4	c	c	PROPN
ma-179	119	5	denotes	denote	VERB
ma-179	119	6	a	a	DET
ma-179	119	7	generic	generic	ADJ
ma-179	119	8	constant	constant	ADJ
ma-179	119	9	(	(	PUNCT
ma-179	119	10	perhaps	perhaps	ADV
ma-179	119	11	depending	depend	VERB
ma-179	119	12	on	on	ADP
ma-179	119	13	θ	θ	PROPN
ma-179	119	14	,	,	PUNCT
ma-179	119	15	but	but	CCONJ
ma-179	119	16	not	not	PART
ma-179	119	17	on	on	ADP
ma-179	119	18	anything	anything	PRON
ma-179	119	19	else).we	else).we	NOUN
ma-179	119	20	need	need	VERB
ma-179	119	21	the	the	DET
ma-179	119	22	following	follow	VERB
ma-179	119	23	well	well	ADV
ma-179	119	24	known	know	VERB
ma-179	119	25	inequality	inequality	NOUN
ma-179	119	26	.	.	PUNCT
ma-179	120	1	lemma	lemma	PROPN
ma-179	120	2	1.2	1.2	NUM
ma-179	120	3	1√	1√	PROPN
ma-179	120	4	2π	2π	NUM
ma-179	120	5	exp	exp	NOUN
ma-179	120	6	(	(	PUNCT
ma-179	120	7	−x2	−x2	PROPN
ma-179	120	8	2	2	NUM
ma-179	120	9	)	)	PUNCT
ma-179	120	10	(	(	PUNCT
ma-179	120	11	1	1	NUM
ma-179	120	12	x	x	SYM
ma-179	120	13	−	−	PROPN
ma-179	120	14	1	1	NUM
ma-179	120	15	x3	x3	ADJ
ma-179	120	16	)	)	PUNCT
ma-179	120	17	≤	≤	NOUN
ma-179	120	18	1−φ(x	1−φ(x	NUM
ma-179	120	19	)	)	PUNCT
ma-179	120	20	≤	≤	NOUN
ma-179	120	21	1√	1√	NUM
ma-179	120	22	2πx	2πx	ADJ
ma-179	120	23	exp	exp	NOUN
ma-179	120	24	(	(	PUNCT
ma-179	120	25	−x2	−x2	PROPN
ma-179	120	26	2	2	NUM
ma-179	120	27	)	)	PUNCT
ma-179	120	28	for	for	ADP
ma-179	120	29	x	x	PUNCT
ma-179	120	30	>	>	X
ma-179	120	31	0	0	NUM
ma-179	120	32	.	.	PUNCT
ma-179	121	1	as	as	ADP
ma-179	121	2	x	x	PROPN
ma-179	121	3	→∞	→∞	PROPN
ma-179	121	4	,	,	PUNCT
ma-179	121	5	1−φ(x)∼	1−φ(x)∼	PROPN
ma-179	121	6	1√	1√	NUM
ma-179	121	7	2πx	2πx	ADJ
ma-179	121	8	exp	exp	NOUN
ma-179	121	9	(	(	PUNCT
ma-179	121	10	−x2	−x2	PROPN
ma-179	121	11	2	2	NUM
ma-179	121	12	)	)	PUNCT
ma-179	121	13	.	.	PUNCT
ma-179	122	1	proof	proof	NOUN
ma-179	122	2	:	:	PUNCT
ma-179	122	3	see	see	VERB
ma-179	122	4	feller	feller	NOUN
ma-179	122	5	(	(	PUNCT
ma-179	122	6	[	[	X
ma-179	122	7	17	17	NUM
ma-179	122	8	]	]	PUNCT
ma-179	122	9	,	,	PUNCT
ma-179	122	10	p.166	p.166	NOUN
ma-179	122	11	)	)	PUNCT
ma-179	122	12	.	.	PUNCT
ma-179	123	1	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	PROPN
ma-179	123	2	eur	eur	PROPN
ma-179	123	3	.	.	PUNCT
ma-179	124	1	j.	j.	PROPN
ma-179	124	2	math	math	PROPN
ma-179	124	3	.	.	PUNCT
ma-179	125	1	anal	anal	PROPN
ma-179	125	2	.	.	PUNCT
ma-179	126	1	10.28924	10.28924	NUM
ma-179	126	2	/	/	SYM
ma-179	126	3	ada	ada	PROPN
ma-179	126	4	/	/	SYM
ma-179	126	5	ma.3.25	ma.3.25	NOUN
ma-179	126	6	6	6	NUM
ma-179	126	7	2	2	NUM
ma-179	126	8	.	.	PUNCT
ma-179	126	9	main	main	ADJ
ma-179	126	10	results	result	NOUN
ma-179	126	11	we	we	PRON
ma-179	126	12	start	start	VERB
ma-179	126	13	with	with	ADP
ma-179	126	14	the	the	DET
ma-179	126	15	dambis	dambis	NOUN
ma-179	126	16	-	-	PUNCT
ma-179	126	17	dubins	dubin	NOUN
ma-179	126	18	-	-	PUNCT
ma-179	126	19	schwarz	schwarz	NOUN
ma-179	126	20	(	(	PUNCT
ma-179	126	21	dds	dds	PROPN
ma-179	126	22	)	)	PUNCT
ma-179	126	23	theorem	theorem	PROPN
ma-179	126	24	,	,	PUNCT
ma-179	126	25	see	see	VERB
ma-179	126	26	protter	protter	NOUN
ma-179	126	27	[	[	X
ma-179	126	28	29	29	NUM
ma-179	126	29	]	]	PUNCT
ma-179	126	30	.	.	PUNCT
ma-179	127	1	since	since	SCONJ
ma-179	127	2	zt	zt	PROPN
ma-179	127	3	is	be	AUX
ma-179	127	4	a	a	DET
ma-179	127	5	contin	contin	NOUN
ma-179	127	6	-	-	PUNCT
ma-179	127	7	uous	uous	ADJ
ma-179	127	8	time	time	NOUN
ma-179	127	9	martingale	martingale	NOUN
ma-179	127	10	,	,	PUNCT
ma-179	127	11	due	due	ADP
ma-179	127	12	to	to	ADP
ma-179	127	13	time	time	NOUN
ma-179	127	14	change	change	NOUN
ma-179	127	15	(	(	PUNCT
ma-179	127	16	skorohod	skorohod	ADJ
ma-179	127	17	embedding	embedding	NOUN
ma-179	127	18	)	)	PUNCT
ma-179	127	19	,	,	PUNCT
ma-179	127	20	zt	zt	PROPN
ma-179	127	21	=	=	PUNCT
ma-179	127	22	bit	bit	NOUN
ma-179	127	23	where	where	SCONJ
ma-179	127	24	b	b	NOUN
ma-179	127	25	is	be	AUX
ma-179	127	26	a	a	DET
ma-179	127	27	brownianmotion	brownianmotion	NOUN
ma-179	127	28	independent	independent	ADJ
ma-179	127	29	of	of	ADP
ma-179	127	30	w	w	PROPN
ma-179	127	31	,	,	PUNCT
ma-179	127	32	we	we	PRON
ma-179	127	33	have	have	VERB
ma-179	127	34	e(exp(iuzt	e(exp(iuzt	NOUN
ma-179	127	35	)	)	PUNCT
ma-179	127	36	)	)	PUNCT
ma-179	128	1	=	=	PUNCT
ma-179	128	2	e	e	PROPN
ma-179	128	3	exp(−	exp(−	PROPN
ma-179	128	4	u2	u2	PROPN
ma-179	128	5	2	2	NUM
ma-179	128	6	it	it	PRON
ma-179	128	7	)	)	PUNCT
ma-179	128	8	,	,	PUNCT
ma-179	128	9	(	(	PUNCT
ma-179	128	10	2.1	2.1	NUM
ma-179	128	11	)	)	PUNCT
ma-179	128	12	e(exp(iue−θt	e(exp(iue−θt	NOUN
ma-179	128	13	√	√	SYM
ma-179	128	14	2θzt	2θzt	PROPN
ma-179	128	15	)	)	PUNCT
ma-179	128	16	)	)	PUNCT
ma-179	129	1	=	=	PUNCT
ma-179	129	2	e	e	PROPN
ma-179	129	3	exp(−	exp(−	PROPN
ma-179	129	4	u2	u2	PROPN
ma-179	129	5	2	2	NUM
ma-179	129	6	e−2θt	e−2θt	ADJ
ma-179	129	7	2θit	2θit	PROPN
ma-179	129	8	)	)	PUNCT
ma-179	129	9	,	,	PUNCT
ma-179	129	10	(	(	PUNCT
ma-179	129	11	2.2	2.2	NUM
ma-179	129	12	)	)	PUNCT
ma-179	129	13	θt	θt	NOUN
ma-179	129	14	−	−	PROPN
ma-179	129	15	θ	θ	PROPN
ma-179	129	16	=	=	PUNCT
ma-179	129	17	bit	bit	ADP
ma-179	129	18	it	it	PRON
ma-179	129	19	,	,	PUNCT
ma-179	129	20	(	(	PUNCT
ma-179	129	21	2.3	2.3	NUM
ma-179	129	22	)	)	PUNCT
ma-179	129	23	eθt	eθt	NOUN
ma-179	129	24	2θ	2θ	NUM
ma-179	129	25	(	(	PUNCT
ma-179	129	26	θt	θt	PROPN
ma-179	129	27	−	−	PROPN
ma-179	129	28	θ	θ	NOUN
ma-179	129	29	)	)	PUNCT
ma-179	129	30	=	=	SYM
ma-179	129	31	e−θtbit	e−θtbit	NOUN
ma-179	129	32	e−2θt	e−2θt	ADJ
ma-179	129	33	2θit	2θit	PROPN
ma-179	129	34	=	=	SYM
ma-179	129	35	(	(	PUNCT
ma-179	129	36	e−2θt	e−2θt	PROPN
ma-179	129	37	4θ2	4θ2	NUM
ma-179	129	38	)	)	PUNCT
ma-179	129	39	1/2	1/2	NUM
ma-179	129	40	bit	bit	NOUN
ma-179	129	41	e−2θt	e−2θt	VERB
ma-179	129	42	4θ2it	4θ2it	NUM
ma-179	130	1	=	=	NOUN
ma-179	130	2	:	:	PUNCT
ma-179	130	3	yt	yt	PROPN
ma-179	130	4	(	(	PUNCT
ma-179	130	5	2.4	2.4	NUM
ma-179	130	6	)	)	PUNCT
ma-179	130	7	where	where	SCONJ
ma-179	130	8	yt	yt	X
ma-179	130	9	=	=	PUNCT
ma-179	130	10	e−θtbit	e−θtbit	NUM
ma-179	130	11	e−2θt	e−2θt	ADJ
ma-179	130	12	2θit	2θit	PROPN
ma-179	130	13	.	.	PUNCT
ma-179	131	1	(	(	PUNCT
ma-179	131	2	2.5	2.5	NUM
ma-179	131	3	)	)	PUNCT
ma-179	131	4	our	our	PRON
ma-179	131	5	main	main	ADJ
ma-179	131	6	claim	claim	NOUN
ma-179	131	7	in	in	ADP
ma-179	131	8	the	the	DET
ma-179	131	9	paper	paper	NOUN
ma-179	131	10	is	be	AUX
ma-179	131	11	to	to	PART
ma-179	131	12	show	show	VERB
ma-179	131	13	that	that	SCONJ
ma-179	131	14	|e(e	|e(e	PROPN
ma-179	131	15	iuyt	iuyt	VERB
ma-179	131	16	)	)	PUNCT
ma-179	131	17	−	−	ADP
ma-179	131	18	e−|u||	e−|u||	ADP
ma-179	131	19	≤	≤	ADJ
ma-179	131	20	c|u|e−|u|/2e−θt	c|u|e−|u|/2e−θt	NOUN
ma-179	131	21	.	.	PUNCT
ma-179	132	1	(	(	PUNCT
ma-179	132	2	2.6	2.6	NUM
ma-179	132	3	)	)	PUNCT
ma-179	132	4	this	this	PRON
ma-179	132	5	is	be	AUX
ma-179	132	6	done	do	VERB
ma-179	132	7	through	through	ADP
ma-179	132	8	several	several	ADJ
ma-179	132	9	lemmas	lemma	NOUN
ma-179	132	10	.	.	PUNCT
ma-179	133	1	once	once	SCONJ
ma-179	133	2	it	it	PRON
ma-179	133	3	is	be	AUX
ma-179	133	4	shown	show	VERB
ma-179	133	5	,	,	PUNCT
ma-179	133	6	let	let	VERB
ma-179	133	7	f	f	PROPN
ma-179	133	8	(	(	PUNCT
ma-179	133	9	x	x	X
ma-179	133	10	)	)	PUNCT
ma-179	134	1	=	=	SYM
ma-179	134	2	p	p	X
ma-179	134	3	(	(	PUNCT
ma-179	134	4	yt	yt	PROPN
ma-179	134	5	≤	≤	NUM
ma-179	134	6	x	x	X
ma-179	134	7	)	)	PUNCT
ma-179	134	8	,	,	PUNCT
ma-179	134	9	(	(	PUNCT
ma-179	134	10	2.7	2.7	NUM
ma-179	134	11	)	)	PUNCT
ma-179	134	12	c(x	c(x	NOUN
ma-179	134	13	)	)	PUNCT
ma-179	134	14	=	=	SYM
ma-179	135	1	1	1	NUM
ma-179	135	2	2	2	NUM
ma-179	135	3	+	+	SYM
ma-179	135	4	1	1	NUM
ma-179	135	5	π	π	PROPN
ma-179	135	6	arctan	arctan	PROPN
ma-179	135	7	x	x	PROPN
ma-179	135	8	,	,	PUNCT
ma-179	135	9	x	x	SYM
ma-179	135	10	∈	∈	PROPN
ma-179	135	11	r	r	NOUN
ma-179	135	12	,	,	PUNCT
ma-179	135	13	(	(	PUNCT
ma-179	135	14	2.8	2.8	NUM
ma-179	135	15	)	)	PUNCT
ma-179	135	16	take	take	VERB
ma-179	135	17	λ	λ	X
ma-179	135	18	=	=	PUNCT
ma-179	135	19	eθt	eθt	PROPN
ma-179	135	20	.	.	PUNCT
ma-179	136	1	then	then	ADV
ma-179	136	2	sup	sup	NOUN
ma-179	136	3	x∈r	x∈r	PROPN
ma-179	136	4	|f	|f	PROPN
ma-179	137	1	(	(	PUNCT
ma-179	137	2	x)−	x)−	NOUN
ma-179	137	3	c(x)|	c(x)|	VERB
ma-179	137	4	≤	≤	NUM
ma-179	137	5	1	1	NUM
ma-179	137	6	π	π	PROPN
ma-179	137	7	j	j	PROPN
ma-179	138	1	+	+	CCONJ
ma-179	138	2	24	24	NUM
ma-179	138	3	πeθt	πeθt	NOUN
ma-179	138	4	sup	sup	NOUN
ma-179	138	5	c′(x	c′(x	NOUN
ma-179	138	6	)	)	PUNCT
ma-179	138	7	(	(	PUNCT
ma-179	138	8	2.9	2.9	NUM
ma-179	138	9	)	)	PUNCT
ma-179	139	1	where	where	SCONJ
ma-179	139	2	j	j	NOUN
ma-179	139	3	:	:	PUNCT
ma-179	139	4	=	=	SYM
ma-179	139	5	1	1	NUM
ma-179	139	6	π	π	SYM
ma-179	139	7	∫	∫	PROPN
ma-179	139	8	|λ|≤eθt	|λ|≤eθt	X
ma-179	139	9	∣∣∣f̂	∣∣∣f̂	NOUN
ma-179	139	10	(	(	PUNCT
ma-179	139	11	λ)−	λ)−	X
ma-179	139	12	ĉ(λ	ĉ(λ	NOUN
ma-179	139	13	)	)	PUNCT
ma-179	139	14	∣∣∣	∣∣∣	NOUN
ma-179	139	15	|λ|	|λ|	PROPN
ma-179	139	16	dλ	dλ	NOUN
ma-179	139	17	.	.	PUNCT
ma-179	140	1	(	(	PUNCT
ma-179	140	2	2.10	2.10	NUM
ma-179	140	3	)	)	PUNCT
ma-179	140	4	clearly	clearly	ADV
ma-179	140	5	sup	sup	NOUN
ma-179	140	6	c′(x	c′(x	NOUN
ma-179	140	7	)	)	PUNCT
ma-179	140	8	<	<	X
ma-179	140	9	∞and	∞and	X
ma-179	140	10	j	j	PROPN
ma-179	140	11	≤	≤	PROPN
ma-179	140	12	c	c	PROPN
ma-179	140	13	eθt	eθt	PROPN
ma-179	140	14	∫	∫	PROPN
ma-179	140	15	|λ|≤eθt	|λ|≤eθt	X
ma-179	140	16	e−|λ|/2dλ	e−|λ|/2dλ	X
ma-179	140	17	≤	≤	PROPN
ma-179	140	18	c	c	NOUN
ma-179	140	19	eθt	eθt	PROPN
ma-179	140	20	∫	∫	PROPN
ma-179	140	21	∞	∞	PROPN
ma-179	140	22	−∞	−∞	ADP
ma-179	140	23	e−|λ|/2dλ	e−|λ|/2dλ	X
ma-179	140	24	=	=	SYM
ma-179	140	25	o(e−θt	o(e−θt	PROPN
ma-179	140	26	)	)	PUNCT
ma-179	140	27	.	.	PUNCT
ma-179	141	1	(	(	PUNCT
ma-179	141	2	2.11	2.11	NUM
ma-179	141	3	)	)	PUNCT
ma-179	141	4	which	which	PRON
ma-179	141	5	would	would	AUX
ma-179	141	6	ultimately	ultimately	ADV
ma-179	141	7	give	give	VERB
ma-179	141	8	sup	sup	NOUN
ma-179	141	9	x∈r	x∈r	PROPN
ma-179	141	10	|f	|f	PROPN
ma-179	142	1	(	(	PUNCT
ma-179	142	2	x)−	x)−	PROPN
ma-179	142	3	c(x)|	c(x)|	NOUN
ma-179	142	4	=	=	PUNCT
ma-179	142	5	o(e−θt	o(e−θt	NOUN
ma-179	142	6	)	)	PUNCT
ma-179	142	7	.	.	PUNCT
ma-179	143	1	(	(	PUNCT
ma-179	143	2	2.12	2.12	NUM
ma-179	143	3	)	)	PUNCT
ma-179	143	4	first	first	ADV
ma-179	143	5	we	we	PRON
ma-179	143	6	start	start	VERB
ma-179	143	7	with	with	ADP
ma-179	143	8	kolmogorov	kolmogorov	ADJ
ma-179	143	9	distance	distance	NOUN
ma-179	143	10	for	for	ADP
ma-179	143	11	wiener	wiener	NOUN
ma-179	143	12	chaos	chaos	NOUN
ma-179	143	13	and	and	CCONJ
ma-179	143	14	its	its	PRON
ma-179	143	15	relative	relative	ADJ
ma-179	143	16	:	:	PUNCT
ma-179	143	17	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	PROPN
ma-179	143	18	eur	eur	PROPN
ma-179	143	19	.	.	PUNCT
ma-179	144	1	j.	j.	PROPN
ma-179	144	2	math	math	PROPN
ma-179	144	3	.	.	PUNCT
ma-179	145	1	anal	anal	PROPN
ma-179	145	2	.	.	PUNCT
ma-179	146	1	10.28924	10.28924	NUM
ma-179	146	2	/	/	SYM
ma-179	146	3	ada	ada	PROPN
ma-179	146	4	/	/	SYM
ma-179	146	5	ma.3.25	ma.3.25	VERB
ma-179	146	6	7	7	NUM
ma-179	147	1	lemma	lemma	PROPN
ma-179	147	2	2.1	2.1	NUM
ma-179	147	3	we	we	PRON
ma-179	147	4	have	have	VERB
ma-179	147	5	the	the	DET
ma-179	147	6	following	follow	VERB
ma-179	147	7	rate	rate	NOUN
ma-179	147	8	of	of	ADP
ma-179	147	9	convergence	convergence	NOUN
ma-179	147	10	for	for	ADP
ma-179	147	11	the	the	DET
ma-179	147	12	double	double	ADJ
ma-179	147	13	-	-	PUNCT
ma-179	147	14	stochastic	stochastic	NOUN
ma-179	147	15	integral	integral	ADJ
ma-179	147	16	or	or	CCONJ
ma-179	147	17	thesecond	thesecond	NOUN
ma-179	147	18	wiener	wiener	NOUN
ma-179	147	19	chaos	chaos	NOUN
ma-179	147	20	∫	∫	PROPN
ma-179	147	21	t0	t0	PROPN
ma-179	147	22	eθt	eθt	PROPN
ma-179	148	1	(	(	PUNCT
ma-179	148	2	∫	∫	PROPN
ma-179	148	3	t	t	PROPN
ma-179	148	4	0	0	NUM
ma-179	148	5	e	e	X
ma-179	148	6	−θsdws	−θsdws	PUNCT
ma-179	148	7	)	)	PUNCT
ma-179	148	8	dwt	dwt	NOUN
ma-179	148	9	:	:	PUNCT
ma-179	148	10	(	(	PUNCT
ma-179	148	11	a	a	X
ma-179	148	12	)	)	PUNCT
ma-179	148	13	sup	sup	NOUN
ma-179	148	14	x∈r	x∈r	PROPN
ma-179	148	15	∣∣∣∣p	∣∣∣∣p	ADP
ma-179	148	16	{	{	PUNCT
ma-179	148	17	eθt	eθt	PROPN
ma-179	148	18	(	(	PUNCT
ma-179	148	19	2θe−2θt	2θe−2θt	NUM
ma-179	148	20	∫	∫	NOUN
ma-179	148	21	t	t	PROPN
ma-179	148	22	0	0	NUM
ma-179	148	23	eθt	eθt	PROPN
ma-179	148	24	(	(	PUNCT
ma-179	148	25	∫	∫	PROPN
ma-179	148	26	t	t	PROPN
ma-179	148	27	0	0	NUM
ma-179	148	28	e−θsdws	e−θsdws	PROPN
ma-179	148	29	)	)	PUNCT
ma-179	148	30	dwt	dwt	NOUN
ma-179	148	31	)	)	PUNCT
ma-179	148	32	≤	≤	NUM
ma-179	148	33	x	x	PUNCT
ma-179	148	34	}	}	PUNCT
ma-179	148	35	−φ(x	−φ(x	NOUN
ma-179	148	36	)	)	PUNCT
ma-179	148	37	∣∣∣∣	∣∣∣∣	NOUN
ma-179	148	38	≤	≤	NOUN
ma-179	148	39	ce−θt	ce−θt	NOUN
ma-179	148	40	.	.	PUNCT
ma-179	149	1	(	(	PUNCT
ma-179	149	2	b	b	X
ma-179	149	3	)	)	PUNCT
ma-179	149	4	sup	sup	NOUN
ma-179	149	5	x∈r	x∈r	PROPN
ma-179	149	6	∣∣∣∣p	∣∣∣∣p	ADP
ma-179	149	7	{	{	PUNCT
ma-179	149	8	eθt	eθt	PROPN
ma-179	149	9	(	(	PUNCT
ma-179	149	10	2θe−2θt	2θe−2θt	NUM
ma-179	149	11	∫	∫	PROPN
ma-179	149	12	t	t	PROPN
ma-179	149	13	0	0	NUM
ma-179	150	1	e2θtξ2	e2θtξ2	PROPN
ma-179	150	2	t	t	X
ma-179	150	3	dt	dt	X
ma-179	150	4	−	−	PROPN
ma-179	150	5	ξ2	ξ2	PROPN
ma-179	150	6	)	)	PUNCT
ma-179	150	7	≤	≤	NUM
ma-179	150	8	x	x	PUNCT
ma-179	150	9	}	}	PUNCT
ma-179	150	10	−φ(x	−φ(x	NOUN
ma-179	150	11	)	)	PUNCT
ma-179	150	12	∣∣∣∣	∣∣∣∣	NOUN
ma-179	150	13	≤	≤	NOUN
ma-179	150	14	ce−θt	ce−θt	NOUN
ma-179	150	15	.	.	PUNCT
ma-179	151	1	proof	proof	NOUN
ma-179	151	2	.	.	PUNCT
ma-179	152	1	observe	observe	VERB
ma-179	152	2	that	that	SCONJ
ma-179	152	3	zt	zt	PROPN
ma-179	152	4	=	=	SYM
ma-179	152	5	∫	∫	PROPN
ma-179	152	6	t	t	PROPN
ma-179	152	7	0	0	NUM
ma-179	153	1	xtdwt	xtdwt	PROPN
ma-179	153	2	=	=	SYM
ma-179	154	1	∫	∫	PROPN
ma-179	154	2	t	t	PROPN
ma-179	154	3	0	0	NUM
ma-179	154	4	eθt	eθt	PROPN
ma-179	154	5	(	(	PUNCT
ma-179	154	6	∫	∫	PROPN
ma-179	154	7	t	t	PROPN
ma-179	154	8	0	0	NUM
ma-179	154	9	e−θsdws	e−θsdws	PROPN
ma-179	154	10	)	)	PUNCT
ma-179	154	11	dwt	dwt	VERB
ma-179	154	12	the	the	DET
ma-179	154	13	integral	integral	ADJ
ma-179	154	14	∫	∫	PROPN
ma-179	154	15	t	t	PROPN
ma-179	154	16	0	0	NUM
ma-179	154	17	eθt	eθt	PROPN
ma-179	154	18	(	(	PUNCT
ma-179	154	19	∫	∫	PROPN
ma-179	154	20	t	t	PROPN
ma-179	154	21	0	0	NUM
ma-179	154	22	e−θsdws	e−θsdws	PROPN
ma-179	154	23	)	)	PUNCT
ma-179	154	24	dwtis	dwtis	PROPN
ma-179	154	25	second	second	ADJ
ma-179	154	26	wiener	wiener	NOUN
ma-179	154	27	chaos	chaos	NOUN
ma-179	154	28	.	.	PUNCT
ma-179	155	1	one	one	PRON
ma-179	155	2	can	can	AUX
ma-179	155	3	use	use	VERB
ma-179	155	4	the	the	DET
ma-179	155	5	stein	stein	PROPN
ma-179	155	6	-	-	PUNCT
ma-179	155	7	malliavin	malliavin	PROPN
ma-179	155	8	method	method	NOUN
ma-179	155	9	(	(	PUNCT
ma-179	155	10	see	see	VERB
ma-179	155	11	nourdin	nourdin	VERB
ma-179	155	12	and	and	CCONJ
ma-179	155	13	peccati	peccati	NOUN
ma-179	155	14	(	(	PUNCT
ma-179	155	15	[	[	X
ma-179	155	16	25	25	NUM
ma-179	155	17	]	]	PUNCT
ma-179	155	18	,	,	PUNCT
ma-179	155	19	[	[	X
ma-179	155	20	26	26	NUM
ma-179	155	21	]	]	PUNCT
ma-179	155	22	)	)	PUNCT
ma-179	155	23	and	and	CCONJ
ma-179	155	24	estimate	estimate	VERB
ma-179	155	25	the	the	DET
ma-179	155	26	kolmogorov	kolmogorov	ADJ
ma-179	155	27	distance	distance	NOUN
ma-179	155	28	for	for	ADP
ma-179	155	29	zt	zt	PROPN
ma-179	155	30	.	.	PUNCT
ma-179	156	1	however	however	ADV
ma-179	156	2	,	,	PUNCT
ma-179	156	3	part	part	NOUN
ma-179	156	4	(	(	PUNCT
ma-179	156	5	a	a	PRON
ma-179	156	6	)	)	PUNCT
ma-179	156	7	follows	follow	VERB
ma-179	156	8	as	as	ADP
ma-179	156	9	a	a	DET
ma-179	156	10	conse	conse	NOUN
ma-179	156	11	-	-	PUNCT
ma-179	156	12	quence	quence	NOUN
ma-179	156	13	of	of	ADP
ma-179	156	14	lemma	lemma	PROPN
ma-179	156	15	2.4(c	2.4(c	NUM
ma-179	156	16	)	)	PUNCT
ma-179	156	17	below	below	ADP
ma-179	156	18	along	along	ADP
ma-179	156	19	with	with	ADP
ma-179	156	20	lemma	lemma	PROPN
ma-179	156	21	1.1	1.1	NUM
ma-179	156	22	above	above	ADV
ma-179	156	23	.	.	PUNCT
ma-179	157	1	part	part	NOUN
ma-179	157	2	(	(	PUNCT
ma-179	157	3	b	b	NOUN
ma-179	157	4	)	)	PUNCT
ma-179	157	5	follows	follow	VERB
ma-179	157	6	as	as	ADP
ma-179	157	7	a	a	DET
ma-179	157	8	consequence	consequence	NOUN
ma-179	157	9	oflemma	oflemma	NOUN
ma-179	157	10	2.2	2.2	NUM
ma-179	157	11	below	below	ADV
ma-179	157	12	along	along	ADV
ma-179	157	13	with	with	ADP
ma-179	157	14	lemma	lemma	PROPN
ma-179	157	15	1.1	1.1	NUM
ma-179	157	16	above	above	ADV
ma-179	157	17	.	.	PUNCT
ma-179	158	1	note	note	VERB
ma-179	158	2	that	that	DET
ma-179	158	3	ξ2	ξ2	ADJ
ma-179	158	4	∼	∼	NOUN
ma-179	158	5	χ2	χ2	NOUN
ma-179	158	6	1	1	NUM
ma-179	158	7	.	.	PUNCT
ma-179	159	1	the	the	DET
ma-179	159	2	next	next	ADJ
ma-179	159	3	theorem	theorem	NOUN
ma-179	159	4	gives	give	VERB
ma-179	159	5	an	an	DET
ma-179	159	6	exponential	exponential	ADJ
ma-179	159	7	estimate	estimate	NOUN
ma-179	159	8	on	on	ADP
ma-179	159	9	the	the	DET
ma-179	159	10	rate	rate	NOUN
ma-179	159	11	of	of	ADP
ma-179	159	12	convergenceto	convergenceto	NOUN
ma-179	159	13	the	the	DET
ma-179	159	14	chi	chi	ADJ
ma-179	159	15	-	-	PUNCT
ma-179	159	16	square	square	ADJ
ma-179	159	17	distribution	distribution	NOUN
ma-179	159	18	for	for	ADP
ma-179	159	19	energy	energy	NOUN
ma-179	159	20	it	it	PRON
ma-179	159	21	of	of	ADP
ma-179	159	22	the	the	DET
ma-179	159	23	o	o	ADJ
ma-179	159	24	-	-	PUNCT
ma-179	159	25	u	u	NOUN
ma-179	159	26	process	process	NOUN
ma-179	159	27	.	.	PUNCT
ma-179	160	1	theorem	theorem	VERB
ma-179	160	2	2.1	2.1	NUM
ma-179	160	3	sup	sup	NOUN
ma-179	160	4	x∈r	x∈r	PROPN
ma-179	160	5	∣∣p	∣∣p	PROPN
ma-179	160	6	{	{	PUNCT
ma-179	160	7	e−2θt	e−2θt	ADJ
ma-179	160	8	2θit	2θit	PROPN
ma-179	160	9	≤	≤	NOUN
ma-179	160	10	x	x	PUNCT
ma-179	160	11	}	}	PUNCT
ma-179	161	1	−	−	PROPN
ma-179	161	2	p	p	NOUN
ma-179	161	3	{	{	PUNCT
ma-179	161	4	ξ2	ξ2	PROPN
ma-179	161	5	≤	≤	NOUN
ma-179	161	6	x	x	PUNCT
ma-179	161	7	}	}	PUNCT
ma-179	161	8	∣∣	∣∣	X
ma-179	161	9	=	=	SYM
ma-179	161	10	o(e−θt	o(e−θt	PROPN
ma-179	161	11	)	)	PUNCT
ma-179	161	12	.	.	PUNCT
ma-179	162	1	the	the	DET
ma-179	162	2	above	above	ADJ
ma-179	162	3	theorem	theorem	NOUN
ma-179	162	4	is	be	AUX
ma-179	162	5	a	a	DET
ma-179	162	6	consequence	consequence	NOUN
ma-179	162	7	of	of	ADP
ma-179	162	8	the	the	DET
ma-179	162	9	following	follow	VERB
ma-179	162	10	lemma	lemma	PROPN
ma-179	162	11	and	and	CCONJ
ma-179	162	12	the	the	DET
ma-179	162	13	esseen	esseen	AUX
ma-179	162	14	’s	’s	PART
ma-179	162	15	smoothing	smooth	VERB
ma-179	162	16	lemma	lemma	PROPN
ma-179	162	17	1.1	1.1	NUM
ma-179	162	18	lemma	lemma	PROPN
ma-179	162	19	2.2	2.2	NUM
ma-179	162	20	for	for	ADP
ma-179	162	21	|u|	|u|	PROPN
ma-179	162	22	≤	≤	PROPN
ma-179	162	23	eθt	eθt	PROPN
ma-179	162	24	ε	ε	PROPN
ma-179	162	25	,	,	PUNCT
ma-179	162	26	ε	ε	PROPN
ma-179	162	27	sufficiently	sufficiently	ADV
ma-179	162	28	small	small	ADJ
ma-179	162	29	,	,	PUNCT
ma-179	162	30	we	we	PRON
ma-179	162	31	have∣∣∣∣∣e	have∣∣∣∣∣e	VERB
ma-179	162	32	exp	exp	NOUN
ma-179	162	33	(	(	PUNCT
ma-179	162	34	iue−2θt	iue−2θt	PROPN
ma-179	162	35	2θit	2θit	PROPN
ma-179	162	36	)	)	PUNCT
ma-179	162	37	−	−	PROPN
ma-179	162	38	1	1	NUM
ma-179	162	39	(	(	PUNCT
ma-179	162	40	1−	1−	NUM
ma-179	162	41	2iu	2iu	NOUN
ma-179	162	42	)	)	PUNCT
ma-179	162	43	1	1	NUM
ma-179	162	44	2	2	NUM
ma-179	162	45	∣∣∣∣∣	∣∣∣∣∣	SYM
ma-179	162	46	≤	≤	NOUN
ma-179	162	47	c(|u|+	c(|u|+	PUNCT
ma-179	162	48	|u|3)e−θt	|u|3)e−θt	X
ma-179	162	49	.	.	PUNCT
ma-179	163	1	proof	proof	NOUN
ma-179	163	2	.	.	PUNCT
ma-179	164	1	from	from	ADP
ma-179	164	2	liptser	liptser	NOUN
ma-179	164	3	and	and	CCONJ
ma-179	164	4	shiryayev	shiryayev	VERB
ma-179	164	5	[	[	X
ma-179	164	6	23	23	NUM
ma-179	164	7	]	]	PUNCT
ma-179	164	8	,	,	PUNCT
ma-179	164	9	we	we	PRON
ma-179	164	10	have	have	VERB
ma-179	164	11	e	e	NOUN
ma-179	164	12	exp	exp	X
ma-179	164	13	(	(	PUNCT
ma-179	164	14	iue−2θt	iue−2θt	PROPN
ma-179	164	15	2θit	2θit	PROPN
ma-179	164	16	)	)	PUNCT
ma-179	164	17	=	=	SYM
ma-179	164	18	exp	exp	NOUN
ma-179	164	19	(	(	PUNCT
ma-179	164	20	θt	θt	PROPN
ma-179	164	21	2	2	NUM
ma-179	164	22	)	)	PUNCT
ma-179	164	23	[	[	PUNCT
ma-179	164	24	2γ	2γ	NOUN
ma-179	164	25	(	(	PUNCT
ma-179	164	26	γ	γ	X
ma-179	164	27	−	−	PROPN
ma-179	164	28	θ)e−γt	θ)e−γt	PROPN
ma-179	164	29	+	+	PROPN
ma-179	164	30	(	(	PUNCT
ma-179	164	31	γ	γ	X
ma-179	164	32	+	+	X
ma-179	164	33	θ)eγt	θ)eγt	NOUN
ma-179	164	34	]	]	SYM
ma-179	164	35	1/2	1/2	NUM
ma-179	164	36	(	(	PUNCT
ma-179	164	37	2.12	2.12	NUM
ma-179	164	38	)	)	PUNCT
ma-179	164	39	where	where	SCONJ
ma-179	164	40	γ	γ	X
ma-179	164	41	:	:	PUNCT
ma-179	164	42	=	=	SYM
ma-179	164	43	(	(	PUNCT
ma-179	164	44	θ2	θ2	ADV
ma-179	164	45	−	−	PROPN
ma-179	164	46	2iue−2θt	2iue−2θt	NUM
ma-179	164	47	2θ	2θ	NUM
ma-179	164	48	)	)	PUNCT
ma-179	164	49	1/2	1/2	NUM
ma-179	164	50	.	.	PUNCT
ma-179	165	1	(	(	PUNCT
ma-179	165	2	2.13)the	2.13)the	DET
ma-179	165	3	lemma	lemma	PROPN
ma-179	165	4	is	be	AUX
ma-179	165	5	an	an	DET
ma-179	165	6	easy	easy	ADJ
ma-179	165	7	consequence	consequence	NOUN
ma-179	165	8	of	of	ADP
ma-179	165	9	this	this	DET
ma-179	165	10	result	result	NOUN
ma-179	165	11	.	.	PUNCT
ma-179	166	1	lemma	lemma	PROPN
ma-179	166	2	2.3	2.3	NUM
ma-179	166	3	for	for	ADP
ma-179	166	4	every	every	DET
ma-179	166	5	δ	δ	PROPN
ma-179	166	6	>	>	X
ma-179	166	7	0	0	PROPN
ma-179	166	8	,	,	PUNCT
ma-179	166	9	p	p	X
ma-179	166	10	{	{	PUNCT
ma-179	166	11	∣∣e−2θt	∣∣e−2θt	NOUN
ma-179	166	12	2θit	2θit	NOUN
ma-179	166	13	−	−	PROPN
ma-179	166	14	ξ2	ξ2	NOUN
ma-179	166	15	∣∣	∣∣	NUM
ma-179	166	16	≥	≥	X
ma-179	166	17	δ	δ	PROPN
ma-179	166	18	}	}	PUNCT
ma-179	166	19	≤	≤	NOUN
ma-179	166	20	ce−2θt	ce−2θt	NUM
ma-179	166	21	δ−2	δ−2	PROPN
ma-179	166	22	.	.	PUNCT
ma-179	166	23	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	PROPN
ma-179	166	24	eur	eur	PROPN
ma-179	166	25	.	.	PUNCT
ma-179	167	1	j.	j.	PROPN
ma-179	167	2	math	math	PROPN
ma-179	167	3	.	.	PUNCT
ma-179	168	1	anal	anal	PROPN
ma-179	168	2	.	.	PUNCT
ma-179	169	1	10.28924	10.28924	NUM
ma-179	169	2	/	/	SYM
ma-179	169	3	ada	ada	PROPN
ma-179	169	4	/	/	SYM
ma-179	169	5	ma.3.25	ma.3.25	NOUN
ma-179	169	6	8	8	NUM
ma-179	169	7	proof	proof	NOUN
ma-179	169	8	:	:	PUNCT
ma-179	169	9	it	it	PRON
ma-179	169	10	is	be	AUX
ma-179	169	11	clear	clear	ADJ
ma-179	169	12	that	that	SCONJ
ma-179	169	13	xt	xt	PUNCT
ma-179	170	1	=	=	SYM
ma-179	170	2	∫	∫	PROPN
ma-179	170	3	t	t	PROPN
ma-179	170	4	0	0	NUM
ma-179	170	5	e−θ(t−s)dws	e−θ(t−s)dws	PROPN
ma-179	170	6	.	.	PUNCT
ma-179	171	1	(	(	PUNCT
ma-179	171	2	2.14	2.14	NUM
ma-179	171	3	)	)	PUNCT
ma-179	171	4	further	far	ADV
ma-179	171	5	,	,	PUNCT
ma-179	171	6	itô	itô	ADJ
ma-179	171	7	formula	formula	NOUN
ma-179	171	8	(	(	PUNCT
ma-179	171	9	see	see	VERB
ma-179	171	10	friedman	friedman	PROPN
ma-179	171	11	[	[	X
ma-179	171	12	19	19	NUM
ma-179	171	13	]	]	NUM
ma-179	171	14	)	)	PUNCT
ma-179	171	15	,	,	PUNCT
ma-179	171	16	we	we	PRON
ma-179	171	17	have∫	have∫	VERB
ma-179	171	18	t	t	PROPN
ma-179	171	19	0	0	NUM
ma-179	171	20	eθ(t−s)dws	eθ(t−s)dws	NOUN
ma-179	171	21	=	=	PUNCT
ma-179	172	1	wt	wt	ADP
ma-179	172	2	−	−	NUM
ma-179	172	3	θ	θ	PROPN
ma-179	172	4	∫	∫	PROPN
ma-179	173	1	t	t	NOUN
ma-179	173	2	0	0	NUM
ma-179	173	3	eθ(t−s)wsds	eθ(t−s)wsds	PROPN
ma-179	173	4	,	,	PUNCT
ma-179	173	5	ξt	ξt	PROPN
ma-179	173	6	=	=	SYM
ma-179	173	7	∫	∫	PROPN
ma-179	173	8	t	t	PROPN
ma-179	173	9	0	0	NUM
ma-179	173	10	e−θsdws	e−θsdws	PROPN
ma-179	174	1	=	=	PUNCT
ma-179	174	2	e−θtwt	e−θtwt	NOUN
ma-179	174	3	−	−	PROPN
ma-179	175	1	θ	θ	PROPN
ma-179	175	2	∫	∫	PROPN
ma-179	175	3	t	t	PROPN
ma-179	175	4	0	0	NUM
ma-179	175	5	e−θsdws	e−θsdws	PROPN
ma-179	175	6	,	,	PUNCT
ma-179	175	7	ηt	ηt	ADP
ma-179	175	8	=	=	SYM
ma-179	175	9	∫	∫	PROPN
ma-179	175	10	t	t	PROPN
ma-179	175	11	0	0	NUM
ma-179	175	12	eθsdws	eθsdws	NOUN
ma-179	175	13	=	=	NOUN
ma-179	175	14	eθtwt	eθtwt	NOUN
ma-179	175	15	+	+	NUM
ma-179	175	16	θ	θ	PROPN
ma-179	175	17	∫	∫	PROPN
ma-179	175	18	t	t	PROPN
ma-179	175	19	0	0	NUM
ma-179	175	20	eθsdws	eθsdws	NOUN
ma-179	175	21	.note	.note	PUNCT
ma-179	175	22	that	that	SCONJ
ma-179	175	23	e(x2	e(x2	NOUN
ma-179	175	24	t	t	PROPN
ma-179	175	25	)	)	PUNCT
ma-179	176	1	=	=	SYM
ma-179	177	1	1−	1−	NUM
ma-179	177	2	e−2θt	e−2θt	ADJ
ma-179	177	3	2θ	2θ	NUM
ma-179	177	4	,	,	PUNCT
ma-179	177	5	e(x4	e(x4	NOUN
ma-179	177	6	t	t	NOUN
ma-179	177	7	)	)	PUNCT
ma-179	177	8	=	=	PUNCT
ma-179	178	1	3(1−	3(1−	NUM
ma-179	178	2	e−2θt	e−2θt	ADJ
ma-179	178	3	)	)	PUNCT
ma-179	178	4	2	2	NUM
ma-179	178	5	4θ	4θ	NOUN
ma-179	178	6	and	and	CCONJ
ma-179	178	7	e(it	e(it	ADV
ma-179	178	8	)	)	PUNCT
ma-179	179	1	=	=	PUNCT
ma-179	179	2	2θt	2θt	NOUN
ma-179	179	3	−	−	NOUN
ma-179	179	4	1	1	NUM
ma-179	179	5	+	+	CCONJ
ma-179	179	6	e−2θt	e−2θt	ADJ
ma-179	179	7	4θ2	4θ2	NUM
ma-179	179	8	.	.	PUNCT
ma-179	180	1	(	(	PUNCT
ma-179	180	2	2.15	2.15	NUM
ma-179	180	3	)	)	PUNCT
ma-179	180	4	by	by	ADP
ma-179	180	5	itô	itô	PROPN
ma-179	180	6	formula	formula	NOUN
ma-179	180	7	,	,	PUNCT
ma-179	180	8	we	we	PRON
ma-179	180	9	have	have	VERB
ma-179	180	10	it	it	PRON
ma-179	181	1	=	=	PUNCT
ma-179	181	2	x2	x2	PROPN
ma-179	181	3	t	t	NOUN
ma-179	181	4	2θ	2θ	NUM
ma-179	181	5	−	−	PROPN
ma-179	181	6	t	t	NOUN
ma-179	181	7	2θ	2θ	NUM
ma-179	181	8	−	−	NOUN
ma-179	181	9	zt	zt	PROPN
ma-179	181	10	θ	θ	PROPN
ma-179	181	11	.	.	PUNCT
ma-179	182	1	(	(	PUNCT
ma-179	182	2	2.16)by	2.16)by	NUM
ma-179	182	3	chebyshev	chebyshev	NOUN
ma-179	182	4	inequality	inequality	NOUN
ma-179	182	5	,	,	PUNCT
ma-179	182	6	we	we	PRON
ma-179	182	7	have	have	VERB
ma-179	182	8	p	p	X
ma-179	182	9	{	{	PUNCT
ma-179	182	10	∣∣e−2θt	∣∣e−2θt	NOUN
ma-179	182	11	2θit	2θit	NOUN
ma-179	182	12	−	−	PROPN
ma-179	182	13	ξ2	ξ2	NOUN
ma-179	182	14	∣∣	∣∣	NUM
ma-179	182	15	≥	≥	X
ma-179	182	16	δ	δ	PROPN
ma-179	182	17	}	}	PUNCT
ma-179	182	18	≤	≤	NUM
ma-179	182	19	1	1	NUM
ma-179	182	20	δ2	δ2	VERB
ma-179	182	21	e	e	NOUN
ma-179	182	22	∣∣e−2θt	∣∣e−2θt	NOUN
ma-179	182	23	2θit	2θit	NOUN
ma-179	182	24	−	−	PROPN
ma-179	182	25	ξ2	ξ2	PROPN
ma-179	182	26	∣∣2	∣∣2	PROPN
ma-179	182	27	=	=	SYM
ma-179	182	28	1	1	NUM
ma-179	182	29	δ2	δ2	VERB
ma-179	182	30	e	e	NOUN
ma-179	182	31	∣∣∣∣e−2θt	∣∣∣∣e−2θt	PROPN
ma-179	182	32	2θ	2θ	NUM
ma-179	182	33	∫	∫	PROPN
ma-179	183	1	t	t	PROPN
ma-179	183	2	0	0	NUM
ma-179	184	1	e2θtξ2	e2θtξ2	PROPN
ma-179	185	1	t	t	X
ma-179	185	2	dt	dt	X
ma-179	186	1	−	−	PROPN
ma-179	186	2	ξ2	ξ2	PROPN
ma-179	186	3	∣∣∣∣2	∣∣∣∣2	NOUN
ma-179	186	4	=	=	SYM
ma-179	186	5	1	1	NUM
ma-179	186	6	δ2	δ2	VERB
ma-179	186	7	e	e	NOUN
ma-179	186	8	∣∣∣∣e−2θt	∣∣∣∣e−2θt	PROPN
ma-179	186	9	2θ	2θ	NUM
ma-179	186	10	∫	∫	PROPN
ma-179	186	11	t	t	PROPN
ma-179	186	12	0	0	NUM
ma-179	187	1	e2θtξ2	e2θtξ2	PROPN
ma-179	188	1	t	t	X
ma-179	188	2	dt	dt	NOUN
ma-179	189	1	−	−	PROPN
ma-179	189	2	ξ2	ξ2	PROPN
ma-179	189	3	t	t	NOUN
ma-179	190	1	+	+	CCONJ
ma-179	190	2	ξ2	ξ2	PROPN
ma-179	190	3	t	t	NOUN
ma-179	190	4	−	−	PROPN
ma-179	190	5	ξ2	ξ2	ADJ
ma-179	190	6	∣∣∣∣2	∣∣∣∣2	NOUN
ma-179	190	7	≤	≤	NOUN
ma-179	190	8	2	2	NUM
ma-179	190	9	δ2	δ2	VERB
ma-179	190	10	[	[	PUNCT
ma-179	190	11	e|e−2θt	e|e−2θt	NOUN
ma-179	190	12	2θ	2θ	NUM
ma-179	190	13	∫	∫	PROPN
ma-179	190	14	t	t	PROPN
ma-179	190	15	0	0	NUM
ma-179	191	1	e2θtξ2	e2θtξ2	PROPN
ma-179	192	1	t	t	X
ma-179	192	2	dt	dt	NOUN
ma-179	193	1	−	−	PROPN
ma-179	193	2	ξ2	ξ2	PROPN
ma-179	193	3	t	t	NOUN
ma-179	193	4	|2	|2	NUM
ma-179	194	1	+	+	CCONJ
ma-179	194	2	e|ξ2	e|ξ2	PROPN
ma-179	194	3	t	t	NOUN
ma-179	194	4	−	−	NOUN
ma-179	194	5	ξ2|2	ξ2|2	X
ma-179	194	6	]	]	PUNCT
ma-179	194	7	≤	≤	NUM
ma-179	194	8	2	2	NUM
ma-179	194	9	δ2	δ2	VERB
ma-179	194	10	[	[	PUNCT
ma-179	194	11	e|e−2θt	e|e−2θt	NOUN
ma-179	194	12	2θ	2θ	NUM
ma-179	194	13	∫	∫	PROPN
ma-179	194	14	t	t	PROPN
ma-179	194	15	0	0	NUM
ma-179	195	1	e2θtξ2	e2θtξ2	PROPN
ma-179	196	1	t	t	X
ma-179	196	2	dt	dt	NOUN
ma-179	197	1	−	−	PROPN
ma-179	197	2	ξ2	ξ2	PROPN
ma-179	197	3	t	t	PROPN
ma-179	197	4	|2	|2	NUM
ma-179	198	1	+	+	CCONJ
ma-179	198	2	e|ξt	e|ξt	X
ma-179	198	3	−	−	PROPN
ma-179	198	4	ξ|2e|ξt	ξ|2e|ξt	PROPN
ma-179	199	1	+	+	CCONJ
ma-179	200	1	ξ|2	ξ|2	ADJ
ma-179	200	2	]	]	PUNCT
ma-179	200	3	≤	≤	NUM
ma-179	200	4	2	2	NUM
ma-179	200	5	δ2	δ2	VERB
ma-179	200	6	[	[	PUNCT
ma-179	200	7	e|e−2θt	e|e−2θt	NOUN
ma-179	200	8	2θ	2θ	NUM
ma-179	200	9	∫	∫	PROPN
ma-179	200	10	t	t	PROPN
ma-179	200	11	0	0	NUM
ma-179	201	1	e2θtξ2	e2θtξ2	PROPN
ma-179	202	1	t	t	X
ma-179	202	2	dt	dt	NOUN
ma-179	203	1	−	−	PROPN
ma-179	203	2	ξ2	ξ2	PROPN
ma-179	203	3	t	t	PROPN
ma-179	203	4	|2	|2	NUM
ma-179	204	1	+	+	CCONJ
ma-179	204	2	e−2θt	e−2θt	ADJ
ma-179	204	3	√	√	NUM
ma-179	204	4	2θ	2θ	NUM
ma-179	204	5	]	]	PUNCT
ma-179	204	6	≤	≤	NOUN
ma-179	204	7	ce−2θt	ce−2θt	NUM
ma-179	204	8	δ−2	δ−2	PROPN
ma-179	204	9	(	(	PUNCT
ma-179	204	10	2.17	2.17	NUM
ma-179	204	11	)	)	PUNCT
ma-179	204	12	since	since	SCONJ
ma-179	204	13	e|ξt	e|ξt	NOUN
ma-179	205	1	+	+	CCONJ
ma-179	205	2	ξ|2	ξ|2	ADJ
ma-179	205	3	≤	≤	NUM
ma-179	205	4	2e|ξt	2e|ξt	NUM
ma-179	205	5	|2	|2	NUM
ma-179	206	1	+	+	CCONJ
ma-179	206	2	2e|ξ|2	2e|ξ|2	NUM
ma-179	206	3	<	<	X
ma-179	206	4	∞.since	∞.since	PROPN
ma-179	206	5	e(ξt	e(ξt	PROPN
ma-179	206	6	−	−	PROPN
ma-179	206	7	ξ)2	ξ)2	PROPN
ma-179	207	1	=	=	SYM
ma-179	207	2	∫	∫	PROPN
ma-179	208	1	∞	∞	PROPN
ma-179	208	2	t	t	PROPN
ma-179	208	3	∫	∫	PROPN
ma-179	208	4	∞	∞	PROPN
ma-179	208	5	t	t	PROPN
ma-179	208	6	e−θre−θs	e−θre−θs	PROPN
ma-179	208	7	|r	|r	PROPN
ma-179	208	8	−	−	PROPN
ma-179	208	9	s|−1drds	s|−1drd	NOUN
ma-179	208	10	=	=	PUNCT
ma-179	208	11	e−2θt	e−2θt	ADJ
ma-179	208	12	√	√	ADJ
ma-179	208	13	2θ	2θ	NUM
ma-179	208	14	(	(	PUNCT
ma-179	208	15	2.18	2.18	NUM
ma-179	208	16	)	)	PUNCT
ma-179	208	17	hence	hence	ADV
ma-179	208	18	e(ξt	e(ξt	PROPN
ma-179	208	19	−	−	PROPN
ma-179	208	20	ξ)2	ξ)2	PROPN
ma-179	208	21	=	=	PUNCT
ma-179	209	1	e−2θt	e−2θt	ADJ
ma-179	209	2	√	√	ADJ
ma-179	209	3	2θ	2θ	NUM
ma-179	209	4	(	(	PUNCT
ma-179	209	5	2.19	2.19	NUM
ma-179	209	6	)	)	PUNCT
ma-179	209	7	gives	give	VERB
ma-179	209	8	the	the	DET
ma-179	209	9	l2	l2	NOUN
ma-179	209	10	convergence	convergence	NOUN
ma-179	209	11	rate	rate	NOUN
ma-179	209	12	.	.	PUNCT
ma-179	210	1	recall	recall	VERB
ma-179	210	2	that	that	SCONJ
ma-179	210	3	it	it	PRON
ma-179	211	1	=	=	PUNCT
ma-179	211	2	∫	∫	PROPN
ma-179	212	1	t	t	PROPN
ma-179	212	2	0	0	NUM
ma-179	212	3	e2θtξ2	e2θtξ2	PROPN
ma-179	212	4	t	t	PROPN
ma-179	212	5	dt	dt	PROPN
ma-179	212	6	,	,	PUNCT
ma-179	212	7	(	(	PUNCT
ma-179	212	8	2.20	2.20	NUM
ma-179	212	9	)	)	PUNCT
ma-179	212	10	e(ξt	e(ξt	PROPN
ma-179	212	11	−	−	PROPN
ma-179	212	12	ξ)2	ξ)2	PROPN
ma-179	212	13	→	→	SYM
ma-179	212	14	0	0	PUNCT
ma-179	212	15	as	as	ADP
ma-179	212	16	t	t	PROPN
ma-179	212	17	→∞	→∞	PROPN
ma-179	212	18	,	,	PUNCT
ma-179	212	19	(	(	PUNCT
ma-179	212	20	2.21	2.21	NUM
ma-179	212	21	)	)	PUNCT
ma-179	212	22	e(ξt	e(ξt	NOUN
ma-179	212	23	−	−	PROPN
ma-179	212	24	ξs)2	ξs)2	PROPN
ma-179	212	25	≤	≤	VERB
ma-179	212	26	c(t	c(t	PROPN
ma-179	212	27	−	−	PROPN
ma-179	212	28	s	s	NOUN
ma-179	212	29	)	)	PUNCT
ma-179	212	30	.	.	PUNCT
ma-179	213	1	(	(	PUNCT
ma-179	213	2	2.22)we	2.22)we	NUM
ma-179	213	3	have	have	VERB
ma-179	213	4	e	e	X
ma-179	213	5	(	(	PUNCT
ma-179	213	6	2θe−2θt	2θe−2θt	NUM
ma-179	213	7	it	it	PRON
ma-179	213	8	−	−	NOUN
ma-179	213	9	ξ2	ξ2	NOUN
ma-179	213	10	)	)	PUNCT
ma-179	213	11	2	2	NUM
ma-179	213	12	=	=	SYM
ma-179	213	13	e	e	X
ma-179	213	14	(	(	PUNCT
ma-179	213	15	2θe−2θt	2θe−2θt	NUM
ma-179	213	16	∫	∫	PROPN
ma-179	213	17	t	t	PROPN
ma-179	213	18	0	0	NUM
ma-179	213	19	e2θtξ2	e2θtξ2	PROPN
ma-179	213	20	t	t	X
ma-179	213	21	dt	dt	X
ma-179	213	22	−	−	PROPN
ma-179	213	23	ξ2	ξ2	PROPN
ma-179	213	24	)	)	PUNCT
ma-179	213	25	2	2	NUM
ma-179	213	26	=	=	SYM
ma-179	213	27	e	e	X
ma-179	213	28	(	(	PUNCT
ma-179	213	29	2θ	2θ	NUM
ma-179	213	30	e2θt	e2θt	PUNCT
ma-179	213	31	∫	∫	PROPN
ma-179	213	32	t	t	PROPN
ma-179	213	33	0	0	NUM
ma-179	214	1	e2θtξ2	e2θtξ2	PROPN
ma-179	215	1	t	t	X
ma-179	215	2	dt	dt	X
ma-179	215	3	−	−	PROPN
ma-179	215	4	ξ2	ξ2	PROPN
ma-179	215	5	)	)	PUNCT
ma-179	215	6	2	2	NUM
ma-179	215	7	.	.	PUNCT
ma-179	216	1	(	(	PUNCT
ma-179	216	2	2.23	2.23	NUM
ma-179	216	3	)	)	PUNCT
ma-179	216	4	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	PROPN
ma-179	216	5	eur	eur	PROPN
ma-179	216	6	.	.	PUNCT
ma-179	217	1	j.	j.	PROPN
ma-179	217	2	math	math	PROPN
ma-179	217	3	.	.	PUNCT
ma-179	218	1	anal	anal	PROPN
ma-179	218	2	.	.	PUNCT
ma-179	219	1	10.28924	10.28924	NUM
ma-179	219	2	/	/	SYM
ma-179	219	3	ada	ada	PROPN
ma-179	219	4	/	/	SYM
ma-179	219	5	ma.3.25	ma.3.25	PROPN
ma-179	219	6	9further	9further	NUM
ma-179	219	7	,	,	PUNCT
ma-179	219	8	by	by	ADP
ma-179	219	9	toeplitz	toeplitz	NOUN
ma-179	219	10	’s	’s	PART
ma-179	219	11	lemma	lemma	PROPN
ma-179	219	12	lim	lim	PROPN
ma-179	219	13	t→∞	t→∞	ADP
ma-179	219	14	2θe−2θt	2θe−2θt	NUM
ma-179	219	15	∫	∫	PROPN
ma-179	219	16	t	t	PROPN
ma-179	219	17	0	0	NUM
ma-179	220	1	e2θtξ2	e2θtξ2	PROPN
ma-179	220	2	t	t	NOUN
ma-179	220	3	dt	dt	PROPN
ma-179	221	1	=	=	SYM
ma-179	221	2	lim	lim	PROPN
ma-179	221	3	t→∞	t→∞	ADP
ma-179	222	1	ξ2	ξ2	NOUN
ma-179	222	2	t	t	PROPN
ma-179	222	3	=	=	SYM
ma-179	222	4	ξ2	ξ2	PROPN
ma-179	222	5	almost	almost	ADV
ma-179	222	6	surely	surely	ADV
ma-179	222	7	.	.	PUNCT
ma-179	223	1	(	(	PUNCT
ma-179	223	2	2.24	2.24	NUM
ma-179	223	3	)	)	PUNCT
ma-179	223	4	e(ξ2	e(ξ2	NOUN
ma-179	223	5	)	)	PUNCT
ma-179	224	1	<	<	X
ma-179	224	2	∞	∞	NUM
ma-179	224	3	which	which	PRON
ma-179	224	4	implies	imply	VERB
ma-179	224	5	that	that	SCONJ
ma-179	224	6	p	p	X
ma-179	224	7	(	(	PUNCT
ma-179	224	8	ξ	ξ	X
ma-179	224	9	=	=	SYM
ma-179	224	10	0	0	NUM
ma-179	224	11	)	)	PUNCT
ma-179	224	12	=	=	SYM
ma-179	225	1	0	0	X
ma-179	225	2	.	.	PUNCT
ma-179	226	1	we	we	PRON
ma-179	226	2	have	have	VERB
ma-179	226	3	lim	lim	PROPN
ma-179	226	4	t→∞	t→∞	PRON
ma-179	227	1	[	[	PUNCT
ma-179	227	2	2θe−2θt	2θe−2θt	NUM
ma-179	227	3	∫	∫	PROPN
ma-179	227	4	t	t	PROPN
ma-179	227	5	0	0	NUM
ma-179	227	6	e2θtξ2	e2θtξ2	PROPN
ma-179	227	7	t	t	X
ma-179	227	8	dt	dt	NOUN
ma-179	227	9	−	−	PROPN
ma-179	227	10	ξ2	ξ2	PROPN
ma-179	227	11	t	t	X
ma-179	227	12	]	]	PUNCT
ma-179	228	1	=	=	PUNCT
ma-179	228	2	0	0	NUM
ma-179	228	3	almost	almost	ADV
ma-179	228	4	surely	surely	ADV
ma-179	228	5	.	.	PUNCT
ma-179	229	1	(	(	PUNCT
ma-179	229	2	2.25	2.25	NUM
ma-179	229	3	)	)	PUNCT
ma-179	229	4	because	because	SCONJ
ma-179	229	5	of	of	ADP
ma-179	229	6	the	the	DET
ma-179	229	7	continuity	continuity	NOUN
ma-179	229	8	of	of	ADP
ma-179	229	9	ξt	ξt	NUM
ma-179	229	10	,	,	PUNCT
ma-179	229	11	for	for	ADP
ma-179	229	12	every	every	DET
ma-179	229	13	t	t	PROPN
ma-179	229	14	≥	≥	NOUN
ma-179	229	15	0,∫	0,∫	PROPN
ma-179	229	16	t	t	PROPN
ma-179	229	17	0	0	PUNCT
ma-179	230	1	e2θtξ2	e2θtξ2	PROPN
ma-179	230	2	t	t	PROPN
ma-179	230	3	dt	dt	X
ma-179	230	4	≥	≥	PROPN
ma-179	231	1	∫	∫	PROPN
ma-179	231	2	t	t	PROPN
ma-179	231	3	t	t	PROPN
ma-179	231	4	2	2	NUM
ma-179	231	5	e2θtξ2	e2θtξ2	PROPN
ma-179	231	6	t	t	PROPN
ma-179	231	7	dt	dt	X
ma-179	231	8	≥	≥	PROPN
ma-179	231	9	t	t	PROPN
ma-179	231	10	2	2	NUM
ma-179	231	11	eθt	eθt	NOUN
ma-179	231	12	(	(	PUNCT
ma-179	231	13	inf	inf	NOUN
ma-179	231	14	t	t	PROPN
ma-179	231	15	2	2	NUM
ma-179	231	16	<	<	X
ma-179	231	17	t	t	PROPN
ma-179	231	18	<	<	X
ma-179	231	19	t	t	PROPN
ma-179	231	20	ξ2	ξ2	PROPN
ma-179	231	21	t	t	PROPN
ma-179	231	22	)	)	PUNCT
ma-179	231	23	almost	almost	ADV
ma-179	231	24	surely	surely	ADV
ma-179	231	25	.	.	PUNCT
ma-179	232	1	(	(	PUNCT
ma-179	232	2	2.26	2.26	NUM
ma-179	232	3	)	)	PUNCT
ma-179	232	4	furthermore	furthermore	ADV
ma-179	232	5	the	the	DET
ma-179	232	6	continuity	continuity	NOUN
ma-179	232	7	of	of	ADP
ma-179	232	8	ξt	ξt	NUM
ma-179	232	9	,	,	PUNCT
ma-179	232	10	gives	give	VERB
ma-179	232	11	lim	lim	PROPN
ma-179	232	12	t→∞	t→∞	X
ma-179	232	13	(	(	PUNCT
ma-179	232	14	inf	inf	PROPN
ma-179	232	15	t	t	PROPN
ma-179	232	16	2	2	NUM
ma-179	232	17	<	<	X
ma-179	232	18	t	t	PROPN
ma-179	232	19	<	<	X
ma-179	232	20	t	t	PROPN
ma-179	232	21	ξ2	ξ2	PROPN
ma-179	232	22	t	t	PROPN
ma-179	232	23	)	)	PUNCT
ma-179	233	1	=	=	SYM
ma-179	233	2	ξ2	ξ2	ADJ
ma-179	233	3	almost	almost	ADV
ma-179	233	4	surely	surely	ADV
ma-179	233	5	.	.	PUNCT
ma-179	234	1	(	(	PUNCT
ma-179	234	2	2.27	2.27	NUM
ma-179	234	3	)	)	PUNCT
ma-179	234	4	lim	lim	PROPN
ma-179	234	5	t→∞	t→∞	X
ma-179	235	1	∫	∫	PROPN
ma-179	235	2	t	t	PROPN
ma-179	235	3	0	0	NUM
ma-179	236	1	e2θtξ2	e2θtξ2	PROPN
ma-179	236	2	t	t	X
ma-179	236	3	dt	dt	PUNCT
ma-179	237	1	=	=	NOUN
ma-179	237	2	∞	∞	PROPN
ma-179	237	3	almost	almost	ADV
ma-179	237	4	surely	surely	ADV
ma-179	237	5	.	.	PUNCT
ma-179	238	1	(	(	PUNCT
ma-179	238	2	2.28	2.28	NUM
ma-179	238	3	)	)	PUNCT
ma-179	238	4	by	by	ADP
ma-179	238	5	l’hopital	l’hopital	ADJ
ma-179	238	6	rule	rule	NOUN
ma-179	238	7	,	,	PUNCT
ma-179	238	8	lim	lim	PROPN
ma-179	238	9	t→∞	t→∞	X
ma-179	239	1	∫	∫	PROPN
ma-179	239	2	t	t	PROPN
ma-179	239	3	0	0	NUM
ma-179	240	1	e2θtξ2	e2θtξ2	PROPN
ma-179	240	2	t	t	PROPN
ma-179	240	3	dt	dt	PROPN
ma-179	240	4	e2θt	e2θt	PUNCT
ma-179	241	1	=	=	SYM
ma-179	241	2	lim	lim	PROPN
ma-179	241	3	t→∞	t→∞	ADP
ma-179	241	4	ξ2	ξ2	NOUN
ma-179	241	5	t	t	NOUN
ma-179	241	6	2θ	2θ	NUM
ma-179	241	7	=	=	SYM
ma-179	241	8	ξ2	ξ2	ADJ
ma-179	241	9	2θ	2θ	NUM
ma-179	241	10	almost	almost	ADV
ma-179	241	11	surely	surely	ADV
ma-179	241	12	.	.	PUNCT
ma-179	242	1	(	(	PUNCT
ma-179	242	2	2.29	2.29	NUM
ma-179	242	3	)	)	PUNCT
ma-179	242	4	θt	θt	NOUN
ma-179	243	1	−	−	PROPN
ma-179	243	2	θ	θ	PROPN
ma-179	243	3	=	=	SYM
ma-179	243	4	∫	∫	PROPN
ma-179	243	5	t	t	PROPN
ma-179	243	6	0	0	NUM
ma-179	243	7	eθtξtdwt∫	eθtξtdwt∫	VERB
ma-179	244	1	t	t	PROPN
ma-179	244	2	0	0	NUM
ma-179	244	3	e2θtξ2	e2θtξ2	PROPN
ma-179	244	4	t	t	NOUN
ma-179	244	5	dt	dt	NOUN
ma-179	245	1	=	=	SYM
ma-179	245	2	ξ2	ξ2	PROPN
ma-179	245	3	t	t	PROPN
ma-179	245	4	2e−2θt	2e−2θt	NUM
ma-179	245	5	∫	∫	PROPN
ma-179	245	6	t	t	PROPN
ma-179	245	7	0	0	NUM
ma-179	246	1	e2θtξ2	e2θtξ2	PROPN
ma-179	246	2	t	t	X
ma-179	246	3	dt	dt	X
ma-179	247	1	−	−	PROPN
ma-179	247	2	θ	θ	PROPN
ma-179	247	3	.	.	PUNCT
ma-179	247	4	(	(	PUNCT
ma-179	247	5	2.30	2.30	NUM
ma-179	247	6	)	)	PUNCT
ma-179	247	7	θt	θt	NOUN
ma-179	247	8	−	−	PROPN
ma-179	247	9	θ	θ	PROPN
ma-179	247	10	→	→	SYM
ma-179	247	11	0	0	NUM
ma-179	247	12	almost	almost	ADV
ma-179	247	13	surely	surely	ADV
ma-179	247	14	.	.	PUNCT
ma-179	248	1	(	(	PUNCT
ma-179	248	2	2.31	2.31	NUM
ma-179	248	3	)	)	PUNCT
ma-179	248	4	θ̂t	θ̂t	X
ma-179	249	1	−	−	PROPN
ma-179	249	2	θ	θ	PROPN
ma-179	249	3	=	=	SYM
ma-179	249	4	ξ2	ξ2	PROPN
ma-179	249	5	t	t	NOUN
ma-179	249	6	−	−	PROPN
ma-179	249	7	2θe−2θt	2θe−2θt	NUM
ma-179	249	8	∫	∫	PROPN
ma-179	249	9	t	t	PROPN
ma-179	249	10	0	0	NUM
ma-179	250	1	e2θtξ2	e2θtξ2	PROPN
ma-179	250	2	t	t	PROPN
ma-179	250	3	dt	dt	X
ma-179	251	1	2e−2θt	2e−2θt	NUM
ma-179	251	2	∫	∫	PROPN
ma-179	251	3	t	t	PROPN
ma-179	251	4	0	0	NUM
ma-179	251	5	e2θtξ2	e2θtξ2	PROPN
ma-179	251	6	t	t	PROPN
ma-179	251	7	dt	dt	X
ma-179	251	8	.	.	PUNCT
ma-179	252	1	(	(	PUNCT
ma-179	252	2	2.32	2.32	NUM
ma-179	252	3	)	)	PUNCT
ma-179	252	4	it	it	PRON
ma-179	252	5	is	be	AUX
ma-179	252	6	easy	easy	ADJ
ma-179	252	7	to	to	PART
ma-179	252	8	verify	verify	VERB
ma-179	252	9	that	that	SCONJ
ma-179	253	1	e	e	NOUN
ma-179	253	2	[	[	PUNCT
ma-179	253	3	ξ2	ξ2	NOUN
ma-179	253	4	t	t	PROPN
ma-179	253	5	−	−	PROPN
ma-179	253	6	2θe−2θt	2θe−2θt	NUM
ma-179	253	7	∫	∫	PROPN
ma-179	253	8	t	t	PROPN
ma-179	253	9	0	0	NUM
ma-179	254	1	e2θtξ2	e2θtξ2	PROPN
ma-179	254	2	t	t	X
ma-179	254	3	dt	dt	X
ma-179	254	4	]	]	SYM
ma-179	254	5	2	2	NUM
ma-179	254	6	≤	≤	NOUN
ma-179	254	7	ce−2θt	ce−2θt	NUM
ma-179	254	8	.	.	PUNCT
ma-179	255	1	(	(	PUNCT
ma-179	255	2	2.33	2.33	NUM
ma-179	255	3	)	)	PUNCT
ma-179	255	4	this	this	PRON
ma-179	255	5	completes	complete	VERB
ma-179	255	6	the	the	DET
ma-179	255	7	proof	proof	NOUN
ma-179	255	8	of	of	ADP
ma-179	255	9	the	the	DET
ma-179	255	10	lemma	lemma	PROPN
ma-179	255	11	.	.	PUNCT
ma-179	256	1	the	the	DET
ma-179	256	2	following	follow	VERB
ma-179	256	3	lemma	lemma	PROPN
ma-179	256	4	(	(	PUNCT
ma-179	256	5	cameron	cameron	PROPN
ma-179	256	6	-	-	PUNCT
ma-179	256	7	martin	martin	PROPN
ma-179	256	8	type	type	NOUN
ma-179	256	9	theorem	theorem	VERB
ma-179	256	10	)	)	PUNCT
ma-179	256	11	gives	give	VERB
ma-179	256	12	the	the	DET
ma-179	256	13	bound	bind	VERB
ma-179	256	14	on	on	ADP
ma-179	256	15	the	the	DET
ma-179	256	16	joint	joint	ADJ
ma-179	256	17	characteristicfunctions	characteristicfunction	NOUN
ma-179	256	18	of	of	ADP
ma-179	256	19	the	the	DET
ma-179	256	20	sufficient	sufficient	ADJ
ma-179	256	21	statistics	statistic	NOUN
ma-179	256	22	defining	define	VERB
ma-179	256	23	the	the	DET
ma-179	256	24	mle	mle	NOUN
ma-179	256	25	:	:	PUNCT
ma-179	256	26	lemma	lemma	PROPN
ma-179	256	27	2.4	2.4	NUM
ma-179	256	28	(	(	PUNCT
ma-179	256	29	a	a	X
ma-179	256	30	)	)	PUNCT
ma-179	256	31	let	let	VERB
ma-179	256	32	φt	φt	INTJ
ma-179	256	33	(	(	PUNCT
ma-179	256	34	z1	z1	PROPN
ma-179	256	35	,	,	PUNCT
ma-179	256	36	z2	z2	PROPN
ma-179	256	37	)	)	PUNCT
ma-179	256	38	:	:	PUNCT
ma-179	257	1	=	=	SYM
ma-179	257	2	e	e	X
ma-179	257	3	exp(z1it	exp(z1it	PROPN
ma-179	257	4	+	+	PROPN
ma-179	257	5	z2x	z2x	PROPN
ma-179	257	6	2	2	NUM
ma-179	257	7	t	t	NOUN
ma-179	257	8	)	)	PUNCT
ma-179	257	9	,	,	PUNCT
ma-179	257	10	z1	z1	PROPN
ma-179	257	11	,	,	PUNCT
ma-179	257	12	z2	z2	PROPN
ma-179	257	13	∈	∈	PROPN
ma-179	257	14	c.	c.	NOUN
ma-179	257	15	then	then	ADV
ma-179	257	16	φt	φt	PROPN
ma-179	257	17	(	(	PUNCT
ma-179	257	18	z1	z1	PROPN
ma-179	257	19	,	,	PUNCT
ma-179	257	20	z2	z2	PROPN
ma-179	257	21	)	)	PUNCT
ma-179	257	22	exists	exist	VERB
ma-179	257	23	for	for	ADP
ma-179	257	24	|zi	|zi	ADP
ma-179	257	25	|	|	ADV
ma-179	257	26	≤	≤	NUM
ma-179	257	27	δ	δ	PROPN
ma-179	257	28	,	,	PUNCT
ma-179	257	29	1	1	NUM
ma-179	257	30	=	=	SYM
ma-179	257	31	1,2	1,2	NUM
ma-179	257	32	for	for	ADP
ma-179	257	33	some	some	DET
ma-179	257	34	δ	δ	PROPN
ma-179	257	35	>	>	X
ma-179	257	36	0	0	PUNCT
ma-179	257	37	and	and	CCONJ
ma-179	257	38	is	be	AUX
ma-179	257	39	given	give	VERB
ma-179	257	40	by	by	ADP
ma-179	257	41	φt	φt	PROPN
ma-179	257	42	(	(	PUNCT
ma-179	257	43	z1	z1	PROPN
ma-179	257	44	,	,	PUNCT
ma-179	257	45	z2	z2	NUM
ma-179	257	46	)	)	PUNCT
ma-179	257	47	=	=	SYM
ma-179	257	48	exp	exp	NOUN
ma-179	257	49	(	(	PUNCT
ma-179	257	50	θt	θt	PROPN
ma-179	257	51	2	2	NUM
ma-179	257	52	)	)	PUNCT
ma-179	257	53	[	[	PUNCT
ma-179	257	54	2γ	2γ	NOUN
ma-179	257	55	(	(	PUNCT
ma-179	257	56	γ	γ	NOUN
ma-179	257	57	−	−	PROPN
ma-179	257	58	θ	θ	PROPN
ma-179	257	59	+	+	CCONJ
ma-179	257	60	2z2)e−γt	2z2)e−γt	NUM
ma-179	257	61	+	+	CCONJ
ma-179	257	62	(	(	PUNCT
ma-179	257	63	γ	γ	X
ma-179	257	64	+	+	ADJ
ma-179	257	65	θ	θ	PROPN
ma-179	257	66	−	−	PROPN
ma-179	258	1	2z2)eγt	2z2)eγt	PROPN
ma-179	258	2	]	]	PUNCT
ma-179	258	3	1/2	1/2	NUM
ma-179	258	4	where	where	SCONJ
ma-179	258	5	γ	γ	X
ma-179	258	6	=	=	SYM
ma-179	258	7	(	(	PUNCT
ma-179	258	8	θ2	θ2	ADV
ma-179	258	9	−	−	PROPN
ma-179	258	10	2z1)1/2	2z1)1/2	NUM
ma-179	258	11	and	and	CCONJ
ma-179	258	12	we	we	PRON
ma-179	258	13	choose	choose	VERB
ma-179	258	14	the	the	DET
ma-179	258	15	principal	principal	ADJ
ma-179	258	16	branch	branch	NOUN
ma-179	258	17	of	of	ADP
ma-179	258	18	the	the	DET
ma-179	258	19	square	square	ADJ
ma-179	258	20	root	root	NOUN
ma-179	258	21	.	.	PUNCT
ma-179	259	1	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	PROPN
ma-179	259	2	eur	eur	PROPN
ma-179	259	3	.	.	PUNCT
ma-179	260	1	j.	j.	PROPN
ma-179	260	2	math	math	PROPN
ma-179	260	3	.	.	PUNCT
ma-179	261	1	anal	anal	PROPN
ma-179	261	2	.	.	PUNCT
ma-179	262	1	10.28924	10.28924	NUM
ma-179	262	2	/	/	SYM
ma-179	262	3	ada	ada	PROPN
ma-179	262	4	/	/	SYM
ma-179	262	5	ma.3.25	ma.3.25	NOUN
ma-179	262	6	10	10	NUM
ma-179	262	7	(	(	PUNCT
ma-179	262	8	b	b	X
ma-179	262	9	)	)	PUNCT
ma-179	262	10	let	let	VERB
ma-179	262	11	ht	ht	INTJ
ma-179	262	12	,	,	PUNCT
ma-179	262	13	x	x	X
ma-179	262	14	:	:	PUNCT
ma-179	262	15	=	=	SYM
ma-179	262	16	(	(	PUNCT
ma-179	262	17	e−2θt	e−2θt	PROPN
ma-179	262	18	4θ2	4θ2	NUM
ma-179	263	1	)	)	SYM
ma-179	263	2	1/2	1/2	NUM
ma-179	263	3	zt	zt	PROPN
ma-179	263	4	−	−	PROPN
ma-179	263	5	(	(	PUNCT
ma-179	263	6	e−2θt	e−2θt	PROPN
ma-179	263	7	4θ2it	4θ2it	NUM
ma-179	264	1	−	−	PROPN
ma-179	264	2	ξ2	ξ2	PROPN
ma-179	264	3	)	)	PUNCT
ma-179	265	1	x.	x.	NOUN
ma-179	266	1	then	then	ADV
ma-179	266	2	for	for	ADP
ma-179	266	3	|x	|x	NOUN
ma-179	266	4	|	|	ADV
ma-179	266	5	≤	≤	NUM
ma-179	266	6	2(log	2(log	NOUN
ma-179	266	7	e2θt	e2θt	PUNCT
ma-179	266	8	)	)	PUNCT
ma-179	266	9	1/2	1/2	NUM
ma-179	266	10	and	and	CCONJ
ma-179	266	11	for	for	ADP
ma-179	266	12	|u|	|u|	ADJ
ma-179	266	13	≤	≤	NOUN
ma-179	266	14	εeθt	εeθt	ADV
ma-179	266	15	,	,	PUNCT
ma-179	266	16	where	where	SCONJ
ma-179	266	17	ε	ε	PROPN
ma-179	266	18	is	be	AUX
ma-179	266	19	sufficiently	sufficiently	ADV
ma-179	266	20	small∣∣∣∣e	small∣∣∣∣e	ADJ
ma-179	266	21	exp(iuht	exp(iuht	PROPN
ma-179	266	22	,	,	PUNCT
ma-179	266	23	x)−	x)−	PROPN
ma-179	266	24	exp(−	exp(−	PROPN
ma-179	266	25	u2	u2	PROPN
ma-179	266	26	2	2	NUM
ma-179	266	27	)	)	PUNCT
ma-179	266	28	∣∣∣∣	∣∣∣∣	NOUN
ma-179	266	29	≤	≤	NUM
ma-179	266	30	c	c	NOUN
ma-179	266	31	exp	exp	NOUN
ma-179	266	32	(	(	PUNCT
ma-179	266	33	−|u|	−|u|	NOUN
ma-179	266	34	2	2	NUM
ma-179	266	35	)	)	PUNCT
ma-179	266	36	(	(	PUNCT
ma-179	266	37	|u|+	|u|+	NOUN
ma-179	266	38	|u|3)e−θt	|u|3)e−θt	VERB
ma-179	266	39	.	.	PUNCT
ma-179	267	1	(	(	PUNCT
ma-179	267	2	c	c	X
ma-179	267	3	)	)	PUNCT
ma-179	267	4	for	for	ADP
ma-179	267	5	|u|	|u|	ADJ
ma-179	267	6	≤	≤	NUM
ma-179	267	7	ε1e	ε1e	NOUN
ma-179	267	8	θt	θt	PROPN
ma-179	267	9	,	,	PUNCT
ma-179	267	10	where	where	SCONJ
ma-179	267	11	ε1	ε1	PROPN
ma-179	267	12	is	be	AUX
ma-179	267	13	sufficiently	sufficiently	ADV
ma-179	267	14	small	small	ADJ
ma-179	267	15	,	,	PUNCT
ma-179	267	16	we	we	PRON
ma-179	267	17	have	have	VERB
ma-179	267	18	as	as	ADP
ma-179	267	19	t	t	PROPN
ma-179	267	20	→∞,∣∣∣∣e	→∞,∣∣∣∣e	PUNCT
ma-179	267	21	exp	exp	NOUN
ma-179	267	22	{	{	PUNCT
ma-179	267	23	iu	iu	ADV
ma-179	267	24	(	(	PUNCT
ma-179	267	25	e−θt	e−θt	PROPN
ma-179	267	26	2θ	2θ	NUM
ma-179	267	27	)	)	PUNCT
ma-179	268	1	zt	zt	PROPN
ma-179	268	2	}	}	PUNCT
ma-179	268	3	−	−	PROPN
ma-179	268	4	exp(−	exp(−	PROPN
ma-179	268	5	u2	u2	PROPN
ma-179	268	6	2	2	NUM
ma-179	268	7	)	)	PUNCT
ma-179	268	8	∣∣∣∣	∣∣∣∣	NOUN
ma-179	268	9	≤	≤	NUM
ma-179	268	10	c	c	PROPN
ma-179	268	11	exp(−	exp(−	PROPN
ma-179	268	12	|u|	|u|	PROPN
ma-179	268	13	2	2	NUM
ma-179	268	14	)	)	PUNCT
ma-179	268	15	(	(	PUNCT
ma-179	268	16	|u|+	|u|+	NOUN
ma-179	268	17	|u|3)e−θt	|u|3)e−θt	VERB
ma-179	268	18	.	.	PUNCT
ma-179	269	1	part	part	NOUN
ma-179	269	2	(	(	PUNCT
ma-179	269	3	a	a	NOUN
ma-179	269	4	)	)	PUNCT
ma-179	269	5	is	be	AUX
ma-179	269	6	from	from	ADP
ma-179	269	7	bishwal	bishwal	NOUN
ma-179	269	8	[	[	X
ma-179	269	9	5].we	5].we	PRON
ma-179	269	10	shall	shall	AUX
ma-179	269	11	prove	prove	VERB
ma-179	269	12	part	part	NOUN
ma-179	269	13	(	(	PUNCT
ma-179	269	14	b	b	NOUN
ma-179	269	15	)	)	PUNCT
ma-179	269	16	in	in	ADP
ma-179	269	17	details	detail	NOUN
ma-179	269	18	.	.	PUNCT
ma-179	270	1	proof	proof	NOUN
ma-179	270	2	of	of	ADP
ma-179	270	3	part	part	NOUN
ma-179	270	4	(	(	PUNCT
ma-179	270	5	c	c	NOUN
ma-179	270	6	)	)	PUNCT
ma-179	270	7	is	be	AUX
ma-179	270	8	very	very	ADV
ma-179	270	9	similar	similar	ADJ
ma-179	270	10	to	to	ADP
ma-179	270	11	part	part	NOUN
ma-179	270	12	(	(	PUNCT
ma-179	270	13	b	b	NOUN
ma-179	270	14	)	)	PUNCT
ma-179	270	15	and	and	CCONJ
ma-179	270	16	will	will	AUX
ma-179	270	17	be	be	AUX
ma-179	270	18	omitted	omit	VERB
ma-179	270	19	.	.	PUNCT
ma-179	271	1	proof	proof	NOUN
ma-179	271	2	:	:	PUNCT
ma-179	271	3	by	by	ADP
ma-179	271	4	itô	itô	PROPN
ma-179	271	5	formula	formula	NOUN
ma-179	271	6	,	,	PUNCT
ma-179	271	7	zt	zt	PROPN
ma-179	271	8	=	=	SYM
ma-179	271	9	θit	θit	PROPN
ma-179	272	1	+	+	CCONJ
ma-179	272	2	x2	x2	PROPN
ma-179	272	3	t	t	NOUN
ma-179	272	4	2	2	NUM
ma-179	272	5	−	−	NOUN
ma-179	272	6	t	t	PROPN
ma-179	272	7	2	2	NUM
ma-179	272	8	.note	.note	PUNCT
ma-179	272	9	that	that	SCONJ
ma-179	272	10	e	e	SYM
ma-179	272	11	exp(iuht	exp(iuht	PROPN
ma-179	272	12	,	,	PUNCT
ma-179	272	13	x	x	X
ma-179	272	14	)	)	PUNCT
ma-179	272	15	=	=	SYM
ma-179	272	16	e	e	NOUN
ma-179	272	17	exp	exp	X
ma-179	272	18	[	[	PUNCT
ma-179	272	19	−iu	−iu	PROPN
ma-179	272	20	(	(	PUNCT
ma-179	272	21	e−2θt	e−2θt	PROPN
ma-179	272	22	4θ2	4θ2	NUM
ma-179	272	23	)	)	SYM
ma-179	272	24	1/2	1/2	NUM
ma-179	272	25	zt	zt	PROPN
ma-179	272	26	−	−	NOUN
ma-179	272	27	iu	iu	ADP
ma-179	272	28	(	(	PUNCT
ma-179	272	29	(	(	PUNCT
ma-179	272	30	e−2θt	e−2θt	PROPN
ma-179	272	31	4θ2	4θ2	NUM
ma-179	272	32	)	)	PUNCT
ma-179	273	1	it	it	PRON
ma-179	273	2	−	−	PROPN
ma-179	273	3	ξ2	ξ2	NOUN
ma-179	273	4	)	)	PUNCT
ma-179	273	5	x	x	X
ma-179	273	6	]	]	PUNCT
ma-179	274	1	=	=	PUNCT
ma-179	274	2	e	e	X
ma-179	274	3	exp	exp	X
ma-179	274	4	[	[	PUNCT
ma-179	274	5	−iu	−iu	PROPN
ma-179	274	6	(	(	PUNCT
ma-179	274	7	e−2θt	e−2θt	PROPN
ma-179	274	8	4θ2	4θ2	NUM
ma-179	274	9	)	)	PUNCT
ma-179	274	10	1/2	1/2	NUM
ma-179	274	11	{	{	PUNCT
ma-179	274	12	θit	θit	NOUN
ma-179	274	13	+	+	CCONJ
ma-179	274	14	x2	x2	PROPN
ma-179	274	15	t	t	NOUN
ma-179	274	16	2	2	NUM
ma-179	274	17	−	−	NOUN
ma-179	274	18	t	t	NOUN
ma-179	274	19	2	2	NUM
ma-179	274	20	}	}	PUNCT
ma-179	274	21	−	−	PROPN
ma-179	275	1	i	i	PRON
ma-179	275	2	t	t	X
ma-179	275	3	(	(	PUNCT
ma-179	275	4	(	(	PUNCT
ma-179	275	5	e−2θt	e−2θt	PROPN
ma-179	275	6	4θ2	4θ2	NUM
ma-179	275	7	)	)	PUNCT
ma-179	276	1	it	it	PRON
ma-179	276	2	−	−	PROPN
ma-179	276	3	ξ2	ξ2	NOUN
ma-179	276	4	)	)	PUNCT
ma-179	276	5	x	x	X
ma-179	276	6	]	]	PUNCT
ma-179	277	1	=	=	PUNCT
ma-179	277	2	e	e	X
ma-179	277	3	exp(z1it	exp(z1it	PROPN
ma-179	277	4	+	+	PROPN
ma-179	277	5	z2x	z2x	PROPN
ma-179	277	6	2	2	NUM
ma-179	277	7	t	t	NOUN
ma-179	277	8	+	+	CCONJ
ma-179	277	9	z3	z3	NOUN
ma-179	277	10	)	)	PUNCT
ma-179	277	11	=	=	PUNCT
ma-179	278	1	exp(z3)φt	exp(z3)φt	NOUN
ma-179	278	2	(	(	PUNCT
ma-179	278	3	z1	z1	PROPN
ma-179	278	4	,	,	PUNCT
ma-179	278	5	z2	z2	PROPN
ma-179	278	6	)	)	PUNCT
ma-179	278	7	where	where	SCONJ
ma-179	278	8	z1	z1	NOUN
ma-179	278	9	=	=	SYM
ma-179	278	10	−iuθδt	−iuθδt	NOUN
ma-179	278	11	,	,	PUNCT
ma-179	278	12	x	x	NOUN
ma-179	278	13	,	,	PUNCT
ma-179	278	14	z2	z2	PROPN
ma-179	278	15	=	=	SYM
ma-179	278	16	−	−	PROPN
ma-179	278	17	iu	iu	ADP
ma-179	278	18	2	2	NUM
ma-179	278	19	(	(	PUNCT
ma-179	278	20	e−2θt	e−2θt	PROPN
ma-179	278	21	4θ2	4θ2	NUM
ma-179	278	22	)	)	PUNCT
ma-179	278	23	1/2	1/2	NUM
ma-179	278	24	,	,	PUNCT
ma-179	278	25	z3	z3	PROPN
ma-179	278	26	=	=	SYM
ma-179	278	27	iut	iut	PROPN
ma-179	278	28	2	2	NUM
ma-179	278	29	δt	δt	NOUN
ma-179	278	30	,	,	PUNCT
ma-179	278	31	x	x	X
ma-179	278	32	,	,	PUNCT
ma-179	278	33	δt	δt	X
ma-179	278	34	,	,	PUNCT
ma-179	278	35	x	x	SYM
ma-179	278	36	=	=	PRON
ma-179	278	37	(	(	PUNCT
ma-179	278	38	e−2θt	e−2θt	PROPN
ma-179	278	39	4θ2	4θ2	NUM
ma-179	278	40	)	)	PUNCT
ma-179	278	41	1/2	1/2	NUM
ma-179	279	1	+	+	NUM
ma-179	279	2	2x	2x	NUM
ma-179	279	3	t	t	NOUN
ma-179	279	4	.	.	PUNCT
ma-179	280	1	note	note	VERB
ma-179	280	2	that	that	SCONJ
ma-179	280	3	(	(	PUNCT
ma-179	280	4	z1	z1	PROPN
ma-179	280	5	,	,	PUNCT
ma-179	280	6	z2	z2	PROPN
ma-179	280	7	)	)	PUNCT
ma-179	280	8	satisfies	satisfy	VERB
ma-179	280	9	the	the	DET
ma-179	280	10	conditions	condition	NOUN
ma-179	280	11	of	of	ADP
ma-179	280	12	(	(	PUNCT
ma-179	280	13	a	a	NOUN
ma-179	280	14	)	)	PUNCT
ma-179	280	15	by	by	ADP
ma-179	280	16	choosing	choose	VERB
ma-179	280	17	ε	ε	PROPN
ma-179	280	18	sufficiently	sufficiently	ADV
ma-179	280	19	small	small	ADJ
ma-179	280	20	.	.	PUNCT
ma-179	281	1	let	let	VERB
ma-179	281	2	α1,t	α1,t	PROPN
ma-179	281	3	(	(	PUNCT
ma-179	281	4	u	u	NOUN
ma-179	281	5	)	)	PUNCT
ma-179	281	6	,	,	PUNCT
ma-179	281	7	α2,t	α2,t	PROPN
ma-179	281	8	(	(	PUNCT
ma-179	281	9	u	u	NOUN
ma-179	281	10	)	)	PUNCT
ma-179	281	11	,	,	PUNCT
ma-179	281	12	α3,t	α3,t	PROPN
ma-179	281	13	(	(	PUNCT
ma-179	281	14	u	u	NOUN
ma-179	281	15	)	)	PUNCT
ma-179	281	16	and	and	CCONJ
ma-179	281	17	α4,t	α4,t	PROPN
ma-179	281	18	(	(	PUNCT
ma-179	281	19	u	u	NOUN
ma-179	281	20	)	)	PUNCT
ma-179	281	21	be	be	AUX
ma-179	281	22	functions	function	NOUN
ma-179	281	23	which	which	PRON
ma-179	281	24	are	be	AUX
ma-179	281	25	of	of	ADP
ma-179	281	26	the	the	DET
ma-179	281	27	orders	order	NOUN
ma-179	281	28	o(|u|e−θt/2	o(|u|e−θt/2	NOUN
ma-179	281	29	)	)	PUNCT
ma-179	281	30	,	,	PUNCT
ma-179	281	31	o(|u|2e−θt/2	o(|u|2e−θt/2	PROPN
ma-179	281	32	)	)	PUNCT
ma-179	281	33	,	,	PUNCT
ma-179	281	34	o(|u|3e−3θt/2	o(|u|3e−3θt/2	NOUN
ma-179	281	35	)	)	PUNCT
ma-179	281	36	and	and	CCONJ
ma-179	281	37	o(|u|3e−θt/2	o(|u|3e−θt/2	NOUN
ma-179	281	38	)	)	PUNCT
ma-179	281	39	respectively	respectively	ADV
ma-179	281	40	.	.	PUNCT
ma-179	282	1	note	note	VERB
ma-179	282	2	that	that	SCONJ
ma-179	282	3	for	for	ADP
ma-179	282	4	the	the	DET
ma-179	282	5	given	give	VERB
ma-179	282	6	range	range	NOUN
ma-179	282	7	of	of	ADP
ma-179	282	8	values	value	NOUN
ma-179	282	9	of	of	ADP
ma-179	282	10	xand	xand	PROPN
ma-179	282	11	u	u	PROPN
ma-179	282	12	,	,	PUNCT
ma-179	282	13	the	the	DET
ma-179	282	14	conditions	condition	NOUN
ma-179	282	15	on	on	ADP
ma-179	282	16	zi	zi	NOUN
ma-179	282	17	for	for	ADP
ma-179	282	18	part	part	NOUN
ma-179	282	19	(	(	PUNCT
ma-179	282	20	a	a	NOUN
ma-179	282	21	)	)	PUNCT
ma-179	282	22	of	of	ADP
ma-179	282	23	lemma	lemma	PROPN
ma-179	282	24	are	be	AUX
ma-179	282	25	satisfied	satisfied	ADJ
ma-179	282	26	.	.	PUNCT
ma-179	283	1	note	note	VERB
ma-179	283	2	also	also	ADV
ma-179	283	3	that	that	SCONJ
ma-179	283	4	z2	z2	NOUN
ma-179	283	5	=	=	SYM
ma-179	283	6	α1,t	α1,t	PROPN
ma-179	283	7	(	(	PUNCT
ma-179	283	8	u).further	u).further	PROPN
ma-179	283	9	,	,	PUNCT
ma-179	283	10	with	with	ADP
ma-179	283	11	βt	βt	PROPN
ma-179	283	12	(	(	PUNCT
ma-179	283	13	t	t	NOUN
ma-179	283	14	)	)	PUNCT
ma-179	283	15	=	=	SYM
ma-179	283	16	1	1	NUM
ma-179	283	17	+	+	CCONJ
ma-179	283	18	iu	iu	ADP
ma-179	283	19	δt	δt	NOUN
ma-179	283	20	,	,	PUNCT
ma-179	283	21	x	x	X
ma-179	283	22	θ	θ	PROPN
ma-179	283	23	+	+	CCONJ
ma-179	283	24	u2δ2	u2δ2	PROPN
ma-179	283	25	t	t	PROPN
ma-179	283	26	,	,	PUNCT
ma-179	283	27	x	x	PROPN
ma-179	283	28	2θ2	2θ2	NUM
ma-179	283	29	,	,	PUNCT
ma-179	283	30	γ	γ	X
ma-179	283	31	=	=	SYM
ma-179	283	32	(	(	PUNCT
ma-179	283	33	θ2	θ2	ADV
ma-179	283	34	−	−	PROPN
ma-179	283	35	2z1)1/2	2z1)1/2	NUM
ma-179	283	36	=	=	SYM
ma-179	283	37	θ	θ	PROPN
ma-179	283	38	[	[	PUNCT
ma-179	283	39	1−	1−	NUM
ma-179	283	40	z1	z1	VERB
ma-179	283	41	θ2	θ2	PROPN
ma-179	283	42	−	−	PROPN
ma-179	283	43	z2	z2	PROPN
ma-179	283	44	1	1	NUM
ma-179	283	45	2θ4	2θ4	NUM
ma-179	284	1	+	+	CCONJ
ma-179	284	2	z3	z3	PROPN
ma-179	284	3	1	1	NUM
ma-179	284	4	2θ8	2θ8	NUM
ma-179	284	5	+	+	PUNCT
ma-179	284	6	·	·	PUNCT
ma-179	284	7	·	·	PUNCT
ma-179	284	8	·	·	PUNCT
ma-179	284	9	]	]	PUNCT
ma-179	285	1	=	=	PUNCT
ma-179	285	2	θ	θ	X
ma-179	285	3	[	[	PUNCT
ma-179	285	4	1	1	NUM
ma-179	285	5	+	+	CCONJ
ma-179	285	6	iu	iu	ADP
ma-179	285	7	δt	δt	NOUN
ma-179	285	8	,	,	PUNCT
ma-179	285	9	x	x	X
ma-179	285	10	θ	θ	PROPN
ma-179	285	11	+	+	CCONJ
ma-179	285	12	u2δ2	u2δ2	PROPN
ma-179	285	13	t	t	PROPN
ma-179	285	14	,	,	PUNCT
ma-179	285	15	x	x	PRON
ma-179	285	16	2θ2	2θ2	NUM
ma-179	285	17	+	+	CCONJ
ma-179	285	18	iu3δ3	iu3δ3	PROPN
ma-179	285	19	t	t	PROPN
ma-179	285	20	,	,	PUNCT
ma-179	285	21	x	x	PROPN
ma-179	285	22	2θ3	2θ3	NUM
ma-179	285	23	+	+	NUM
ma-179	285	24	·	·	PUNCT
ma-179	285	25	·	·	PUNCT
ma-179	285	26	·	·	PUNCT
ma-179	285	27	]	]	PUNCT
ma-179	286	1	=	=	PUNCT
ma-179	286	2	θ[1	θ[1	PROPN
ma-179	286	3	+	+	X
ma-179	287	1	α1,t	α1,t	NOUN
ma-179	287	2	(	(	PUNCT
ma-179	287	3	u	u	NOUN
ma-179	287	4	)	)	PUNCT
ma-179	287	5	+	+	CCONJ
ma-179	287	6	α2,t	α2,t	PROPN
ma-179	287	7	(	(	PUNCT
ma-179	287	8	u	u	NOUN
ma-179	287	9	)	)	PUNCT
ma-179	288	1	+	+	CCONJ
ma-179	288	2	α3,t	α3,t	PROPN
ma-179	288	3	(	(	PUNCT
ma-179	288	4	u	u	NOUN
ma-179	288	5	)	)	PUNCT
ma-179	288	6	]	]	PUNCT
ma-179	289	1	=	=	PUNCT
ma-179	289	2	θβt	θβt	PROPN
ma-179	289	3	(	(	PUNCT
ma-179	289	4	u	u	NOUN
ma-179	289	5	)	)	PUNCT
ma-179	289	6	+	+	CCONJ
ma-179	289	7	α3,t	α3,t	PROPN
ma-179	289	8	(	(	PUNCT
ma-179	289	9	u	u	NOUN
ma-179	289	10	)	)	PUNCT
ma-179	289	11	=	=	PUNCT
ma-179	289	12	θ[1	θ[1	PROPN
ma-179	290	1	+	+	X
ma-179	290	2	α1,t	α1,t	PROPN
ma-179	290	3	(	(	PUNCT
ma-179	290	4	u	u	NOUN
ma-179	290	5	)	)	PUNCT
ma-179	290	6	]	]	PUNCT
ma-179	290	7	.	.	PUNCT
ma-179	291	1	thus	thus	ADV
ma-179	291	2	γ	γ	X
ma-179	291	3	−	−	PROPN
ma-179	291	4	θ	θ	NOUN
ma-179	291	5	=	=	SYM
ma-179	291	6	α1,t	α1,t	PROPN
ma-179	291	7	,	,	PUNCT
ma-179	291	8	γ	γ	X
ma-179	291	9	+	+	NOUN
ma-179	291	10	θ	θ	NOUN
ma-179	291	11	=	=	PUNCT
ma-179	291	12	2θ	2θ	NUM
ma-179	291	13	+	+	CCONJ
ma-179	292	1	α1,t	α1,t	NOUN
ma-179	292	2	.	.	PUNCT
ma-179	293	1	hence	hence	ADV
ma-179	293	2	the	the	DET
ma-179	293	3	above	above	ADJ
ma-179	293	4	expectation	expectation	NOUN
ma-179	293	5	equals	equal	VERB
ma-179	293	6	exp	exp	NOUN
ma-179	293	7	(	(	PUNCT
ma-179	293	8	z3	z3	PROPN
ma-179	293	9	+	+	CCONJ
ma-179	293	10	θt	θt	PROPN
ma-179	293	11	2	2	NUM
ma-179	293	12	)	)	PUNCT
ma-179	294	1	[	[	PUNCT
ma-179	294	2	2θβt	2θβt	NUM
ma-179	294	3	(	(	PUNCT
ma-179	294	4	u	u	NOUN
ma-179	294	5	)	)	PUNCT
ma-179	294	6	+	+	CCONJ
ma-179	294	7	α3,t	α3,t	PROPN
ma-179	294	8	(	(	PUNCT
ma-179	294	9	u	u	NOUN
ma-179	294	10	)	)	PUNCT
ma-179	294	11	α1,t	α1,t	NOUN
ma-179	294	12	exp{−θtβt	exp{−θtβt	PUNCT
ma-179	294	13	(	(	PUNCT
ma-179	294	14	u	u	NOUN
ma-179	294	15	)	)	PUNCT
ma-179	294	16	+	+	CCONJ
ma-179	294	17	α4,t	α4,t	PROPN
ma-179	294	18	(	(	PUNCT
ma-179	294	19	u)}+	u)}+	NUM
ma-179	294	20	(	(	PUNCT
ma-179	294	21	2θ	2θ	NUM
ma-179	294	22	+	+	X
ma-179	294	23	α1,t	α1,t	NOUN
ma-179	294	24	(	(	PUNCT
ma-179	294	25	u	u	NOUN
ma-179	294	26	)	)	PUNCT
ma-179	294	27	)	)	PUNCT
ma-179	294	28	exp{θtβt	exp{θtβt	ADP
ma-179	294	29	(	(	PUNCT
ma-179	294	30	u	u	NOUN
ma-179	294	31	)	)	PUNCT
ma-179	294	32	+	+	CCONJ
ma-179	294	33	α4,t	α4,t	PROPN
ma-179	294	34	(	(	PUNCT
ma-179	294	35	u	u	NOUN
ma-179	294	36	)	)	PUNCT
ma-179	294	37	}	}	PUNCT
ma-179	294	38	]	]	PUNCT
ma-179	294	39	1/2	1/2	NUM
ma-179	294	40	=	=	PUNCT
ma-179	294	41	[	[	PUNCT
ma-179	294	42	1	1	NUM
ma-179	294	43	+	+	NUM
ma-179	294	44	α1,t	α1,t	PROPN
ma-179	294	45	(	(	PUNCT
ma-179	294	46	u	u	NOUN
ma-179	294	47	)	)	PUNCT
ma-179	294	48	α1,t	α1,t	NOUN
ma-179	294	49	exp(χt	exp(χt	X
ma-179	294	50	(	(	PUNCT
ma-179	294	51	u	u	NOUN
ma-179	294	52	)	)	PUNCT
ma-179	294	53	)	)	PUNCT
ma-179	295	1	+	+	CCONJ
ma-179	295	2	(	(	PUNCT
ma-179	295	3	1	1	NUM
ma-179	295	4	+	+	NUM
ma-179	295	5	α1,t	α1,t	PROPN
ma-179	295	6	(	(	PUNCT
ma-179	295	7	u	u	NOUN
ma-179	295	8	)	)	PUNCT
ma-179	295	9	)	)	PUNCT
ma-179	295	10	exp(ψt	exp(ψt	NOUN
ma-179	295	11	(	(	PUNCT
ma-179	295	12	u	u	NOUN
ma-179	295	13	)	)	PUNCT
ma-179	295	14	)	)	PUNCT
ma-179	296	1	]	]	PUNCT
ma-179	296	2	1/2	1/2	NUM
ma-179	296	3	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	NOUN
ma-179	296	4	eur	eur	NOUN
ma-179	296	5	.	.	PUNCT
ma-179	297	1	j.	j.	PROPN
ma-179	297	2	math	math	PROPN
ma-179	297	3	.	.	PUNCT
ma-179	298	1	anal	anal	PROPN
ma-179	298	2	.	.	PUNCT
ma-179	299	1	10.28924	10.28924	NUM
ma-179	299	2	/	/	SYM
ma-179	299	3	ada	ada	PROPN
ma-179	299	4	/	/	SYM
ma-179	299	5	ma.3.25	ma.3.25	NOUN
ma-179	300	1	11where	11where	X
ma-179	300	2	χt	χt	ADP
ma-179	300	3	(	(	PUNCT
ma-179	300	4	u	u	NOUN
ma-179	300	5	)	)	PUNCT
ma-179	300	6	:	:	PUNCT
ma-179	300	7	=	=	SYM
ma-179	300	8	−θtβt	−θtβt	PROPN
ma-179	300	9	(	(	PUNCT
ma-179	300	10	u	u	NOUN
ma-179	300	11	)	)	PUNCT
ma-179	300	12	+	+	CCONJ
ma-179	300	13	α4,t	α4,t	PROPN
ma-179	300	14	(	(	PUNCT
ma-179	300	15	u)−	u)−	PROPN
ma-179	300	16	2z3	2z3	NUM
ma-179	300	17	−	−	NOUN
ma-179	300	18	θt	θt	PROPN
ma-179	300	19	=	=	PUNCT
ma-179	300	20	−2θt	−2θt	PROPN
ma-179	300	21	+	+	PROPN
ma-179	300	22	α1,t	α1,t	PROPN
ma-179	300	23	(	(	PUNCT
ma-179	300	24	u	u	NOUN
ma-179	300	25	)	)	PUNCT
ma-179	301	1	+	+	CCONJ
ma-179	301	2	t2α1,t	t2α1,t	NOUN
ma-179	301	3	(	(	PUNCT
ma-179	301	4	u	u	NOUN
ma-179	301	5	)	)	PUNCT
ma-179	301	6	,	,	PUNCT
ma-179	301	7	ψt	ψt	NOUN
ma-179	301	8	(	(	PUNCT
ma-179	301	9	u	u	NOUN
ma-179	301	10	)	)	PUNCT
ma-179	301	11	:	:	PUNCT
ma-179	301	12	=	=	SYM
ma-179	301	13	θtβt	θtβt	NOUN
ma-179	301	14	(	(	PUNCT
ma-179	301	15	u	u	NOUN
ma-179	301	16	)	)	PUNCT
ma-179	301	17	+	+	CCONJ
ma-179	301	18	α4,t	α4,t	PROPN
ma-179	301	19	(	(	PUNCT
ma-179	301	20	u)−	u)−	PROPN
ma-179	301	21	2z3	2z3	NUM
ma-179	301	22	−	−	NOUN
ma-179	301	23	θeθt	θeθt	NOUN
ma-179	301	24	=	=	PUNCT
ma-179	301	25	θt	θt	ADJ
ma-179	301	26	[	[	PUNCT
ma-179	301	27	1	1	NUM
ma-179	301	28	+	+	CCONJ
ma-179	301	29	iu	iu	ADP
ma-179	301	30	δt	δt	NOUN
ma-179	301	31	,	,	PUNCT
ma-179	301	32	x	x	X
ma-179	301	33	θ	θ	PROPN
ma-179	301	34	+	+	CCONJ
ma-179	301	35	u2δ2	u2δ2	PROPN
ma-179	301	36	t	t	PROPN
ma-179	301	37	,	,	PUNCT
ma-179	301	38	x	x	X
ma-179	301	39	2θ2	2θ2	NUM
ma-179	301	40	]	]	X
ma-179	301	41	+	+	CCONJ
ma-179	301	42	α4,t	α4,t	PROPN
ma-179	301	43	(	(	PUNCT
ma-179	301	44	u)−	u)−	PROPN
ma-179	301	45	i	i	PRON
ma-179	301	46	teθt	teθt	VERB
ma-179	301	47	δt	δt	NOUN
ma-179	301	48	,	,	PUNCT
ma-179	301	49	x	x	NOUN
ma-179	301	50	−	−	NOUN
ma-179	301	51	θeθt	θeθt	NOUN
ma-179	301	52	=	=	PUNCT
ma-179	301	53	u2eθt	u2eθt	NOUN
ma-179	301	54	2θ	2θ	NUM
ma-179	301	55	[	[	X
ma-179	301	56	(	(	PUNCT
ma-179	301	57	4θ2	4θ2	NUM
ma-179	301	58	e2θt	e2θt	PUNCT
ma-179	301	59	)	)	PUNCT
ma-179	301	60	1/2	1/2	NUM
ma-179	302	1	+	+	NUM
ma-179	302	2	2x	2x	NUM
ma-179	302	3	eθt	eθt	X
ma-179	302	4	]	]	SYM
ma-179	302	5	2	2	X
ma-179	302	6	=	=	SYM
ma-179	302	7	u2	u2	NOUN
ma-179	302	8	+	+	NUM
ma-179	302	9	u2α1,t	u2α1,t	PROPN
ma-179	302	10	(	(	PUNCT
ma-179	302	11	u	u	NOUN
ma-179	302	12	)	)	PUNCT
ma-179	302	13	.	.	PUNCT
ma-179	303	1	hence	hence	ADV
ma-179	303	2	,	,	PUNCT
ma-179	303	3	for	for	ADP
ma-179	303	4	the	the	DET
ma-179	303	5	given	give	VERB
ma-179	303	6	range	range	NOUN
ma-179	303	7	of	of	ADP
ma-179	303	8	values	value	NOUN
ma-179	303	9	of	of	ADP
ma-179	303	10	u	u	NOUN
ma-179	303	11	,	,	PUNCT
ma-179	303	12	χt	χt	ADP
ma-179	303	13	(	(	PUNCT
ma-179	303	14	u)−ψt	u)−ψt	X
ma-179	303	15	(	(	PUNCT
ma-179	303	16	u	u	NOUN
ma-179	303	17	)	)	PUNCT
ma-179	303	18	≤	≤	NOUN
ma-179	303	19	−θeθt	−θeθt	ADV
ma-179	303	20	.	.	PUNCT
ma-179	304	1	hence	hence	ADV
ma-179	304	2	the	the	DET
ma-179	304	3	above	above	ADJ
ma-179	304	4	expectationequals	expectationequal	NOUN
ma-179	304	5	exp(−	exp(−	PROPN
ma-179	304	6	t2	t2	PROPN
ma-179	304	7	2	2	NUM
ma-179	304	8	)	)	PUNCT
ma-179	304	9	(	(	PUNCT
ma-179	304	10	1	1	NUM
ma-179	304	11	+	+	CCONJ
ma-179	304	12	α1,t	α1,t	NOUN
ma-179	304	13	)	)	PUNCT
ma-179	304	14	1/2	1/2	NUM
ma-179	304	15	[	[	PUNCT
ma-179	304	16	α1,t	α1,t	PROPN
ma-179	304	17	exp{−2θeθt	exp{−2θeθt	PROPN
ma-179	304	18	+	+	PROPN
ma-179	304	19	α1,t	α1,t	PROPN
ma-179	304	20	+	+	NUM
ma-179	304	21	u2α1,t	u2α1,t	NOUN
ma-179	304	22	}	}	PUNCT
ma-179	304	23	+	+	CCONJ
ma-179	304	24	(	(	PUNCT
ma-179	304	25	1	1	NUM
ma-179	304	26	+	+	NUM
ma-179	304	27	α1,t	α1,t	PROPN
ma-179	304	28	(	(	PUNCT
ma-179	304	29	u	u	NOUN
ma-179	304	30	)	)	PUNCT
ma-179	304	31	)	)	PUNCT
ma-179	305	1	exp{t2α1,t	exp{t2α1,t	NOUN
ma-179	305	2	(	(	PUNCT
ma-179	305	3	u	u	NOUN
ma-179	305	4	)	)	PUNCT
ma-179	305	5	}	}	PUNCT
ma-179	305	6	]	]	PUNCT
ma-179	305	7	−1/2	−1/2	ADJ
ma-179	305	8	=	=	NOUN
ma-179	305	9	exp(−	exp(−	PROPN
ma-179	305	10	u2	u2	PROPN
ma-179	305	11	2	2	NUM
ma-179	305	12	)	)	PUNCT
ma-179	305	13	[	[	PUNCT
ma-179	305	14	1	1	NUM
ma-179	305	15	+	+	NUM
ma-179	305	16	α1,t	α1,t	NOUN
ma-179	305	17	)	)	PUNCT
ma-179	305	18	(	(	PUNCT
ma-179	305	19	1	1	NUM
ma-179	305	20	+	+	CCONJ
ma-179	305	21	α1,t	α1,t	NOUN
ma-179	305	22	(	(	PUNCT
ma-179	305	23	1	1	NUM
ma-179	305	24	+	+	CCONJ
ma-179	305	25	α1,t	α1,t	NOUN
ma-179	305	26	)	)	PUNCT
ma-179	305	27	exp{−θeθt	exp{−θeθt	PROPN
ma-179	306	1	+	+	PUNCT
ma-179	306	2	α1,t	α1,t	NOUN
ma-179	306	3	+	+	NUM
ma-179	306	4	t2α1,t	t2α1,t	NOUN
ma-179	306	5	}	}	PUNCT
ma-179	306	6	]	]	PUNCT
ma-179	306	7	exp(u2α1,t	exp(u2α1,t	ADJ
ma-179	306	8	(	(	PUNCT
ma-179	306	9	u	u	NOUN
ma-179	306	10	)	)	PUNCT
ma-179	306	11	)	)	PUNCT
ma-179	306	12	.	.	PUNCT
ma-179	307	1	lemma	lemma	PROPN
ma-179	307	2	2.4	2.4	NUM
ma-179	307	3	(	(	PUNCT
ma-179	307	4	c	c	NOUN
ma-179	307	5	)	)	PUNCT
ma-179	307	6	and	and	CCONJ
ma-179	307	7	lemma	lemma	PROPN
ma-179	307	8	2.2	2.2	NUM
ma-179	307	9	respectively	respectively	ADV
ma-179	307	10	give	give	VERB
ma-179	307	11	the	the	DET
ma-179	307	12	berry	berry	NOUN
ma-179	307	13	-	-	PUNCT
ma-179	307	14	esseen	esseen	VERB
ma-179	307	15	rate	rate	NOUN
ma-179	307	16	for	for	ADP
ma-179	307	17	zt	zt	PROPN
ma-179	307	18	and	and	CCONJ
ma-179	307	19	it	it	PRON
ma-179	307	20	immediatelyby	immediatelyby	ADV
ma-179	307	21	using	use	VERB
ma-179	307	22	the	the	DET
ma-179	307	23	esseen	esseen	PROPN
ma-179	307	24	’s	’s	PART
ma-179	307	25	lemma	lemma	PROPN
ma-179	307	26	1.1	1.1	NUM
ma-179	307	27	.	.	PUNCT
ma-179	308	1	corollary	corollary	ADJ
ma-179	308	2	2.1	2.1	NUM
ma-179	308	3	(	(	PUNCT
ma-179	308	4	a	a	NOUN
ma-179	308	5	)	)	PUNCT
ma-179	308	6	sup	sup	NOUN
ma-179	308	7	xεr	xεr	NOUN
ma-179	308	8	∣∣∣∣∣p	∣∣∣∣∣p	ADP
ma-179	308	9	{	{	PUNCT
ma-179	308	10	(	(	PUNCT
ma-179	308	11	4θ2	4θ2	NUM
ma-179	308	12	e2θt	e2θt	PUNCT
ma-179	308	13	)	)	PUNCT
ma-179	308	14	1/2	1/2	NUM
ma-179	308	15	zt	zt	PROPN
ma-179	308	16	≤	≤	NUM
ma-179	308	17	x	x	PUNCT
ma-179	308	18	}	}	PUNCT
ma-179	308	19	−φ(x	−φ(x	NOUN
ma-179	308	20	)	)	PUNCT
ma-179	308	21	∣∣∣∣∣	∣∣∣∣∣	ADP
ma-179	308	22	≤	≤	PROPN
ma-179	308	23	ce−θt	ce−θt	ADJ
ma-179	308	24	.	.	PUNCT
ma-179	309	1	(	(	PUNCT
ma-179	309	2	b	b	X
ma-179	309	3	)	)	PUNCT
ma-179	309	4	sup	sup	NOUN
ma-179	309	5	x∈r	x∈r	PROPN
ma-179	309	6	∣∣∣∣∣p	∣∣∣∣∣p	ADP
ma-179	309	7	{	{	PUNCT
ma-179	309	8	(	(	PUNCT
ma-179	309	9	4θ2	4θ2	NUM
ma-179	309	10	e2θt	e2θt	PUNCT
ma-179	309	11	)	)	PUNCT
ma-179	309	12	1/2	1/2	NUM
ma-179	309	13	(	(	PUNCT
ma-179	309	14	θit	θit	NOUN
ma-179	309	15	−	−	PROPN
ma-179	309	16	ξ2	ξ2	NOUN
ma-179	309	17	e	e	NOUN
ma-179	309	18	θt	θt	PROPN
ma-179	309	19	2	2	NUM
ma-179	309	20	)	)	PUNCT
ma-179	309	21	≤	≤	NOUN
ma-179	309	22	x	x	PUNCT
ma-179	309	23	}	}	PUNCT
ma-179	309	24	−φ(x	−φ(x	NOUN
ma-179	309	25	)	)	PUNCT
ma-179	310	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ma-179	310	2	≤	≤	PROPN
ma-179	310	3	ce−θt	ce−θt	NOUN
ma-179	310	4	.	.	PUNCT
ma-179	311	1	remark	remark	NOUN
ma-179	311	2	though	though	SCONJ
ma-179	311	3	this	this	PRON
ma-179	311	4	was	be	AUX
ma-179	311	5	basically	basically	ADV
ma-179	311	6	shown	show	VERB
ma-179	311	7	in	in	ADP
ma-179	311	8	lemma	lemma	PROPN
ma-179	311	9	2.1	2.1	NUM
ma-179	311	10	,	,	PUNCT
ma-179	311	11	here	here	ADV
ma-179	311	12	we	we	PRON
ma-179	311	13	obtain	obtain	VERB
ma-179	311	14	kolmogorov	kolmogorov	ADJ
ma-179	311	15	distance	distance	NOUN
ma-179	311	16	fora	forum	NOUN
ma-179	311	17	martingale	martingale	NOUN
ma-179	311	18	and	and	CCONJ
ma-179	311	19	kolmogorov	kolmogorov	ADJ
ma-179	311	20	distance	distance	NOUN
ma-179	311	21	for	for	ADP
ma-179	311	22	its	its	PRON
ma-179	311	23	quadratic	quadratic	ADJ
ma-179	311	24	variation	variation	NOUN
ma-179	311	25	through	through	ADP
ma-179	311	26	cameron	cameron	PROPN
ma-179	311	27	-	-	PUNCT
ma-179	311	28	matin	matin	PROPN
ma-179	311	29	typeresults	typeresult	NOUN
ma-179	311	30	which	which	PRON
ma-179	311	31	are	be	AUX
ma-179	311	32	generalization	generalization	NOUN
ma-179	311	33	of	of	ADP
ma-179	311	34	levy	levy	NOUN
ma-179	311	35	area	area	NOUN
ma-179	311	36	formula	formula	NOUN
ma-179	311	37	.	.	PUNCT
ma-179	312	1	in	in	ADP
ma-179	312	2	lemma	lemma	PROPN
ma-179	312	3	2.1	2.1	NUM
ma-179	312	4	,	,	PUNCT
ma-179	312	5	one	one	PRON
ma-179	312	6	could	could	AUX
ma-179	312	7	go	go	VERB
ma-179	312	8	directly	directly	ADV
ma-179	312	9	to	to	ADP
ma-179	312	10	thestein	thestein	ADJ
ma-179	312	11	-	-	PUNCT
ma-179	312	12	malliavin	malliavin	NOUN
ma-179	312	13	way	way	NOUN
ma-179	312	14	through	through	ADP
ma-179	312	15	wiener	wiener	NOUN
ma-179	312	16	chaos	chaos	NOUN
ma-179	312	17	expansion	expansion	NOUN
ma-179	312	18	which	which	PRON
ma-179	312	19	does	do	AUX
ma-179	312	20	not	not	PART
ma-179	312	21	depend	depend	VERB
ma-179	312	22	on	on	ADP
ma-179	312	23	any	any	DET
ma-179	312	24	martingalecharacteristics.before	martingalecharacteristics.before	PROPN
ma-179	312	25	we	we	PRON
ma-179	312	26	prove	prove	VERB
ma-179	312	27	the	the	DET
ma-179	312	28	results	result	NOUN
ma-179	312	29	on	on	ADP
ma-179	312	30	the	the	DET
ma-179	312	31	berry	berry	NOUN
ma-179	312	32	-	-	PUNCT
ma-179	312	33	esseen	esseen	PROPN
ma-179	312	34	bound	bind	VERB
ma-179	312	35	on	on	ADP
ma-179	312	36	the	the	DET
ma-179	312	37	kolmogorov	kolmogorov	ADJ
ma-179	312	38	distance	distance	NOUN
ma-179	312	39	for	for	ADP
ma-179	312	40	themle	themle	NOUN
ma-179	312	41	with	with	ADP
ma-179	312	42	random	random	ADJ
ma-179	312	43	norming	norming	NOUN
ma-179	312	44	we	we	PRON
ma-179	312	45	need	need	VERB
ma-179	312	46	the	the	DET
ma-179	312	47	following	follow	VERB
ma-179	312	48	large	large	ADJ
ma-179	312	49	deviation	deviation	NOUN
ma-179	312	50	result	result	NOUN
ma-179	312	51	for	for	ADP
ma-179	312	52	the	the	DET
ma-179	312	53	mle	mle	NOUN
ma-179	312	54	.	.	PUNCT
ma-179	313	1	this	this	DET
ma-179	313	2	canbe	canbe	NOUN
ma-179	313	3	obtained	obtain	VERB
ma-179	313	4	as	as	ADP
ma-179	313	5	a	a	DET
ma-179	313	6	consequence	consequence	NOUN
ma-179	313	7	of	of	ADP
ma-179	313	8	lemma	lemma	PROPN
ma-179	313	9	3.1	3.1	NUM
ma-179	313	10	of	of	ADP
ma-179	313	11	bercu	bercu	PROPN
ma-179	313	12	et	et	PROPN
ma-179	313	13	al	al	PROPN
ma-179	313	14	.	.	PUNCT
ma-179	314	1	[	[	X
ma-179	314	2	3	3	NUM
ma-179	314	3	]	]	PUNCT
ma-179	314	4	or	or	CCONJ
ma-179	314	5	bercu	bercu	NOUN
ma-179	314	6	and	and	CCONJ
ma-179	314	7	richou	richou	VERB
ma-179	314	8	[	[	X
ma-179	314	9	4	4	NUM
ma-179	314	10	]	]	PUNCT
ma-179	314	11	who	who	PRON
ma-179	314	12	usethe	usethe	VERB
ma-179	314	13	gartner	gartner	PROPN
ma-179	314	14	-	-	PUNCT
ma-179	314	15	ellis	ellis	PROPN
ma-179	314	16	’s	’s	PART
ma-179	314	17	theorem	theorem	NOUN
ma-179	314	18	and	and	CCONJ
ma-179	314	19	the	the	DET
ma-179	314	20	contraction	contraction	NOUN
ma-179	314	21	principle	principle	NOUN
ma-179	314	22	.	.	PUNCT
ma-179	315	1	however	however	ADV
ma-179	315	2	we	we	PRON
ma-179	315	3	give	give	VERB
ma-179	315	4	a	a	DET
ma-179	315	5	direct	direct	ADJ
ma-179	315	6	proof	proof	NOUN
ma-179	315	7	usingfeller	usingfeller	NOUN
ma-179	315	8	’s	’s	PART
ma-179	315	9	approach	approach	NOUN
ma-179	315	10	.	.	PUNCT
ma-179	316	1	lemma	lemma	PROPN
ma-179	316	2	2.5	2.5	NUM
ma-179	316	3	p	p	NOUN
ma-179	316	4	{	{	PUNCT
ma-179	316	5	(	(	PUNCT
ma-179	316	6	e2θt	e2θt	X
ma-179	316	7	4θ2	4θ2	NUM
ma-179	316	8	)	)	PUNCT
ma-179	316	9	1/2	1/2	NUM
ma-179	316	10	|θt	|θt	X
ma-179	316	11	−	−	PUNCT
ma-179	316	12	θ|	θ|	NOUN
ma-179	316	13	≥	≥	NOUN
ma-179	316	14	2(2θt	2(2θt	NUM
ma-179	316	15	)	)	PUNCT
ma-179	316	16	1/2	1/2	NUM
ma-179	316	17	}	}	PUNCT
ma-179	316	18	≤	≤	PROPN
ma-179	316	19	ce−θt	ce−θt	ADJ
ma-179	316	20	.	.	PUNCT
ma-179	317	1	proof	proof	NOUN
ma-179	317	2	:	:	PUNCT
ma-179	317	3	observe	observe	VERB
ma-179	317	4	that	that	SCONJ
ma-179	317	5	p	p	X
ma-179	317	6	{	{	PUNCT
ma-179	317	7	(	(	PUNCT
ma-179	317	8	e2θt	e2θt	X
ma-179	317	9	4θ2	4θ2	NUM
ma-179	317	10	)	)	PUNCT
ma-179	317	11	1/2	1/2	NUM
ma-179	317	12	|θt	|θt	X
ma-179	317	13	−	−	PUNCT
ma-179	317	14	θ|	θ|	NOUN
ma-179	317	15	≥	≥	NOUN
ma-179	317	16	2(2θt	2(2θt	NUM
ma-179	317	17	)	)	PUNCT
ma-179	317	18	1/2	1/2	NUM
ma-179	317	19	}	}	PUNCT
ma-179	317	20	=	=	PUNCT
ma-179	317	21	p	p	X
ma-179	317	22			PROPN
ma-179	317	23	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	X
ma-179	317	24	(	(	PUNCT
ma-179	317	25	4θ2	4θ2	NUM
ma-179	317	26	e2θt	e2θt	PUNCT
ma-179	317	27	)	)	PUNCT
ma-179	317	28	1/2	1/2	NUM
ma-179	317	29	zt	zt	PROPN
ma-179	317	30	(	(	PUNCT
ma-179	317	31	2θ	2θ	NUM
ma-179	317	32	e2θt	e2θt	PUNCT
ma-179	317	33	)	)	PUNCT
ma-179	317	34	it	it	PRON
ma-179	317	35	∣∣∣∣∣∣∣	∣∣∣∣∣∣∣	PUNCT
ma-179	317	36	≥	≥	NUM
ma-179	317	37	2(2θt	2(2θt	NUM
ma-179	317	38	)	)	PUNCT
ma-179	317	39	1/2	1/2	NUM
ma-179	317	40			PROPN
ma-179	317	41	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	PROPN
ma-179	317	42	eur	eur	PROPN
ma-179	317	43	.	.	PUNCT
ma-179	318	1	j.	j.	PROPN
ma-179	318	2	math	math	PROPN
ma-179	318	3	.	.	PUNCT
ma-179	319	1	anal	anal	PROPN
ma-179	319	2	.	.	PUNCT
ma-179	320	1	10.28924	10.28924	NUM
ma-179	320	2	/	/	SYM
ma-179	320	3	ada	ada	PROPN
ma-179	320	4	/	/	SYM
ma-179	320	5	ma.3.25	ma.3.25	NOUN
ma-179	321	1	12	12	NUM
ma-179	321	2	≤	≤	NOUN
ma-179	322	1	p	p	NOUN
ma-179	323	1	{	{	PUNCT
ma-179	324	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ma-179	324	2	(	(	PUNCT
ma-179	324	3	4θ2	4θ2	NUM
ma-179	324	4	e2θt	e2θt	PUNCT
ma-179	324	5	)	)	PUNCT
ma-179	324	6	1/2	1/2	NUM
ma-179	324	7	zt	zt	PROPN
ma-179	324	8	∣∣∣∣∣	∣∣∣∣∣	PROPN
ma-179	324	9	≥	≥	NOUN
ma-179	324	10	(	(	PUNCT
ma-179	324	11	θt	θt	PROPN
ma-179	324	12	)	)	PUNCT
ma-179	324	13	1/2	1/2	NUM
ma-179	324	14	}	}	PUNCT
ma-179	325	1	+	+	CCONJ
ma-179	325	2	p	p	X
ma-179	325	3	{	{	PUNCT
ma-179	325	4	∣∣∣∣	∣∣∣∣	NOUN
ma-179	325	5	2θ	2θ	NUM
ma-179	325	6	e2θt	e2θt	PUNCT
ma-179	325	7	it	it	PRON
ma-179	325	8	∣∣∣∣	∣∣∣∣	VERB
ma-179	325	9	≤	≤	NUM
ma-179	325	10	1	1	NUM
ma-179	325	11	2	2	NUM
ma-179	325	12	}	}	PUNCT
ma-179	325	13	≤	≤	X
ma-179	325	14	∣∣∣∣∣p	∣∣∣∣∣p	ADP
ma-179	325	15	{	{	PUNCT
ma-179	325	16	(	(	PUNCT
ma-179	325	17	4θ2	4θ2	NUM
ma-179	325	18	e2θt	e2θt	PUNCT
ma-179	325	19	)	)	PUNCT
ma-179	325	20	1/2	1/2	NUM
ma-179	325	21	|zt	|zt	NUM
ma-179	325	22	|	|	ADV
ma-179	325	23	≥	≥	NOUN
ma-179	325	24	(	(	PUNCT
ma-179	325	25	θt	θt	PROPN
ma-179	325	26	)	)	PUNCT
ma-179	325	27	1/2	1/2	NUM
ma-179	325	28	}	}	PUNCT
ma-179	325	29	−	−	PROPN
ma-179	325	30	2φ(−(2θt	2φ(−(2θt	NUM
ma-179	325	31	)	)	SYM
ma-179	325	32	1/2	1/2	NUM
ma-179	325	33	)	)	PUNCT
ma-179	325	34	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ma-179	325	35	2φ(−(2θt	2φ(−(2θt	NUM
ma-179	325	36	)	)	PUNCT
ma-179	325	37	1/2	1/2	NUM
ma-179	325	38	)	)	PUNCT
ma-179	326	1	+	+	CCONJ
ma-179	326	2	p	p	X
ma-179	326	3	{	{	PUNCT
ma-179	326	4	∣∣∣∣	∣∣∣∣	NOUN
ma-179	326	5	2θ	2θ	NUM
ma-179	326	6	e2θt	e2θt	PUNCT
ma-179	326	7	it	it	PRON
ma-179	326	8	−	−	ADV
ma-179	326	9	ξ2	ξ2	ADJ
ma-179	326	10	∣∣∣∣	∣∣∣∣	NOUN
ma-179	326	11	≥	≥	NUM
ma-179	326	12	1	1	NUM
ma-179	326	13	2	2	NUM
ma-179	326	14	}	}	PUNCT
ma-179	326	15	≤	≤	NUM
ma-179	326	16	sup	sup	NOUN
ma-179	326	17	x∈r	x∈r	PROPN
ma-179	326	18	∣∣∣∣∣p	∣∣∣∣∣p	ADP
ma-179	326	19	{	{	PUNCT
ma-179	326	20	(	(	PUNCT
ma-179	326	21	4θ2	4θ2	NUM
ma-179	326	22	e2θt	e2θt	PUNCT
ma-179	326	23	)	)	PUNCT
ma-179	326	24	1/2	1/2	NUM
ma-179	326	25	|zt	|zt	NUM
ma-179	326	26	|	|	ADV
ma-179	326	27	≥	≥	NOUN
ma-179	326	28	x	x	SYM
ma-179	326	29	}	}	PUNCT
ma-179	326	30	−	−	PROPN
ma-179	326	31	2φ(−x	2φ(−x	NUM
ma-179	326	32	)	)	PUNCT
ma-179	326	33	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ma-179	326	34	2φ(−(2θt	2φ(−(2θt	NUM
ma-179	326	35	)	)	PUNCT
ma-179	326	36	1/2	1/2	NUM
ma-179	326	37	)	)	PUNCT
ma-179	327	1	+	+	CCONJ
ma-179	328	1	p	p	X
ma-179	328	2	{	{	PUNCT
ma-179	328	3	∣∣∣∣	∣∣∣∣	PROPN
ma-179	328	4	(	(	PUNCT
ma-179	328	5	4θ2	4θ2	NUM
ma-179	328	6	e2θt	e2θt	PUNCT
ma-179	328	7	)	)	PUNCT
ma-179	329	1	it	it	PRON
ma-179	329	2	−	−	ADV
ma-179	329	3	ξ2	ξ2	ADJ
ma-179	329	4	∣∣∣∣	∣∣∣∣	NOUN
ma-179	329	5	≥	≥	NUM
ma-179	329	6	1	1	NUM
ma-179	329	7	2	2	NUM
ma-179	329	8	}	}	PUNCT
ma-179	329	9	≤	≤	NUM
ma-179	329	10	sup	sup	NOUN
ma-179	329	11	x∈r	x∈r	PROPN
ma-179	329	12	∣∣∣∣∣p	∣∣∣∣∣p	ADP
ma-179	329	13	{	{	PUNCT
ma-179	329	14	(	(	PUNCT
ma-179	329	15	4θ2	4θ2	NUM
ma-179	329	16	e2θt	e2θt	PUNCT
ma-179	329	17	)	)	PUNCT
ma-179	329	18	1/2	1/2	NUM
ma-179	329	19	|zt	|zt	NUM
ma-179	329	20	|	|	ADV
ma-179	329	21	≥	≥	NOUN
ma-179	329	22	x	x	SYM
ma-179	329	23	}	}	PUNCT
ma-179	329	24	−	−	PROPN
ma-179	329	25	2φ(−x	2φ(−x	NUM
ma-179	329	26	)	)	PUNCT
ma-179	329	27	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ma-179	329	28	2φ(−(2θt	2φ(−(2θt	NUM
ma-179	329	29	)	)	PUNCT
ma-179	329	30	1/2	1/2	NUM
ma-179	329	31	)	)	PUNCT
ma-179	330	1	+	+	CCONJ
ma-179	331	1	p	p	X
ma-179	331	2	{	{	PUNCT
ma-179	331	3	∣∣∣∣	∣∣∣∣	PROPN
ma-179	331	4	(	(	PUNCT
ma-179	331	5	4θ2	4θ2	NUM
ma-179	331	6	e2θt	e2θt	PUNCT
ma-179	331	7	)	)	PUNCT
ma-179	332	1	it	it	PRON
ma-179	332	2	−	−	ADV
ma-179	332	3	ξ2	ξ2	ADJ
ma-179	332	4	∣∣∣∣	∣∣∣∣	NOUN
ma-179	332	5	≥	≥	NUM
ma-179	332	6	1	1	NUM
ma-179	332	7	2	2	NUM
ma-179	332	8	}	}	PUNCT
ma-179	332	9	≤	≤	NOUN
ma-179	332	10	ce−θt	ce−θt	NOUN
ma-179	333	1	+	+	CCONJ
ma-179	333	2	c(e2θt	c(e2θt	AUX
ma-179	333	3	2θt	2θt	ADJ
ma-179	333	4	)	)	PUNCT
ma-179	333	5	−1/2	−1/2	ADJ
ma-179	333	6	+	+	CCONJ
ma-179	333	7	c(e2θt	c(e2θt	NUM
ma-179	333	8	)	)	PUNCT
ma-179	333	9	−1	−1	NOUN
ma-179	333	10	≤	≤	NOUN
ma-179	333	11	ce−θt	ce−θt	ADJ
ma-179	333	12	.	.	PUNCT
ma-179	334	1	the	the	DET
ma-179	334	2	bounds	bound	NOUN
ma-179	334	3	for	for	ADP
ma-179	334	4	the	the	DET
ma-179	334	5	first	first	ADJ
ma-179	334	6	and	and	CCONJ
ma-179	334	7	the	the	DET
ma-179	334	8	third	third	ADJ
ma-179	334	9	terms	term	NOUN
ma-179	334	10	come	come	VERB
ma-179	334	11	from	from	ADP
ma-179	334	12	corollary	corollary	ADJ
ma-179	334	13	2.1	2.1	NUM
ma-179	334	14	(	(	PUNCT
ma-179	334	15	a	a	NOUN
ma-179	334	16	)	)	PUNCT
ma-179	334	17	and	and	CCONJ
ma-179	334	18	lemma	lemma	PROPN
ma-179	334	19	2.3	2.3	NUM
ma-179	334	20	respectivelyand	respectivelyand	NOUN
ma-179	334	21	that	that	PRON
ma-179	334	22	for	for	ADP
ma-179	334	23	the	the	DET
ma-179	334	24	middle	middle	ADJ
ma-179	334	25	term	term	NOUN
ma-179	334	26	comes	come	VERB
ma-179	334	27	from	from	ADP
ma-179	334	28	feller	feller	NOUN
ma-179	334	29	(	(	PUNCT
ma-179	334	30	[	[	X
ma-179	334	31	17	17	NUM
ma-179	334	32	]	]	PUNCT
ma-179	334	33	,	,	PUNCT
ma-179	334	34	p.	p.	NOUN
ma-179	334	35	166	166	NUM
ma-179	334	36	)	)	PUNCT
ma-179	334	37	.	.	PUNCT
ma-179	335	1	we	we	PRON
ma-179	335	2	are	be	AUX
ma-179	335	3	now	now	ADV
ma-179	335	4	in	in	ADP
ma-179	335	5	a	a	DET
ma-179	335	6	position	position	NOUN
ma-179	335	7	to	to	PART
ma-179	335	8	obtain	obtain	VERB
ma-179	335	9	the	the	DET
ma-179	335	10	berry	berry	NOUN
ma-179	335	11	-	-	PUNCT
ma-179	335	12	esseen	esseen	NOUN
ma-179	335	13	bound	bind	VERB
ma-179	335	14	of	of	ADP
ma-179	335	15	the	the	DET
ma-179	335	16	order	order	NOUN
ma-179	335	17	o(e−θt	o(e−θt	NOUN
ma-179	335	18	)	)	PUNCT
ma-179	335	19	on	on	ADP
ma-179	335	20	thekolmogorov	thekolmogorov	NOUN
ma-179	335	21	distance	distance	NOUN
ma-179	335	22	for	for	ADP
ma-179	335	23	the	the	DET
ma-179	335	24	mle	mle	PROPN
ma-179	335	25	.	.	PROPN
ma-179	335	26	theorem	theorem	VERB
ma-179	335	27	2.2	2.2	NUM
ma-179	335	28	sup	sup	NOUN
ma-179	335	29	x∈r	x∈r	NOUN
ma-179	335	30	∣∣∣∣p	∣∣∣∣p	ADP
ma-179	335	31	{	{	PUNCT
ma-179	335	32	(	(	PUNCT
ma-179	335	33	eθt2θ	eθt2θ	PROPN
ma-179	335	34	)	)	PUNCT
ma-179	335	35	(	(	PUNCT
ma-179	335	36	θt	θt	PROPN
ma-179	335	37	−	−	PROPN
ma-179	335	38	θ	θ	PROPN
ma-179	335	39	)	)	PUNCT
ma-179	335	40	≤	≤	NUM
ma-179	335	41	x	x	PUNCT
ma-179	335	42	}	}	PUNCT
ma-179	335	43	−	−	ADP
ma-179	335	44	c(x	c(x	NOUN
ma-179	335	45	)	)	PUNCT
ma-179	335	46	∣∣∣∣	∣∣∣∣	NOUN
ma-179	335	47	=	=	SYM
ma-179	335	48	o(e−θt	o(e−θt	NOUN
ma-179	335	49	)	)	PUNCT
ma-179	335	50	.	.	PUNCT
ma-179	336	1	proof	proof	NOUN
ma-179	336	2	:	:	PUNCT
ma-179	336	3	we	we	PRON
ma-179	336	4	shall	shall	AUX
ma-179	336	5	consider	consider	VERB
ma-179	336	6	two	two	NUM
ma-179	336	7	possibilities	possibility	NOUN
ma-179	336	8	:	:	PUNCT
ma-179	336	9	(	(	PUNCT
ma-179	336	10	i	i	NOUN
ma-179	336	11	)	)	PUNCT
ma-179	336	12	|x	|x	NOUN
ma-179	337	1	|	|	ADV
ma-179	337	2	>	>	X
ma-179	337	3	2(θt	2(θt	NUM
ma-179	337	4	)	)	PUNCT
ma-179	337	5	1/2	1/2	NUM
ma-179	337	6	and	and	CCONJ
ma-179	337	7	(	(	PUNCT
ma-179	337	8	ii	ii	NOUN
ma-179	337	9	)	)	PUNCT
ma-179	337	10	|x	|x	NOUN
ma-179	337	11	|	|	ADV
ma-179	337	12	≤	≤	NOUN
ma-179	337	13	2(θt	2(θt	NUM
ma-179	337	14	)	)	PUNCT
ma-179	338	1	1/2.(i	1/2.(i	NUM
ma-179	338	2	)	)	PUNCT
ma-179	339	1	we	we	PRON
ma-179	339	2	shall	shall	AUX
ma-179	339	3	give	give	VERB
ma-179	339	4	a	a	DET
ma-179	339	5	proof	proof	NOUN
ma-179	339	6	for	for	ADP
ma-179	339	7	the	the	DET
ma-179	339	8	case	case	NOUN
ma-179	339	9	x	x	PUNCT
ma-179	339	10	>	>	X
ma-179	339	11	2(θt	2(θt	NUM
ma-179	339	12	)	)	PUNCT
ma-179	339	13	1/2	1/2	NUM
ma-179	339	14	.	.	PUNCT
ma-179	340	1	the	the	DET
ma-179	340	2	proof	proof	NOUN
ma-179	340	3	for	for	ADP
ma-179	340	4	the	the	DET
ma-179	340	5	case	case	NOUN
ma-179	340	6	x	x	X
ma-179	340	7	<	<	X
ma-179	340	8	−2(θt	−2(θt	X
ma-179	340	9	)	)	PUNCT
ma-179	340	10	1/2	1/2	NUM
ma-179	340	11	runssimilarly	runssimilarly	ADV
ma-179	340	12	.	.	PUNCT
ma-179	341	1	note	note	VERB
ma-179	341	2	that∣∣∣∣p	that∣∣∣∣p	NOUN
ma-179	341	3	{	{	PUNCT
ma-179	341	4	(	(	PUNCT
ma-179	341	5	eθt2θ	eθt2θ	PROPN
ma-179	341	6	)	)	PUNCT
ma-179	341	7	(	(	PUNCT
ma-179	341	8	θt	θt	PROPN
ma-179	341	9	−	−	PROPN
ma-179	341	10	θ	θ	PROPN
ma-179	341	11	)	)	PUNCT
ma-179	341	12	≤	≤	NUM
ma-179	341	13	x	x	PUNCT
ma-179	341	14	}	}	PUNCT
ma-179	341	15	−	−	ADP
ma-179	341	16	c(x	c(x	NOUN
ma-179	341	17	)	)	PUNCT
ma-179	341	18	∣∣∣∣	∣∣∣∣	NOUN
ma-179	341	19	≤	≤	NOUN
ma-179	341	20	p	p	X
ma-179	341	21	{	{	PUNCT
ma-179	341	22	(	(	PUNCT
ma-179	341	23	eθt2θ	eθt2θ	PROPN
ma-179	341	24	)	)	PUNCT
ma-179	341	25	(	(	PUNCT
ma-179	341	26	θt	θt	PROPN
ma-179	341	27	−	−	PROPN
ma-179	341	28	θ	θ	PROPN
ma-179	341	29	)	)	PUNCT
ma-179	341	30	≥	≥	NOUN
ma-179	341	31	x	x	SYM
ma-179	341	32	}	}	PUNCT
ma-179	341	33	+	+	CCONJ
ma-179	341	34	c(−x	c(−x	X
ma-179	341	35	)	)	PUNCT
ma-179	341	36	but	but	CCONJ
ma-179	341	37	c(−x	c(−x	X
ma-179	341	38	)	)	PUNCT
ma-179	341	39	≤	≤	NOUN
ma-179	341	40	c(−2(θt	c(−2(θt	PROPN
ma-179	341	41	)	)	PUNCT
ma-179	342	1	1/2	1/2	NUM
ma-179	342	2	)	)	PUNCT
ma-179	342	3	≤	≤	NOUN
ma-179	342	4	ce−2θt	ce−2θt	NUM
ma-179	342	5	.	.	PUNCT
ma-179	343	1	moreover	moreover	ADV
ma-179	343	2	by	by	ADP
ma-179	343	3	lemma	lemma	PROPN
ma-179	343	4	2.5	2.5	NUM
ma-179	343	5	,	,	PUNCT
ma-179	343	6	we	we	PRON
ma-179	343	7	have	have	VERB
ma-179	343	8	p	p	NOUN
ma-179	343	9	{	{	PUNCT
ma-179	343	10	(	(	PUNCT
ma-179	343	11	eθt	eθt	NOUN
ma-179	343	12	2θ	2θ	NUM
ma-179	343	13	)	)	PUNCT
ma-179	343	14	(	(	PUNCT
ma-179	343	15	θt	θt	PROPN
ma-179	343	16	−	−	PROPN
ma-179	343	17	θ	θ	PROPN
ma-179	343	18	)	)	PUNCT
ma-179	343	19	≥	≥	NOUN
ma-179	343	20	2(θt	2(θt	NUM
ma-179	343	21	)	)	PUNCT
ma-179	343	22	1/2	1/2	NUM
ma-179	343	23	}	}	PUNCT
ma-179	343	24	≤	≤	NOUN
ma-179	343	25	ce−θt/2	ce−θt/2	NOUN
ma-179	343	26	.	.	PUNCT
ma-179	344	1	hence	hence	ADV
ma-179	344	2	∣∣∣∣∣p	∣∣∣∣∣p	VERB
ma-179	344	3	{	{	PUNCT
ma-179	344	4	(	(	PUNCT
ma-179	344	5	eθt	eθt	NOUN
ma-179	344	6	2θ	2θ	NUM
ma-179	344	7	)	)	PUNCT
ma-179	344	8	1/2	1/2	NUM
ma-179	344	9	(	(	PUNCT
ma-179	344	10	θt	θt	PROPN
ma-179	344	11	−	−	PROPN
ma-179	344	12	θ	θ	PROPN
ma-179	344	13	)	)	PUNCT
ma-179	344	14	≤	≤	NUM
ma-179	344	15	x	x	PUNCT
ma-179	344	16	}	}	PUNCT
ma-179	344	17	−	−	ADP
ma-179	344	18	c(x	c(x	NOUN
ma-179	344	19	)	)	PUNCT
ma-179	344	20	∣∣∣∣∣	∣∣∣∣∣	ADP
ma-179	344	21	≤	≤	NOUN
ma-179	344	22	ce−θt/2	ce−θt/2	NOUN
ma-179	344	23	.	.	PUNCT
ma-179	345	1	(	(	PUNCT
ma-179	345	2	ii	ii	NOUN
ma-179	345	3	)	)	PUNCT
ma-179	345	4	let	let	VERB
ma-179	345	5	at	at	ADP
ma-179	345	6	:	:	PUNCT
ma-179	345	7	=	=	SYM
ma-179	345	8	{	{	PUNCT
ma-179	345	9	(	(	PUNCT
ma-179	345	10	eθt	eθt	NOUN
ma-179	345	11	2θ	2θ	NUM
ma-179	345	12	)	)	PUNCT
ma-179	345	13	|θt	|θt	X
ma-179	345	14	−	−	PUNCT
ma-179	345	15	θ|	θ|	PROPN
ma-179	345	16	≤	≤	VERB
ma-179	345	17	2(θt	2(θt	NUM
ma-179	345	18	)	)	PUNCT
ma-179	345	19	1/2	1/2	NUM
ma-179	345	20	}	}	PUNCT
ma-179	345	21	and	and	CCONJ
ma-179	345	22	bt	bt	X
ma-179	345	23	:	:	PUNCT
ma-179	345	24	=	=	SYM
ma-179	345	25	{	{	PUNCT
ma-179	345	26	it	it	PRON
ma-179	345	27	eθt	eθt	VERB
ma-179	345	28	>	>	X
ma-179	345	29	c0	c0	PROPN
ma-179	345	30	}	}	PUNCT
ma-179	345	31	where	where	SCONJ
ma-179	345	32	0	0	NUM
ma-179	345	33	<	<	X
ma-179	345	34	c0	c0	X
ma-179	345	35	<	<	X
ma-179	345	36	1	1	NUM
ma-179	345	37	2θ	2θ	NUM
ma-179	345	38	.	.	PUNCT
ma-179	346	1	by	by	ADP
ma-179	346	2	lemma	lemma	PROPN
ma-179	346	3	2.5	2.5	NUM
ma-179	346	4	,	,	PUNCT
ma-179	346	5	we	we	PRON
ma-179	346	6	have	have	VERB
ma-179	346	7	p	p	NOUN
ma-179	346	8	(	(	PUNCT
ma-179	346	9	act	act	PROPN
ma-179	346	10	)	)	PUNCT
ma-179	346	11	≤	≤	NUM
ma-179	346	12	ce−θt	ce−θt	ADJ
ma-179	346	13	.	.	PUNCT
ma-179	347	1	(	(	PUNCT
ma-179	347	2	2.34	2.34	NUM
ma-179	347	3	)	)	PUNCT
ma-179	347	4	by	by	ADP
ma-179	347	5	lemma	lemma	PROPN
ma-179	347	6	2.3	2.3	NUM
ma-179	347	7	,	,	PUNCT
ma-179	347	8	we	we	PRON
ma-179	347	9	have	have	VERB
ma-179	347	10	p	p	NOUN
ma-179	347	11	(	(	PUNCT
ma-179	347	12	bct	bct	NOUN
ma-179	347	13	)	)	PUNCT
ma-179	348	1	=	=	SYM
ma-179	348	2	p	p	NOUN
ma-179	348	3	{	{	PUNCT
ma-179	348	4	2θ	2θ	NUM
ma-179	348	5	eθt	eθt	ADV
ma-179	348	6	it	it	PRON
ma-179	348	7	−	−	PROPN
ma-179	348	8	ξ2	ξ2	VERB
ma-179	348	9	<	<	X
ma-179	348	10	2θc0	2θc0	NUM
ma-179	348	11	−	−	ADP
ma-179	348	12	ξ2	ξ2	NOUN
ma-179	348	13	}	}	PUNCT
ma-179	348	14	<	<	X
ma-179	348	15	p	p	X
ma-179	348	16	{	{	PUNCT
ma-179	348	17	∣∣∣∣	∣∣∣∣	NOUN
ma-179	348	18	2θ	2θ	NUM
ma-179	348	19	eθt	eθt	VERB
ma-179	348	20	it	it	PRON
ma-179	348	21	−	−	ADP
ma-179	348	22	ξ2	ξ2	ADJ
ma-179	348	23	∣∣∣∣	∣∣∣∣	PROPN
ma-179	348	24	>	>	X
ma-179	348	25	ξ2	ξ2	NOUN
ma-179	348	26	−	−	PROPN
ma-179	348	27	2θc0	2θc0	NUM
ma-179	348	28	}	}	PUNCT
ma-179	348	29	≤	≤	PROPN
ma-179	348	30	ce−θt	ce−θt	ADJ
ma-179	348	31	.	.	PUNCT
ma-179	349	1	(	(	PUNCT
ma-179	349	2	2.35	2.35	NUM
ma-179	349	3	)	)	PUNCT
ma-179	349	4	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	NOUN
ma-179	349	5	eur	eur	PROPN
ma-179	349	6	.	.	PUNCT
ma-179	350	1	j.	j.	PROPN
ma-179	350	2	math	math	PROPN
ma-179	350	3	.	.	PUNCT
ma-179	351	1	anal	anal	PROPN
ma-179	351	2	.	.	PUNCT
ma-179	352	1	10.28924	10.28924	NUM
ma-179	352	2	/	/	SYM
ma-179	352	3	ada	ada	PROPN
ma-179	352	4	/	/	PROPN
ma-179	352	5	ma.3.25	ma.3.25	NOUN
ma-179	352	6	13let	13let	PROPN
ma-179	352	7	b0	b0	NOUN
ma-179	352	8	be	be	AUX
ma-179	352	9	some	some	DET
ma-179	352	10	positive	positive	ADJ
ma-179	352	11	number	number	NOUN
ma-179	352	12	.	.	PUNCT
ma-179	353	1	for	for	ADP
ma-179	353	2	ω	ω	PROPN
ma-179	353	3	∈	∈	PROPN
ma-179	353	4	at	at	ADP
ma-179	353	5	∩bt	∩bt	NOUN
ma-179	353	6	and	and	CCONJ
ma-179	353	7	for	for	ADP
ma-179	353	8	all	all	DET
ma-179	353	9	t	t	PROPN
ma-179	353	10	>	>	X
ma-179	353	11	t0	t0	PROPN
ma-179	353	12	with	with	ADP
ma-179	353	13	4b0(2θt0)1/2	4b0(2θt0)1/2	PROPN
ma-179	353	14	(	(	PUNCT
ma-179	353	15	2θ	2θ	NUM
ma-179	353	16	eθt0	eθt0	PROPN
ma-179	353	17	)	)	PUNCT
ma-179	354	1	1/2	1/2	NUM
ma-179	354	2	≤	≤	NUM
ma-179	354	3	c0	c0	NOUN
ma-179	354	4	,	,	PUNCT
ma-179	354	5	we	we	PRON
ma-179	354	6	have	have	VERB
ma-179	354	7	(	(	PUNCT
ma-179	354	8	eθt	eθt	NOUN
ma-179	354	9	2θ	2θ	NUM
ma-179	354	10	)	)	PUNCT
ma-179	355	1	(	(	PUNCT
ma-179	355	2	θt	θt	PROPN
ma-179	355	3	−	−	PROPN
ma-179	355	4	θ	θ	PROPN
ma-179	355	5	)	)	PUNCT
ma-179	355	6	≤	≤	NOUN
ma-179	355	7	x	x	PUNCT
ma-179	355	8	⇒	⇒	VERB
ma-179	355	9	it	it	PRON
ma-179	355	10	+	+	CCONJ
ma-179	355	11	b0e	b0e	PUNCT
ma-179	355	12	θt	θt	PROPN
ma-179	355	13	(	(	PUNCT
ma-179	355	14	θt	θt	PROPN
ma-179	355	15	−	−	PROPN
ma-179	355	16	θ	θ	PROPN
ma-179	355	17	)	)	PUNCT
ma-179	355	18	<	<	X
ma-179	356	1	it	it	PRON
ma-179	356	2	+	+	CCONJ
ma-179	356	3	(	(	PUNCT
ma-179	356	4	eθt	eθt	NOUN
ma-179	356	5	2θ	2θ	NUM
ma-179	356	6	)	)	PUNCT
ma-179	356	7	2b0θx	2b0θx	NUM
ma-179	356	8	⇒	⇒	NOUN
ma-179	356	9	(	(	PUNCT
ma-179	356	10	eθt	eθt	NOUN
ma-179	356	11	2θ	2θ	NUM
ma-179	356	12	)	)	PUNCT
ma-179	356	13	(	(	PUNCT
ma-179	356	14	θt	θt	ADP
ma-179	356	15	−	−	PROPN
ma-179	356	16	θ)[it	θ)[it	PROPN
ma-179	356	17	+	+	CCONJ
ma-179	356	18	b0e	b0e	PUNCT
ma-179	356	19	θt	θt	PROPN
ma-179	356	20	(	(	PUNCT
ma-179	356	21	θt	θt	PROPN
ma-179	356	22	−	−	PROPN
ma-179	356	23	θ	θ	PROPN
ma-179	356	24	)	)	PUNCT
ma-179	356	25	]	]	PUNCT
ma-179	357	1	<	<	X
ma-179	357	2	x	x	PUNCT
ma-179	358	1	[	[	X
ma-179	358	2	it	it	PRON
ma-179	358	3	+	+	CCONJ
ma-179	358	4	(	(	PUNCT
ma-179	358	5	eθt	eθt	NOUN
ma-179	358	6	2θ	2θ	NUM
ma-179	358	7	)	)	PUNCT
ma-179	358	8	2b0θx	2b0θx	NUM
ma-179	358	9	]	]	PUNCT
ma-179	358	10	⇒	⇒	NOUN
ma-179	358	11	(	(	PUNCT
ma-179	358	12	θt	θt	ADP
ma-179	358	13	−	−	PROPN
ma-179	358	14	θ)it	θ)it	PROPN
ma-179	358	15	+	+	SYM
ma-179	358	16	b0	b0	PROPN
ma-179	358	17	t	t	PROPN
ma-179	358	18	(	(	PUNCT
ma-179	358	19	θt	θt	PROPN
ma-179	358	20	−	−	PROPN
ma-179	358	21	θ)2	θ)2	NOUN
ma-179	358	22	<	<	X
ma-179	358	23	(	(	PUNCT
ma-179	358	24	2θ	2θ	NUM
ma-179	358	25	eθt	eθt	X
ma-179	358	26	)	)	PUNCT
ma-179	358	27	it	it	PRON
ma-179	358	28	x	x	PUNCT
ma-179	359	1	+	+	CCONJ
ma-179	359	2	2b0θx	2b0θx	NUM
ma-179	359	3	2	2	NUM
ma-179	359	4	⇒	⇒	NOUN
ma-179	359	5	zt	zt	PROPN
ma-179	359	6	+	+	CCONJ
ma-179	359	7	(	(	PUNCT
ma-179	359	8	θt	θt	X
ma-179	359	9	−	−	PROPN
ma-179	359	10	θ)it	θ)it	PROPN
ma-179	359	11	+	+	CCONJ
ma-179	359	12	b0e	b0e	PUNCT
ma-179	359	13	θt	θt	PROPN
ma-179	359	14	(	(	PUNCT
ma-179	359	15	θt	θt	PROPN
ma-179	359	16	−	−	PROPN
ma-179	359	17	θ)2	θ)2	NOUN
ma-179	359	18	<	<	X
ma-179	359	19	zt	zt	PROPN
ma-179	359	20	+	+	CCONJ
ma-179	359	21	(	(	PUNCT
ma-179	359	22	2θ	2θ	NUM
ma-179	359	23	eθt	eθt	X
ma-179	359	24	)	)	PUNCT
ma-179	359	25	it	it	PRON
ma-179	359	26	x	x	PUNCT
ma-179	360	1	+	+	CCONJ
ma-179	360	2	2b0θx	2b0θx	NUM
ma-179	360	3	2	2	NUM
ma-179	360	4	⇒	⇒	NOUN
ma-179	360	5	0	0	PUNCT
ma-179	360	6	<	<	X
ma-179	360	7	zt	zt	PROPN
ma-179	360	8	+	+	CCONJ
ma-179	360	9	(	(	PUNCT
ma-179	360	10	2θ	2θ	NUM
ma-179	360	11	eθt	eθt	X
ma-179	360	12	)	)	PUNCT
ma-179	360	13	it	it	PRON
ma-179	360	14	x	x	PUNCT
ma-179	361	1	+	+	CCONJ
ma-179	361	2	2b0θx	2b0θx	NUM
ma-179	361	3	2	2	NUM
ma-179	361	4	since	since	SCONJ
ma-179	361	5	it	it	PRON
ma-179	361	6	+	+	CCONJ
ma-179	361	7	b0e	b0e	PUNCT
ma-179	361	8	θt	θt	PROPN
ma-179	361	9	(	(	PUNCT
ma-179	361	10	θt	θt	PROPN
ma-179	361	11	−	−	PROPN
ma-179	361	12	θ	θ	PROPN
ma-179	361	13	)	)	PUNCT
ma-179	361	14	>	>	X
ma-179	361	15	eθt	eθt	PROPN
ma-179	361	16	c0	c0	PROPN
ma-179	361	17	+	+	CCONJ
ma-179	361	18	b0e	b0e	PUNCT
ma-179	361	19	θt	θt	PROPN
ma-179	361	20	(	(	PUNCT
ma-179	361	21	θt	θt	PROPN
ma-179	361	22	−	−	PROPN
ma-179	361	23	θ	θ	PROPN
ma-179	361	24	)	)	PUNCT
ma-179	361	25	>	>	X
ma-179	361	26	4b0(θt	4b0(θt	PUNCT
ma-179	362	1	)	)	PUNCT
ma-179	362	2	1/2	1/2	NUM
ma-179	362	3	(	(	PUNCT
ma-179	362	4	2θ	2θ	NUM
ma-179	362	5	eθt	eθt	NOUN
ma-179	362	6	)	)	PUNCT
ma-179	363	1	−	−	PROPN
ma-179	363	2	2b0(θt	2b0(θt	NUM
ma-179	363	3	)	)	PUNCT
ma-179	363	4	1/2	1/2	NUM
ma-179	363	5	(	(	PUNCT
ma-179	363	6	2θ	2θ	NUM
ma-179	363	7	eθt	eθt	X
ma-179	363	8	)	)	PUNCT
ma-179	363	9	=	=	SYM
ma-179	364	1	2b0(θt	2b0(θt	NUM
ma-179	364	2	)	)	PUNCT
ma-179	364	3	1/2	1/2	NUM
ma-179	364	4	(	(	PUNCT
ma-179	364	5	2θ	2θ	NUM
ma-179	364	6	eθt	eθt	X
ma-179	364	7	)	)	PUNCT
ma-179	364	8	>	>	X
ma-179	365	1	0	0	X
ma-179	365	2	.	.	PUNCT
ma-179	366	1	hence	hence	ADV
ma-179	366	2	,	,	PUNCT
ma-179	366	3	for	for	ADP
ma-179	366	4	ω	ω	PROPN
ma-179	366	5	∈	∈	PROPN
ma-179	366	6	at	at	ADP
ma-179	366	7	∩	∩	PROPN
ma-179	366	8	bt	bt	PROPN
ma-179	366	9	,	,	PUNCT
ma-179	366	10	(	(	PUNCT
ma-179	366	11	eθt	eθt	NOUN
ma-179	366	12	2θ	2θ	NUM
ma-179	366	13	)	)	PUNCT
ma-179	366	14	(	(	PUNCT
ma-179	366	15	θt	θt	PROPN
ma-179	366	16	−	−	PROPN
ma-179	366	17	θ	θ	PROPN
ma-179	366	18	)	)	PUNCT
ma-179	366	19	≤	≤	NOUN
ma-179	366	20	x	x	PUNCT
ma-179	366	21	⇒	⇒	NOUN
ma-179	366	22	zt	zt	PROPN
ma-179	367	1	+	+	CCONJ
ma-179	367	2	(	(	PUNCT
ma-179	367	3	2θ	2θ	NUM
ma-179	367	4	eθt	eθt	X
ma-179	367	5	)	)	PUNCT
ma-179	367	6	it	it	PRON
ma-179	367	7	x	x	PUNCT
ma-179	368	1	+	+	CCONJ
ma-179	368	2	2b0θx	2b0θx	NUM
ma-179	368	3	2	2	NUM
ma-179	368	4	>	>	X
ma-179	368	5	0	0	NUM
ma-179	368	6	.	.	PUNCT
ma-179	369	1	on	on	ADP
ma-179	369	2	the	the	DET
ma-179	369	3	other	other	ADJ
ma-179	369	4	hand	hand	NOUN
ma-179	369	5	,	,	PUNCT
ma-179	369	6	for	for	SCONJ
ma-179	369	7	ω	ω	PROPN
ma-179	369	8	∈	∈	PROPN
ma-179	369	9	at	at	ADP
ma-179	369	10	∩	∩	ADJ
ma-179	369	11	bt	bt	NOUN
ma-179	369	12	and	and	CCONJ
ma-179	369	13	for	for	ADP
ma-179	369	14	all	all	DET
ma-179	369	15	t	t	PROPN
ma-179	369	16	>	>	X
ma-179	369	17	t0	t0	PROPN
ma-179	369	18	with	with	ADP
ma-179	369	19	4b0(2θt0)1/2	4b0(2θt0)1/2	PROPN
ma-179	369	20	(	(	PUNCT
ma-179	369	21	2θ	2θ	NUM
ma-179	369	22	eθt0	eθt0	NOUN
ma-179	369	23	)	)	PUNCT
ma-179	369	24	≤	≤	NUM
ma-179	369	25	c0	c0	NOUN
ma-179	369	26	,	,	PUNCT
ma-179	369	27	we	we	PRON
ma-179	369	28	have	have	VERB
ma-179	369	29	(	(	PUNCT
ma-179	369	30	eθt	eθt	NOUN
ma-179	369	31	2θ	2θ	NUM
ma-179	369	32	)	)	PUNCT
ma-179	370	1	(	(	PUNCT
ma-179	370	2	θt	θt	PROPN
ma-179	370	3	−	−	PROPN
ma-179	370	4	θ	θ	PROPN
ma-179	370	5	)	)	PUNCT
ma-179	370	6	>	>	X
ma-179	370	7	x	x	PUNCT
ma-179	370	8	⇒	⇒	VERB
ma-179	370	9	it	it	PRON
ma-179	370	10	−	−	PROPN
ma-179	370	11	b0e	b0e	X
ma-179	370	12	θt	θt	PROPN
ma-179	370	13	(	(	PUNCT
ma-179	370	14	θt	θt	PROPN
ma-179	370	15	−	−	PROPN
ma-179	370	16	θ	θ	PROPN
ma-179	370	17	)	)	PUNCT
ma-179	370	18	<	<	X
ma-179	371	1	it	it	PRON
ma-179	371	2	−	−	PROPN
ma-179	371	3	(	(	PUNCT
ma-179	371	4	eθt	eθt	NOUN
ma-179	371	5	2θ	2θ	NUM
ma-179	371	6	)	)	PUNCT
ma-179	371	7	2b0θx	2b0θx	NUM
ma-179	371	8	⇒	⇒	NOUN
ma-179	371	9	(	(	PUNCT
ma-179	371	10	eθt	eθt	NOUN
ma-179	371	11	2θ	2θ	NUM
ma-179	371	12	)	)	PUNCT
ma-179	371	13	(	(	PUNCT
ma-179	371	14	θt	θt	NUM
ma-179	371	15	−	−	PROPN
ma-179	371	16	θ)[it	θ)[it	PROPN
ma-179	371	17	−	−	PROPN
ma-179	371	18	b0e	b0e	X
ma-179	371	19	θt	θt	PROPN
ma-179	371	20	(	(	PUNCT
ma-179	371	21	θt	θt	PROPN
ma-179	371	22	−	−	PROPN
ma-179	371	23	θ	θ	PROPN
ma-179	371	24	)	)	PUNCT
ma-179	371	25	]	]	PUNCT
ma-179	371	26	>	>	X
ma-179	371	27	x	x	PUNCT
ma-179	372	1	[	[	X
ma-179	372	2	it	it	PRON
ma-179	372	3	−	−	X
ma-179	372	4	(	(	PUNCT
ma-179	372	5	eθt	eθt	NOUN
ma-179	372	6	2θ	2θ	NUM
ma-179	372	7	)	)	PUNCT
ma-179	372	8	2b0θx	2b0θx	NUM
ma-179	372	9	]	]	PUNCT
ma-179	372	10	⇒	⇒	NOUN
ma-179	372	11	(	(	PUNCT
ma-179	372	12	θt	θt	PROPN
ma-179	372	13	−	−	PROPN
ma-179	372	14	θ)it	θ)it	PROPN
ma-179	372	15	−	−	PROPN
ma-179	372	16	b0e	b0e	X
ma-179	372	17	θt	θt	PROPN
ma-179	372	18	(	(	PUNCT
ma-179	372	19	θt	θt	PROPN
ma-179	372	20	−	−	PROPN
ma-179	372	21	θ)2	θ)2	NOUN
ma-179	372	22	>	>	X
ma-179	373	1	(	(	PUNCT
ma-179	373	2	2θ	2θ	NUM
ma-179	373	3	eθt	eθt	X
ma-179	373	4	)	)	PUNCT
ma-179	373	5	it	it	PRON
ma-179	373	6	x	x	PUNCT
ma-179	374	1	−	−	ADP
ma-179	374	2	2b0θx	2b0θx	NUM
ma-179	374	3	2	2	NUM
ma-179	374	4	⇒	⇒	NOUN
ma-179	374	5	zt	zt	PROPN
ma-179	374	6	+	+	CCONJ
ma-179	374	7	(	(	PUNCT
ma-179	374	8	θt	θt	PROPN
ma-179	374	9	−	−	PROPN
ma-179	374	10	θ)it	θ)it	PROPN
ma-179	374	11	−	−	PROPN
ma-179	374	12	b0e	b0e	X
ma-179	374	13	θt	θt	PROPN
ma-179	374	14	(	(	PUNCT
ma-179	374	15	θt	θt	PROPN
ma-179	374	16	−	−	PROPN
ma-179	374	17	θ)2	θ)2	PROPN
ma-179	374	18	>	>	X
ma-179	374	19	zt	zt	PROPN
ma-179	375	1	+	+	CCONJ
ma-179	375	2	(	(	PUNCT
ma-179	375	3	2θ	2θ	NUM
ma-179	375	4	eθt	eθt	X
ma-179	375	5	)	)	PUNCT
ma-179	375	6	it	it	PRON
ma-179	375	7	x	x	PUNCT
ma-179	376	1	−	−	ADP
ma-179	376	2	2b0θx	2b0θx	NUM
ma-179	376	3	2	2	NUM
ma-179	376	4	⇒	⇒	NOUN
ma-179	376	5	0	0	NUM
ma-179	376	6	>	>	X
ma-179	376	7	zt	zt	PROPN
ma-179	376	8	+	+	CCONJ
ma-179	376	9	(	(	PUNCT
ma-179	376	10	2θ	2θ	NUM
ma-179	376	11	eθt	eθt	X
ma-179	376	12	)	)	PUNCT
ma-179	376	13	it	it	PRON
ma-179	377	1	x	x	PUNCT
ma-179	377	2	−	−	NOUN
ma-179	377	3	2b0θx	2b0θx	NUM
ma-179	377	4	2	2	NUM
ma-179	377	5	since	since	SCONJ
ma-179	377	6	it	it	PRON
ma-179	377	7	−	−	NUM
ma-179	377	8	b0e	b0e	VERB
ma-179	377	9	θt	θt	PROPN
ma-179	377	10	(	(	PUNCT
ma-179	377	11	θt	θt	PROPN
ma-179	377	12	−	−	PROPN
ma-179	377	13	θ	θ	PROPN
ma-179	377	14	)	)	PUNCT
ma-179	377	15	>	>	X
ma-179	377	16	eθt	eθt	PROPN
ma-179	377	17	c0	c0	PROPN
ma-179	377	18	−	−	PROPN
ma-179	377	19	b0e	b0e	X
ma-179	377	20	θt	θt	PROPN
ma-179	377	21	(	(	PUNCT
ma-179	377	22	θt	θt	PROPN
ma-179	377	23	−	−	PROPN
ma-179	377	24	θ	θ	PROPN
ma-179	377	25	)	)	PUNCT
ma-179	377	26	>	>	X
ma-179	377	27	4b0(θt	4b0(θt	PUNCT
ma-179	377	28	)	)	PUNCT
ma-179	377	29	1/2	1/2	NUM
ma-179	377	30	(	(	PUNCT
ma-179	377	31	2θ	2θ	NUM
ma-179	377	32	eθt	eθt	NOUN
ma-179	377	33	)	)	PUNCT
ma-179	378	1	−	−	PROPN
ma-179	378	2	2b0(θt	2b0(θt	NUM
ma-179	378	3	)	)	PUNCT
ma-179	378	4	1/2	1/2	NUM
ma-179	378	5	(	(	PUNCT
ma-179	378	6	2θ	2θ	NUM
ma-179	378	7	eθt	eθt	X
ma-179	378	8	)	)	PUNCT
ma-179	378	9	=	=	SYM
ma-179	379	1	2b0(θt	2b0(θt	NUM
ma-179	379	2	)	)	PUNCT
ma-179	379	3	1/2	1/2	NUM
ma-179	379	4	(	(	PUNCT
ma-179	379	5	2θ	2θ	NUM
ma-179	379	6	eθt	eθt	X
ma-179	379	7	)	)	PUNCT
ma-179	379	8	>	>	X
ma-179	380	1	0	0	X
ma-179	380	2	.	.	PUNCT
ma-179	380	3	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	PROPN
ma-179	380	4	eur	eur	PROPN
ma-179	380	5	.	.	PUNCT
ma-179	381	1	j.	j.	PROPN
ma-179	381	2	math	math	PROPN
ma-179	381	3	.	.	PUNCT
ma-179	382	1	anal	anal	PROPN
ma-179	382	2	.	.	PUNCT
ma-179	383	1	10.28924	10.28924	NUM
ma-179	383	2	/	/	SYM
ma-179	383	3	ada	ada	PROPN
ma-179	383	4	/	/	PROPN
ma-179	383	5	ma.3.25	ma.3.25	PROPN
ma-179	383	6	14hence	14hence	NOUN
ma-179	383	7	,	,	PUNCT
ma-179	383	8	for	for	ADP
ma-179	383	9	ω	ω	PROPN
ma-179	383	10	∈	∈	PROPN
ma-179	383	11	at	at	ADP
ma-179	383	12	∩	∩	PROPN
ma-179	383	13	bt	bt	PROPN
ma-179	383	14	,	,	PUNCT
ma-179	383	15	0	0	PUNCT
ma-179	383	16	<	<	X
ma-179	383	17	zt	zt	PROPN
ma-179	383	18	+	+	CCONJ
ma-179	383	19	(	(	PUNCT
ma-179	383	20	2θ	2θ	NUM
ma-179	383	21	eθt	eθt	X
ma-179	383	22	)	)	PUNCT
ma-179	384	1	it	it	PRON
ma-179	384	2	x	x	PUNCT
ma-179	385	1	−	−	ADP
ma-179	385	2	2b0θx	2b0θx	NUM
ma-179	385	3	2	2	NUM
ma-179	385	4	⇒	⇒	NOUN
ma-179	385	5	(	(	PUNCT
ma-179	385	6	eθt	eθt	NOUN
ma-179	385	7	2θ	2θ	NUM
ma-179	385	8	)	)	PUNCT
ma-179	385	9	(	(	PUNCT
ma-179	385	10	θt	θt	PROPN
ma-179	385	11	−	−	PROPN
ma-179	385	12	θ	θ	PROPN
ma-179	385	13	)	)	PUNCT
ma-179	385	14	≤	≤	NUM
ma-179	385	15	x.	x.	NOUN
ma-179	386	1	we	we	PRON
ma-179	386	2	use	use	VERB
ma-179	386	3	the	the	DET
ma-179	386	4	squeezing	squeeze	VERB
ma-179	386	5	method	method	NOUN
ma-179	386	6	developed	develop	VERB
ma-179	386	7	in	in	ADP
ma-179	386	8	pfanzagl	pfanzagl	NOUN
ma-179	386	9	[	[	X
ma-179	386	10	28	28	NUM
ma-179	386	11	]	]	PUNCT
ma-179	386	12	for	for	ADP
ma-179	386	13	the	the	DET
ma-179	386	14	i.i.d	i.i.d	NOUN
ma-179	386	15	.	.	PUNCT
ma-179	387	1	case	case	NOUN
ma-179	387	2	instead	instead	ADV
ma-179	387	3	of	of	ADP
ma-179	387	4	the	the	DET
ma-179	387	5	splittingmethod	splittingmethod	NOUN
ma-179	387	6	of	of	ADP
ma-179	387	7	michel	michel	PROPN
ma-179	387	8	and	and	CCONJ
ma-179	387	9	pfanzagl	pfanzagl	NOUN
ma-179	388	1	[	[	X
ma-179	388	2	28	28	NUM
ma-179	388	3	]	]	PUNCT
ma-179	388	4	.	.	PUNCT
ma-179	389	1	let	let	VERB
ma-179	389	2	us	we	PRON
ma-179	389	3	introduce	introduce	VERB
ma-179	389	4	the	the	DET
ma-179	389	5	piecewise	piecewise	NOUN
ma-179	389	6	quadratic	quadratic	ADJ
ma-179	389	7	random	random	ADJ
ma-179	389	8	functionsinvolving	functionsinvolve	VERB
ma-179	389	9	the	the	DET
ma-179	389	10	martingale	martingale	ADJ
ma-179	389	11	and	and	CCONJ
ma-179	389	12	quadratic	quadratic	ADJ
ma-179	389	13	variation	variation	NOUN
ma-179	389	14	part	part	NOUN
ma-179	389	15	of	of	ADP
ma-179	389	16	θt	θt	PROPN
ma-179	389	17	−	−	PROPN
ma-179	389	18	θ	θ	PROPN
ma-179	389	19	:	:	PUNCT
ma-179	389	20	g±(x	g±(x	PROPN
ma-179	389	21	)	)	PUNCT
ma-179	389	22	:	:	PUNCT
ma-179	390	1	=	=	PUNCT
ma-179	390	2	zt	zt	PROPN
ma-179	390	3	+	+	SYM
ma-179	390	4	(	(	PUNCT
ma-179	390	5	2θ	2θ	NUM
ma-179	390	6	eθt	eθt	X
ma-179	390	7	)	)	PUNCT
ma-179	390	8	it	it	PRON
ma-179	390	9	x	x	SYM
ma-179	390	10	±	±	NOUN
ma-179	390	11	2b0θx	2b0θx	NUM
ma-179	390	12	2	2	NUM
ma-179	390	13	.	.	PUNCT
ma-179	391	1	let	let	VERB
ma-179	391	2	us	we	PRON
ma-179	391	3	introduce	introduce	VERB
ma-179	391	4	the	the	DET
ma-179	391	5	events	event	NOUN
ma-179	391	6	d±t	d±t	NOUN
ma-179	391	7	,	,	PUNCT
ma-179	391	8	x	x	PUNCT
ma-179	391	9	:	:	PUNCT
ma-179	391	10	=	=	X
ma-179	391	11	{	{	PUNCT
ma-179	391	12	zt	zt	PROPN
ma-179	391	13	+	+	CCONJ
ma-179	391	14	(	(	PUNCT
ma-179	391	15	2θ	2θ	NUM
ma-179	391	16	eθt	eθt	X
ma-179	391	17	)	)	PUNCT
ma-179	391	18	it	it	PRON
ma-179	391	19	x	x	SYM
ma-179	391	20	±	±	NOUN
ma-179	391	21	2b0θx	2b0θx	NUM
ma-179	391	22	2	2	NUM
ma-179	391	23	>	>	SYM
ma-179	391	24	0	0	NUM
ma-179	391	25	}	}	PUNCT
ma-179	391	26	.	.	PUNCT
ma-179	392	1	thus	thus	ADV
ma-179	392	2	we	we	PRON
ma-179	392	3	have	have	VERB
ma-179	392	4	d−t	d−t	NOUN
ma-179	392	5	,	,	PUNCT
ma-179	392	6	x	x	SYM
ma-179	392	7	∩	∩	NOUN
ma-179	392	8	at	at	ADP
ma-179	392	9	∩	∩	NOUN
ma-179	392	10	bt	bt	VERB
ma-179	392	11	⊆	⊆	NUM
ma-179	392	12	at	at	ADP
ma-179	392	13	∩	∩	PROPN
ma-179	392	14	bt	bt	NOUN
ma-179	392	15	∩	∩	NOUN
ma-179	392	16	{	{	PUNCT
ma-179	392	17	(	(	PUNCT
ma-179	392	18	eθt	eθt	NOUN
ma-179	392	19	2θ	2θ	NUM
ma-179	392	20	)	)	PUNCT
ma-179	392	21	(	(	PUNCT
ma-179	392	22	θt	θt	PROPN
ma-179	392	23	−	−	PROPN
ma-179	392	24	θ	θ	PROPN
ma-179	392	25	)	)	PUNCT
ma-179	392	26	≤	≤	NOUN
ma-179	392	27	x	x	PUNCT
ma-179	392	28	}	}	PUNCT
ma-179	392	29	⊆	⊆	NUM
ma-179	392	30	d+	d+	NOUN
ma-179	392	31	t	t	NOUN
ma-179	392	32	,	,	PUNCT
ma-179	392	33	x	x	SYM
ma-179	392	34	∩	∩	NOUN
ma-179	392	35	at	at	ADP
ma-179	392	36	∩	∩	PROPN
ma-179	392	37	bt	bt	PROPN
ma-179	392	38	.	.	PUNCT
ma-179	393	1	(	(	PUNCT
ma-179	393	2	2.36	2.36	NUM
ma-179	393	3	)	)	PUNCT
ma-179	393	4	this	this	PRON
ma-179	393	5	gives	give	VERB
ma-179	393	6	p	p	NOUN
ma-179	393	7	(	(	PUNCT
ma-179	393	8	d−t	d−t	NOUN
ma-179	393	9	,	,	PUNCT
ma-179	393	10	x	x	SYM
ma-179	393	11	∩	∩	NOUN
ma-179	393	12	at	at	ADP
ma-179	393	13	∩	∩	ADJ
ma-179	393	14	bt	bt	NOUN
ma-179	393	15	)	)	PUNCT
ma-179	393	16	≤	≤	NOUN
ma-179	393	17	p	p	NOUN
ma-179	393	18	(	(	PUNCT
ma-179	393	19	at	at	ADP
ma-179	393	20	∩	∩	PROPN
ma-179	393	21	bt	bt	NOUN
ma-179	393	22	∩	∩	NOUN
ma-179	393	23	{	{	PUNCT
ma-179	393	24	(	(	PUNCT
ma-179	393	25	eθt	eθt	NOUN
ma-179	393	26	2θ	2θ	NUM
ma-179	393	27	)	)	PUNCT
ma-179	393	28	(	(	PUNCT
ma-179	393	29	θt	θt	PROPN
ma-179	393	30	−	−	PROPN
ma-179	393	31	θ	θ	PROPN
ma-179	393	32	)	)	PUNCT
ma-179	393	33	≤	≤	NOUN
ma-179	393	34	x	x	PUNCT
ma-179	393	35	}	}	PUNCT
ma-179	393	36	)	)	PUNCT
ma-179	394	1	≤	≤	NOUN
ma-179	395	1	p	p	NOUN
ma-179	395	2	(	(	PUNCT
ma-179	395	3	d+	d+	PROPN
ma-179	395	4	t	t	NOUN
ma-179	395	5	,	,	PUNCT
ma-179	395	6	x	x	SYM
ma-179	395	7	∩	∩	NOUN
ma-179	395	8	at	at	ADP
ma-179	395	9	∩	∩	ADJ
ma-179	395	10	bt	bt	NOUN
ma-179	395	11	)	)	PUNCT
ma-179	396	1	so	so	SCONJ
ma-179	396	2	that	that	SCONJ
ma-179	396	3	∣∣∣∣p	∣∣∣∣p	ADP
ma-179	396	4	(	(	PUNCT
ma-179	396	5	at	at	ADP
ma-179	396	6	∩	∩	PROPN
ma-179	396	7	bt	bt	PROPN
ma-179	396	8	∩{(eθt2θ	∩{(eθt2θ	PROPN
ma-179	396	9	)	)	PUNCT
ma-179	396	10	(	(	PUNCT
ma-179	396	11	θt	θt	PROPN
ma-179	396	12	−	−	PROPN
ma-179	396	13	θ	θ	PROPN
ma-179	396	14	)	)	PUNCT
ma-179	396	15	≤	≤	NOUN
ma-179	396	16	x	x	PUNCT
ma-179	396	17	}	}	PUNCT
ma-179	396	18	)	)	PUNCT
ma-179	396	19	−	−	ADP
ma-179	396	20	c(x	c(x	NOUN
ma-179	396	21	)	)	PUNCT
ma-179	396	22	∣∣∣∣	∣∣∣∣	NOUN
ma-179	396	23	≤	≤	NUM
ma-179	396	24	max	max	PROPN
ma-179	396	25	{	{	PUNCT
ma-179	396	26	|p	|p	PROPN
ma-179	396	27	(	(	PUNCT
ma-179	396	28	d−t	d−t	NOUN
ma-179	396	29	,	,	PUNCT
ma-179	396	30	x	x	SYM
ma-179	396	31	∩	∩	NOUN
ma-179	396	32	at	at	ADP
ma-179	396	33	∩	∩	PROPN
ma-179	396	34	bt	bt	NOUN
ma-179	396	35	)	)	PUNCT
ma-179	396	36	−	−	PROPN
ma-179	396	37	c(x)|	c(x)|	PROPN
ma-179	396	38	,	,	PUNCT
ma-179	396	39	|p	|p	PROPN
ma-179	396	40	(	(	PUNCT
ma-179	396	41	d+	d+	PUNCT
ma-179	396	42	t	t	NOUN
ma-179	396	43	,	,	PUNCT
ma-179	396	44	x	x	SYM
ma-179	396	45	∩	∩	NOUN
ma-179	396	46	at	at	ADP
ma-179	396	47	∩	∩	PROPN
ma-179	396	48	bt	bt	NOUN
ma-179	396	49	)	)	PUNCT
ma-179	396	50	−	−	PROPN
ma-179	396	51	c(x)|	c(x)|	PROPN
ma-179	396	52	}	}	PUNCT
ma-179	396	53	≤	≤	NUM
ma-179	396	54	max	max	PROPN
ma-179	396	55	{	{	PUNCT
ma-179	396	56	|p	|p	PROPN
ma-179	396	57	(	(	PUNCT
ma-179	396	58	d−t	d−t	NOUN
ma-179	396	59	,	,	PUNCT
ma-179	396	60	x)−	x)−	PROPN
ma-179	396	61	c(x)|	c(x)|	PROPN
ma-179	396	62	,	,	PUNCT
ma-179	396	63	|p	|p	PROPN
ma-179	396	64	(	(	PUNCT
ma-179	396	65	d+	d+	PUNCT
ma-179	396	66	t	t	PROPN
ma-179	396	67	,	,	PUNCT
ma-179	396	68	x)−	x)−	PROPN
ma-179	396	69	c(x)|	c(x)|	PROPN
ma-179	396	70	}	}	PUNCT
ma-179	396	71	+	+	CCONJ
ma-179	396	72	p	p	X
ma-179	396	73	(	(	PUNCT
ma-179	396	74	at	at	ADP
ma-179	396	75	∩	∩	PROPN
ma-179	396	76	bt	bt	NOUN
ma-179	396	77	)	)	PUNCT
ma-179	396	78	c	c	NOUN
ma-179	396	79	.from	.from	ADP
ma-179	396	80	(	(	PUNCT
ma-179	396	81	2.34	2.34	NUM
ma-179	396	82	)	)	PUNCT
ma-179	396	83	and	and	CCONJ
ma-179	396	84	(	(	PUNCT
ma-179	396	85	2.35	2.35	NUM
ma-179	396	86	)	)	PUNCT
ma-179	396	87	,	,	PUNCT
ma-179	396	88	p	p	X
ma-179	396	89	(	(	PUNCT
ma-179	396	90	at	at	ADP
ma-179	396	91	∩	∩	PROPN
ma-179	396	92	bt	bt	NOUN
ma-179	396	93	)	)	PUNCT
ma-179	396	94	c	c	NOUN
ma-179	396	95	≤	≤	NOUN
ma-179	396	96	ce−θtfor	ce−θtfor	ADP
ma-179	396	97	all	all	DET
ma-179	396	98	t	t	PROPN
ma-179	396	99	>	>	X
ma-179	396	100	t0	t0	PROPN
ma-179	396	101	and	and	CCONJ
ma-179	396	102	|x	|x	NOUN
ma-179	396	103	|	|	ADV
ma-179	396	104	≤	≤	VERB
ma-179	396	105	2(θt	2(θt	NUM
ma-179	396	106	)	)	PUNCT
ma-179	396	107	1/2	1/2	NUM
ma-179	396	108	.	.	PUNCT
ma-179	397	1	if	if	SCONJ
ma-179	397	2	it	it	PRON
ma-179	397	3	is	be	AUX
ma-179	397	4	shown	show	VERB
ma-179	397	5	that∣∣p	that∣∣p	ADP
ma-179	397	6	{	{	PUNCT
ma-179	397	7	d±t	d±t	PROPN
ma-179	397	8	,	,	PUNCT
ma-179	397	9	x}−	x}−	PROPN
ma-179	397	10	c(x	c(x	NOUN
ma-179	397	11	)	)	PUNCT
ma-179	397	12	∣∣	∣∣	NUM
ma-179	397	13	≤	≤	ADV
ma-179	397	14	ce−θt	ce−θt	X
ma-179	397	15	(	(	PUNCT
ma-179	397	16	2.37	2.37	NUM
ma-179	397	17	)	)	PUNCT
ma-179	397	18	for	for	ADP
ma-179	397	19	all	all	DET
ma-179	397	20	t	t	PROPN
ma-179	397	21	>	>	X
ma-179	397	22	t0	t0	PROPN
ma-179	397	23	and	and	CCONJ
ma-179	397	24	|x	|x	NOUN
ma-179	397	25	|	|	ADV
ma-179	397	26	≤	≤	VERB
ma-179	397	27	2(θt	2(θt	NUM
ma-179	397	28	)	)	PUNCT
ma-179	397	29	1/2	1/2	NUM
ma-179	397	30	,	,	PUNCT
ma-179	397	31	then	then	ADV
ma-179	397	32	the	the	DET
ma-179	397	33	theorem	theorem	NOUN
ma-179	397	34	would	would	AUX
ma-179	397	35	follow	follow	VERB
ma-179	397	36	from	from	ADP
ma-179	397	37	(	(	PUNCT
ma-179	397	38	2.34	2.34	NUM
ma-179	397	39	)	)	PUNCT
ma-179	397	40	–	–	PUNCT
ma-179	397	41	(	(	PUNCT
ma-179	397	42	2.37).we	2.37).we	NOUN
ma-179	397	43	shall	shall	AUX
ma-179	397	44	prove	prove	VERB
ma-179	397	45	(	(	PUNCT
ma-179	397	46	2.37	2.37	NUM
ma-179	397	47	)	)	PUNCT
ma-179	397	48	for	for	ADP
ma-179	397	49	d+	d+	NOUN
ma-179	397	50	t	t	PROPN
ma-179	397	51	,	,	PUNCT
ma-179	397	52	x	x	X
ma-179	397	53	.	.	PUNCT
ma-179	398	1	the	the	DET
ma-179	398	2	proof	proof	NOUN
ma-179	398	3	for	for	ADP
ma-179	398	4	d−t	d−t	NOUN
ma-179	398	5	,	,	PUNCT
ma-179	398	6	x	x	PUNCT
ma-179	398	7	is	be	AUX
ma-179	398	8	analogous.note	analogous.note	PRON
ma-179	398	9	that	that	PRON
ma-179	398	10	∣∣p	∣∣p	PROPN
ma-179	398	11	{	{	PUNCT
ma-179	398	12	d+	d+	PROPN
ma-179	398	13	t	t	PROPN
ma-179	398	14	,	,	PUNCT
ma-179	398	15	x	x	NOUN
ma-179	398	16	}	}	PUNCT
ma-179	398	17	−	−	ADP
ma-179	398	18	c(x	c(x	NOUN
ma-179	398	19	)	)	PUNCT
ma-179	398	20	∣∣	∣∣	X
ma-179	399	1	=	=	PUNCT
ma-179	399	2	∣∣∣∣p	∣∣∣∣p	X
ma-179	399	3	{	{	PUNCT
ma-179	399	4	−	−	NOUN
ma-179	399	5	(	(	PUNCT
ma-179	399	6	2θ	2θ	NUM
ma-179	399	7	eθt	eθt	X
ma-179	399	8	)	)	PUNCT
ma-179	399	9	zt	zt	PROPN
ma-179	399	10	−	−	PROPN
ma-179	399	11	(	(	PUNCT
ma-179	399	12	2θ	2θ	NUM
ma-179	399	13	eθt	eθt	VERB
ma-179	399	14	it	it	PRON
ma-179	399	15	−	−	PROPN
ma-179	399	16	ξ2	ξ2	NOUN
ma-179	399	17	)	)	PUNCT
ma-179	400	1	x	x	X
ma-179	400	2	<	<	X
ma-179	400	3	x	x	X
ma-179	401	1	+	+	NUM
ma-179	401	2	2	2	NUM
ma-179	401	3	(	(	PUNCT
ma-179	401	4	2θ	2θ	NUM
ma-179	401	5	eθt	eθt	NOUN
ma-179	401	6	)	)	PUNCT
ma-179	401	7	b0θx	b0θx	PUNCT
ma-179	402	1	2	2	X
ma-179	402	2	}	}	PUNCT
ma-179	402	3	−	−	PROPN
ma-179	402	4	c(x	c(x	NOUN
ma-179	402	5	)	)	PUNCT
ma-179	402	6	∣∣∣∣	∣∣∣∣	NOUN
ma-179	402	7	≤	≤	NUM
ma-179	402	8	sup	sup	NOUN
ma-179	402	9	y∈r	y∈r	NOUN
ma-179	402	10	∣∣∣∣p	∣∣∣∣p	ADP
ma-179	402	11	{	{	PUNCT
ma-179	402	12	−	−	PROPN
ma-179	402	13	(	(	PUNCT
ma-179	402	14	2θ	2θ	NUM
ma-179	402	15	eθt	eθt	X
ma-179	402	16	)	)	PUNCT
ma-179	403	1	zt	zt	PROPN
ma-179	403	2	−	−	PROPN
ma-179	403	3	(	(	PUNCT
ma-179	403	4	2θ	2θ	NUM
ma-179	403	5	eθt	eθt	VERB
ma-179	403	6	it	it	PRON
ma-179	403	7	−	−	PROPN
ma-179	403	8	ξ2	ξ2	NOUN
ma-179	403	9	)	)	PUNCT
ma-179	404	1	x	x	PUNCT
ma-179	404	2	≤	≤	NUM
ma-179	404	3	y	y	PROPN
ma-179	404	4	}	}	PUNCT
ma-179	404	5	−	−	PROPN
ma-179	404	6	c(y	c(y	PROPN
ma-179	404	7	)	)	PUNCT
ma-179	404	8	∣∣∣∣+	∣∣∣∣+	PROPN
ma-179	404	9	∣∣∣∣c	∣∣∣∣c	PROPN
ma-179	404	10	(	(	PUNCT
ma-179	404	11	x	x	SYM
ma-179	404	12	+	+	PUNCT
ma-179	404	13	(	(	PUNCT
ma-179	404	14	2θ	2θ	NUM
ma-179	404	15	eθt	eθt	NOUN
ma-179	404	16	)	)	PUNCT
ma-179	404	17	b0θx	b0θx	PUNCT
ma-179	405	1	2	2	X
ma-179	405	2	)	)	PUNCT
ma-179	405	3	−	−	ADP
ma-179	405	4	c(x	c(x	NOUN
ma-179	405	5	)	)	PUNCT
ma-179	405	6	∣∣∣∣	∣∣∣∣	NOUN
ma-179	405	7	=	=	NOUN
ma-179	405	8	:	:	PUNCT
ma-179	405	9	∆1	∆1	PROPN
ma-179	405	10	+	+	NUM
ma-179	405	11	∆2	∆2	X
ma-179	405	12	.	.	PUNCT
ma-179	406	1	(	(	PUNCT
ma-179	406	2	2.38)lemma	2.38)lemma	NUM
ma-179	406	3	2.4	2.4	NUM
ma-179	406	4	(	(	PUNCT
ma-179	406	5	b	b	NOUN
ma-179	406	6	)	)	PUNCT
ma-179	406	7	and	and	CCONJ
ma-179	406	8	esseen	esseen	AUX
ma-179	406	9	’s	’s	AUX
ma-179	406	10	smoothing	smooth	VERB
ma-179	406	11	lemma	lemma	PROPN
ma-179	406	12	1.1	1.1	NUM
ma-179	406	13	immediately	immediately	ADV
ma-179	406	14	yield	yield	VERB
ma-179	406	15	∆1	∆1	NUM
ma-179	406	16	≤	≤	NUM
ma-179	406	17	ce−θt	ce−θt	ADJ
ma-179	406	18	.	.	PUNCT
ma-179	407	1	(	(	PUNCT
ma-179	407	2	2.39	2.39	NUM
ma-179	407	3	)	)	PUNCT
ma-179	407	4	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	NOUN
ma-179	407	5	eur	eur	PROPN
ma-179	407	6	.	.	PUNCT
ma-179	408	1	j.	j.	PROPN
ma-179	408	2	math	math	PROPN
ma-179	408	3	.	.	PUNCT
ma-179	409	1	anal	anal	PROPN
ma-179	409	2	.	.	PUNCT
ma-179	410	1	10.28924	10.28924	NUM
ma-179	410	2	/	/	SYM
ma-179	410	3	ada	ada	PROPN
ma-179	410	4	/	/	PROPN
ma-179	410	5	ma.3.25	ma.3.25	PROPN
ma-179	410	6	15on	15on	ADJ
ma-179	410	7	the	the	DET
ma-179	410	8	other	other	ADJ
ma-179	410	9	hand	hand	NOUN
ma-179	410	10	,	,	PUNCT
ma-179	410	11	for	for	ADP
ma-179	410	12	all	all	DET
ma-179	410	13	t	t	PROPN
ma-179	410	14	>	>	X
ma-179	410	15	t0	t0	PROPN
ma-179	410	16	,	,	PUNCT
ma-179	410	17	∆2	∆2	PROPN
ma-179	410	18	≤	≤	PROPN
ma-179	410	19	2	2	NUM
ma-179	410	20	(	(	PUNCT
ma-179	410	21	2θ	2θ	NUM
ma-179	410	22	eθt	eθt	NOUN
ma-179	410	23	)	)	PUNCT
ma-179	410	24	b0θx	b0θx	PUNCT
ma-179	410	25	2(2π)−1/2	2(2π)−1/2	NUM
ma-179	410	26	exp(−x2/2	exp(−x2/2	NOUN
ma-179	410	27	)	)	PUNCT
ma-179	411	1	where	where	SCONJ
ma-179	411	2	|x	|x	PUNCT
ma-179	411	3	−	−	NOUN
ma-179	411	4	x	x	SYM
ma-179	411	5	|	|	ADV
ma-179	411	6	≤	≤	ADJ
ma-179	411	7	2	2	NUM
ma-179	411	8	(	(	PUNCT
ma-179	411	9	2θ	2θ	NUM
ma-179	411	10	eθt	eθt	NOUN
ma-179	411	11	)	)	PUNCT
ma-179	411	12	b0θx	b0θx	PUNCT
ma-179	411	13	2	2	X
ma-179	411	14	.	.	PUNCT
ma-179	411	15	since	since	SCONJ
ma-179	411	16	|x	|x	NOUN
ma-179	411	17	|	|	ADV
ma-179	411	18	≤	≤	NOUN
ma-179	411	19	2(θt	2(θt	NUM
ma-179	411	20	)	)	PUNCT
ma-179	411	21	1/2	1/2	NUM
ma-179	411	22	,	,	PUNCT
ma-179	411	23	it	it	PRON
ma-179	411	24	follows	follow	VERB
ma-179	411	25	that	that	DET
ma-179	411	26	|x̄	|x̄	NOUN
ma-179	411	27	|	|	ADV
ma-179	411	28	>	>	X
ma-179	411	29	|x	|x	NOUN
ma-179	411	30	|/2	|/2	VERB
ma-179	411	31	for	for	ADP
ma-179	411	32	all	all	DET
ma-179	411	33	t	t	PROPN
ma-179	411	34	>	>	X
ma-179	411	35	t0	t0	PROPN
ma-179	411	36	and	and	CCONJ
ma-179	412	1	consequently	consequently	ADV
ma-179	412	2	∆2	∆2	PROPN
ma-179	412	3	≤	≤	ADV
ma-179	412	4	2	2	NUM
ma-179	412	5	(	(	PUNCT
ma-179	412	6	2θ	2θ	NUM
ma-179	412	7	eθt	eθt	NOUN
ma-179	412	8	)	)	PUNCT
ma-179	412	9	b0θx	b0θx	PUNCT
ma-179	413	1	2(2π)−1/2x2	2(2π)−1/2x2	NUM
ma-179	413	2	exp(−x2/8	exp(−x2/8	NOUN
ma-179	413	3	)	)	PUNCT
ma-179	413	4	≤	≤	NUM
ma-179	413	5	ce−θt	ce−θt	ADJ
ma-179	413	6	.	.	PUNCT
ma-179	414	1	(	(	PUNCT
ma-179	414	2	2.40	2.40	NUM
ma-179	414	3	)	)	PUNCT
ma-179	414	4	from	from	ADP
ma-179	414	5	(	(	PUNCT
ma-179	414	6	2.38	2.38	NUM
ma-179	414	7	)	)	PUNCT
ma-179	414	8	(	(	PUNCT
ma-179	414	9	2.40	2.40	NUM
ma-179	414	10	)	)	PUNCT
ma-179	414	11	,	,	PUNCT
ma-179	414	12	we	we	PRON
ma-179	414	13	obtain	obtain	VERB
ma-179	414	14	∣∣p	∣∣p	PROPN
ma-179	414	15	{	{	PUNCT
ma-179	414	16	d+	d+	PROPN
ma-179	414	17	t	t	PROPN
ma-179	414	18	,	,	PUNCT
ma-179	414	19	x	x	NOUN
ma-179	414	20	}	}	PUNCT
ma-179	414	21	−	−	ADP
ma-179	414	22	c(x	c(x	NOUN
ma-179	414	23	)	)	PUNCT
ma-179	414	24	∣∣	∣∣	NUM
ma-179	415	1	≤	≤	PROPN
ma-179	415	2	ce−θt	ce−θt	ADJ
ma-179	415	3	.	.	PUNCT
ma-179	416	1	this	this	PRON
ma-179	416	2	completes	complete	VERB
ma-179	416	3	the	the	DET
ma-179	416	4	proof	proof	NOUN
ma-179	416	5	of	of	ADP
ma-179	416	6	the	the	DET
ma-179	416	7	theorem	theorem	PROPN
ma-179	416	8	.	.	PROPN
ma-179	416	9	concluding	conclude	VERB
ma-179	416	10	remarks	remark	NOUN
ma-179	416	11	(	(	PUNCT
ma-179	416	12	1	1	X
ma-179	416	13	)	)	PUNCT
ma-179	416	14	the	the	DET
ma-179	416	15	bound	bind	VERB
ma-179	416	16	in	in	ADP
ma-179	416	17	theorem	theorem	ADJ
ma-179	416	18	2.2	2.2	NUM
ma-179	416	19	is	be	AUX
ma-179	416	20	uniform	uniform	ADJ
ma-179	416	21	over	over	ADP
ma-179	416	22	compact	compact	ADJ
ma-179	416	23	subsets	subset	NOUN
ma-179	416	24	of	of	ADP
ma-179	416	25	the	the	DET
ma-179	416	26	parameter	parameter	NOUN
ma-179	416	27	space	space	NOUN
ma-179	416	28	θ.(2	θ.(2	PROPN
ma-179	416	29	)	)	PUNCT
ma-179	416	30	the	the	DET
ma-179	416	31	bound	bind	VERB
ma-179	416	32	in	in	ADP
ma-179	416	33	theorem	theorem	ADJ
ma-179	416	34	2.2	2.2	NUM
ma-179	416	35	is	be	AUX
ma-179	416	36	optimal	optimal	ADJ
ma-179	416	37	and	and	CCONJ
ma-179	416	38	can	can	AUX
ma-179	416	39	not	not	PART
ma-179	416	40	be	be	AUX
ma-179	416	41	improved	improve	VERB
ma-179	416	42	further.(3	further.(3	NOUN
ma-179	416	43	)	)	PUNCT
ma-179	416	44	note	note	NOUN
ma-179	416	45	that	that	SCONJ
ma-179	416	46	in	in	ADP
ma-179	416	47	the	the	DET
ma-179	416	48	critical	critical	ADJ
ma-179	416	49	case	case	NOUN
ma-179	416	50	,	,	PUNCT
ma-179	416	51	i.e.	i.e.	X
ma-179	416	52	,	,	PUNCT
ma-179	416	53	when	when	SCONJ
ma-179	416	54	θ	θ	PROPN
ma-179	416	55	=	=	SYM
ma-179	416	56	0	0	NUM
ma-179	416	57	,	,	PUNCT
ma-179	416	58	the	the	DET
ma-179	416	59	mle	mle	PROPN
ma-179	416	60	has	have	VERB
ma-179	416	61	a	a	DET
ma-179	416	62	distribution	distribution	NOUN
ma-179	416	63	concentratedon	concentratedon	VERB
ma-179	416	64	a	a	DET
ma-179	416	65	half	half	ADJ
ma-179	416	66	line	line	NOUN
ma-179	416	67	,	,	PUNCT
ma-179	416	68	precisely	precisely	ADV
ma-179	416	69	the	the	DET
ma-179	416	70	distribution	distribution	NOUN
ma-179	416	71	of	of	ADP
ma-179	416	72	the	the	DET
ma-179	416	73	ratio	ratio	NOUN
ma-179	416	74	of	of	ADP
ma-179	416	75	a	a	DET
ma-179	416	76	noncentral	noncentral	ADJ
ma-179	416	77	chisquare	chisquare	NOUN
ma-179	416	78	to	to	ADP
ma-179	416	79	the	the	PRON
ma-179	416	80	to	to	ADP
ma-179	416	81	the	the	DET
ma-179	416	82	sumof	sumof	ADJ
ma-179	416	83	chisquares	chisquare	NOUN
ma-179	416	84	.	.	PUNCT
ma-179	417	1	note	note	VERB
ma-179	417	2	that	that	SCONJ
ma-179	417	3	the	the	DET
ma-179	417	4	behaviour	behaviour	NOUN
ma-179	417	5	of	of	ADP
ma-179	417	6	the	the	DET
ma-179	417	7	o	o	ADJ
ma-179	417	8	-	-	NOUN
ma-179	417	9	u	u	NOUN
ma-179	417	10	process	process	NOUN
ma-179	417	11	depends	depend	VERB
ma-179	417	12	on	on	ADP
ma-179	417	13	both	both	CCONJ
ma-179	417	14	the	the	DET
ma-179	417	15	initial	initial	ADJ
ma-179	417	16	condition	condition	NOUN
ma-179	417	17	x0	x0	PROPN
ma-179	418	1	=	=	PUNCT
ma-179	418	2	x0	x0	PROPN
ma-179	418	3	and	and	CCONJ
ma-179	418	4	the	the	DET
ma-179	418	5	parameter	parameter	NOUN
ma-179	418	6	space	space	NOUN
ma-179	418	7	.	.	PUNCT
ma-179	419	1	classically	classically	ADV
ma-179	419	2	it	it	PRON
ma-179	419	3	has	have	AUX
ma-179	419	4	been	be	AUX
ma-179	419	5	assumed	assume	VERB
ma-179	419	6	that	that	SCONJ
ma-179	419	7	x0	x0	PROPN
ma-179	419	8	is	be	AUX
ma-179	419	9	either	either	PRON
ma-179	419	10	has	have	VERB
ma-179	419	11	a	a	DET
ma-179	419	12	normaldistribution	normaldistribution	NOUN
ma-179	419	13	or	or	CCONJ
ma-179	419	14	a	a	DET
ma-179	419	15	nonzero	nonzero	NOUN
ma-179	419	16	constant	constant	ADJ
ma-179	419	17	and	and	CCONJ
ma-179	419	18	θ	θ	X
ma-179	419	19	<	<	X
ma-179	419	20	0	0	NUM
ma-179	419	21	which	which	PRON
ma-179	419	22	makes	make	VERB
ma-179	419	23	the	the	DET
ma-179	419	24	process	process	NOUN
ma-179	419	25	stationary	stationary	ADJ
ma-179	419	26	with	with	ADP
ma-179	419	27	gaussianinvariant	gaussianinvariant	ADJ
ma-179	419	28	distribution	distribution	NOUN
ma-179	419	29	.	.	PUNCT
ma-179	420	1	if	if	SCONJ
ma-179	420	2	x0	x0	PROPN
ma-179	420	3	=	=	PUNCT
ma-179	420	4	0	0	PUNCT
ma-179	420	5	is	be	AUX
ma-179	420	6	with	with	ADP
ma-179	420	7	θ	θ	PROPN
ma-179	420	8	<	<	X
ma-179	420	9	0	0	PROPN
ma-179	420	10	,	,	PUNCT
ma-179	420	11	then	then	ADV
ma-179	420	12	the	the	DET
ma-179	420	13	process	process	NOUN
ma-179	420	14	is	be	AUX
ma-179	420	15	asymptotically	asymptotically	ADV
ma-179	420	16	stationary	stationary	ADJ
ma-179	420	17	andergodic	andergodic	NOUN
ma-179	420	18	.	.	PUNCT
ma-179	421	1	in	in	ADP
ma-179	421	2	above	above	ADP
ma-179	421	3	two	two	NUM
ma-179	421	4	cases	case	NOUN
ma-179	421	5	the	the	DET
ma-179	421	6	model	model	NOUN
ma-179	421	7	satisfies	satisfy	VERB
ma-179	421	8	the	the	DET
ma-179	421	9	lan	lan	PROPN
ma-179	421	10	(	(	PUNCT
ma-179	421	11	local	local	ADJ
ma-179	421	12	asymptotic	asymptotic	ADJ
ma-179	421	13	normality	normality	NOUN
ma-179	421	14	)	)	PUNCT
ma-179	421	15	property.with	property.with	ADP
ma-179	421	16	x0	x0	PROPN
ma-179	421	17	a	a	DET
ma-179	421	18	nonzero	nonzero	NOUN
ma-179	421	19	constant	constant	ADJ
ma-179	421	20	and	and	CCONJ
ma-179	421	21	θ	θ	X
ma-179	421	22	>	>	PUNCT
ma-179	421	23	0	0	PUNCT
ma-179	422	1	the	the	DET
ma-179	422	2	process	process	NOUN
ma-179	422	3	is	be	AUX
ma-179	422	4	transient	transient	ADJ
ma-179	422	5	and	and	CCONJ
ma-179	422	6	satisfies	satisfy	VERB
ma-179	422	7	the	the	DET
ma-179	422	8	lamn	lamn	NOUN
ma-179	422	9	(	(	PUNCT
ma-179	422	10	localasymptotic	localasymptotic	ADJ
ma-179	422	11	mixed	mixed	ADJ
ma-179	422	12	normality	normality	NOUN
ma-179	422	13	)	)	PUNCT
ma-179	422	14	property	property	NOUN
ma-179	422	15	.	.	PUNCT
ma-179	423	1	with	with	ADP
ma-179	423	2	θ	θ	PROPN
ma-179	423	3	=	=	SYM
ma-179	423	4	0	0	PROPN
ma-179	423	5	,	,	PUNCT
ma-179	423	6	the	the	DET
ma-179	423	7	process	process	NOUN
ma-179	423	8	is	be	AUX
ma-179	423	9	nonstationary	nonstationary	ADJ
ma-179	423	10	and	and	CCONJ
ma-179	423	11	satisfies	satisfy	VERB
ma-179	423	12	thelabf	thelabf	NOUN
ma-179	423	13	(	(	PUNCT
ma-179	423	14	local	local	ADJ
ma-179	423	15	asymptotic	asymptotic	ADJ
ma-179	423	16	brownian	brownian	ADJ
ma-179	423	17	functional	functional	ADJ
ma-179	423	18	)	)	PUNCT
ma-179	423	19	property	property	NOUN
ma-179	423	20	.	.	PUNCT
ma-179	424	1	for	for	ADP
ma-179	424	2	all	all	DET
ma-179	424	3	θ	θ	NOUN
ma-179	424	4	∈	∈	PROPN
ma-179	424	5	r	r	NOUN
ma-179	424	6	,	,	PUNCT
ma-179	424	7	the	the	DET
ma-179	424	8	model	model	NOUN
ma-179	424	9	satisfies	satisfy	VERB
ma-179	424	10	the	the	DET
ma-179	424	11	labfproperty	labfproperty	NOUN
ma-179	424	12	,	,	PUNCT
ma-179	424	13	see	see	VERB
ma-179	424	14	bishwal	bishwal	NOUN
ma-179	425	1	[	[	X
ma-179	425	2	9	9	NUM
ma-179	425	3	]	]	PUNCT
ma-179	425	4	for	for	ADP
ma-179	425	5	the	the	DET
ma-179	425	6	definitions	definition	NOUN
ma-179	425	7	of	of	ADP
ma-179	425	8	these	these	DET
ma-179	425	9	lan	lan	NOUN
ma-179	425	10	,	,	PUNCT
ma-179	425	11	lamn	lamn	ADJ
ma-179	425	12	and	and	CCONJ
ma-179	425	13	labf	labf	VERB
ma-179	425	14	properties	property	NOUN
ma-179	425	15	.	.	PUNCT
ma-179	426	1	bishwal	bishwal	NOUN
ma-179	427	1	[	[	X
ma-179	427	2	9]has	9]has	PROPN
ma-179	427	3	shown	show	VERB
ma-179	427	4	that	that	SCONJ
ma-179	427	5	sequential	sequential	ADJ
ma-179	427	6	sampling	sampling	NOUN
ma-179	427	7	based	base	VERB
ma-179	427	8	on	on	ADP
ma-179	427	9	a	a	DET
ma-179	427	10	stopping	stop	VERB
ma-179	427	11	rule	rule	NOUN
ma-179	427	12	unifies	unify	VERB
ma-179	427	13	the	the	DET
ma-179	427	14	three	three	NUM
ma-179	427	15	properties	property	NOUN
ma-179	427	16	andmakes	andmake	VERB
ma-179	427	17	them	they	PRON
ma-179	427	18	lan.(4	lan.(4	PROPN
ma-179	427	19	)	)	PUNCT
ma-179	427	20	it	it	PRON
ma-179	427	21	remains	remain	VERB
ma-179	427	22	to	to	PART
ma-179	427	23	study	study	VERB
ma-179	427	24	the	the	DET
ma-179	427	25	kolmogorov	kolmogorov	ADJ
ma-179	427	26	distnace	distnace	NOUN
ma-179	427	27	for	for	ADP
ma-179	427	28	bayes	bayes	PROPN
ma-179	427	29	estimator	estimator	NOUN
ma-179	427	30	from	from	ADP
ma-179	427	31	both	both	CCONJ
ma-179	427	32	continuous	continuous	ADJ
ma-179	427	33	andsiscrete	andsiscrete	NOUN
ma-179	427	34	observations	observation	NOUN
ma-179	427	35	and	and	CCONJ
ma-179	427	36	approximate	approximate	ADJ
ma-179	427	37	maximum	maximum	ADJ
ma-179	427	38	likelihood	likelihood	NOUN
ma-179	427	39	estimator	estimator	NOUN
ma-179	427	40	from	from	ADP
ma-179	427	41	discrete	discrete	ADJ
ma-179	427	42	observations	observation	NOUN
ma-179	427	43	inthe	inthe	DET
ma-179	427	44	nonergodic	nonergodic	ADJ
ma-179	427	45	case.(5	case.(5	NOUN
ma-179	427	46	)	)	PUNCT
ma-179	427	47	extension	extension	NOUN
ma-179	427	48	to	to	ADP
ma-179	427	49	multidimensional	multidimensional	ADJ
ma-179	427	50	process	process	NOUN
ma-179	427	51	and	and	CCONJ
ma-179	427	52	to	to	PART
ma-179	427	53	multiparameter	multiparameter	VERB
ma-179	427	54	case	case	NOUN
ma-179	427	55	remains	remain	VERB
ma-179	427	56	to	to	PART
ma-179	427	57	be	be	AUX
ma-179	427	58	investigated.(6	investigated.(6	PROPN
ma-179	427	59	)	)	PUNCT
ma-179	427	60	it	it	PRON
ma-179	427	61	remains	remain	VERB
ma-179	427	62	to	to	PART
ma-179	427	63	investigate	investigate	VERB
ma-179	427	64	the	the	DET
ma-179	427	65	nonuniform	nonuniform	ADJ
ma-179	427	66	rates	rate	NOUN
ma-179	427	67	of	of	ADP
ma-179	427	68	convergence	convergence	NOUN
ma-179	427	69	to	to	ADP
ma-179	427	70	cauchy	cauchy	ADJ
ma-179	427	71	distribution	distribution	NOUN
ma-179	427	72	whichare	whichare	VERB
ma-179	427	73	more	more	ADV
ma-179	427	74	useful	useful	ADJ
ma-179	427	75	.	.	PUNCT
ma-179	428	1	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	PROPN
ma-179	428	2	eur	eur	PROPN
ma-179	428	3	.	.	PUNCT
ma-179	429	1	j.	j.	PROPN
ma-179	429	2	math	math	PROPN
ma-179	429	3	.	.	PUNCT
ma-179	430	1	anal	anal	PROPN
ma-179	430	2	.	.	PUNCT
ma-179	431	1	10.28924	10.28924	NUM
ma-179	431	2	/	/	SYM
ma-179	431	3	ada	ada	PROPN
ma-179	431	4	/	/	SYM
ma-179	431	5	ma.3.25	ma.3.25	NOUN
ma-179	431	6	16references	16reference	NOUN
ma-179	432	1	[	[	X
ma-179	432	2	1	1	NUM
ma-179	432	3	]	]	X
ma-179	432	4	b.	b.	PROPN
ma-179	432	5	bercu	bercu	PROPN
ma-179	432	6	,	,	PUNCT
ma-179	432	7	on	on	ADP
ma-179	432	8	large	large	ADJ
ma-179	432	9	deviations	deviation	NOUN
ma-179	432	10	in	in	ADP
ma-179	432	11	the	the	DET
ma-179	432	12	gaussian	gaussian	ADJ
ma-179	432	13	autoregressive	autoregressive	ADJ
ma-179	432	14	process	process	NOUN
ma-179	432	15	:	:	PUNCT
ma-179	432	16	stable	stable	ADJ
ma-179	432	17	,	,	PUNCT
ma-179	432	18	unstable	unstable	ADJ
ma-179	432	19	and	and	CCONJ
ma-179	432	20	explosive	explosive	ADJ
ma-179	432	21	cases	case	NOUN
ma-179	432	22	,	,	PUNCT
ma-179	432	23	bernoulli	bernoulli	PROPN
ma-179	432	24	.	.	PUNCT
ma-179	433	1	7	7	NUM
ma-179	433	2	(	(	PUNCT
ma-179	433	3	2001	2001	NUM
ma-179	433	4	)	)	PUNCT
ma-179	433	5	299	299	NUM
ma-179	433	6	-	-	SYM
ma-179	433	7	316.[2	316.[2	NUM
ma-179	433	8	]	]	X
ma-179	433	9	b.	b.	PROPN
ma-179	433	10	bercu	bercu	PROPN
ma-179	433	11	,	,	PUNCT
ma-179	433	12	a.	a.	NOUN
ma-179	433	13	roualt	roualt	NOUN
ma-179	433	14	,	,	PUNCT
ma-179	433	15	sharp	sharp	ADJ
ma-179	433	16	large	large	ADJ
ma-179	433	17	deviation	deviation	NOUN
ma-179	433	18	for	for	ADP
ma-179	433	19	the	the	DET
ma-179	433	20	ornstein	ornstein	PROPN
ma-179	433	21	-	-	PUNCT
ma-179	433	22	uhlenbeck	uhlenbeck	PROPN
ma-179	433	23	process	process	NOUN
ma-179	433	24	,	,	PUNCT
ma-179	433	25	theory	theory	NOUN
ma-179	433	26	prob	prob	PROPN
ma-179	433	27	.	.	PUNCT
ma-179	434	1	appl	appl	PROPN
ma-179	434	2	.	.	PUNCT
ma-179	435	1	46	46	NUM
ma-179	435	2	(	(	PUNCT
ma-179	435	3	2002	2002	NUM
ma-179	435	4	)	)	PUNCT
ma-179	435	5	1	1	NUM
ma-179	435	6	-	-	SYM
ma-179	435	7	19.[3	19.[3	NUM
ma-179	435	8	]	]	X
ma-179	435	9	b.	b.	PROPN
ma-179	435	10	bercu	bercu	PROPN
ma-179	435	11	,	,	PUNCT
ma-179	435	12	l.	l.	PROPN
ma-179	435	13	coutin	coutin	PROPN
ma-179	435	14	,	,	PUNCT
ma-179	435	15	n.	n.	PROPN
ma-179	435	16	savy	savy	PROPN
ma-179	435	17	,	,	PUNCT
ma-179	435	18	sharp	sharp	ADJ
ma-179	435	19	large	large	ADJ
ma-179	435	20	deviations	deviation	NOUN
ma-179	435	21	for	for	ADP
ma-179	435	22	the	the	DET
ma-179	435	23	non	non	ADJ
ma-179	435	24	-	-	ADJ
ma-179	435	25	stationary	stationary	ADJ
ma-179	435	26	ornstein	ornstein	PROPN
ma-179	435	27	-	-	PUNCT
ma-179	435	28	uhlenbeck	uhlenbeck	PROPN
ma-179	435	29	process	process	NOUN
ma-179	435	30	,	,	PUNCT
ma-179	435	31	stoch.process	stoch.process	NOUN
ma-179	435	32	appl	appl	NOUN
ma-179	435	33	.	.	PUNCT
ma-179	436	1	122	122	NUM
ma-179	436	2	(	(	PUNCT
ma-179	436	3	2012	2012	NUM
ma-179	436	4	)	)	PUNCT
ma-179	436	5	3393	3393	NUM
ma-179	436	6	-	-	SYM
ma-179	436	7	3424.[4	3424.[4	NUM
ma-179	436	8	]	]	X
ma-179	436	9	b.	b.	PROPN
ma-179	436	10	bercu	bercu	PROPN
ma-179	436	11	,	,	PUNCT
ma-179	436	12	a.	a.	NOUN
ma-179	436	13	richou	richou	PROPN
ma-179	436	14	,	,	PUNCT
ma-179	436	15	large	large	ADJ
ma-179	436	16	deviations	deviation	NOUN
ma-179	436	17	for	for	ADP
ma-179	436	18	the	the	DET
ma-179	436	19	ornstein	ornstein	PROPN
ma-179	436	20	-	-	PUNCT
ma-179	436	21	uhlenbeck	uhlenbeck	PROPN
ma-179	436	22	process	process	NOUN
ma-179	436	23	without	without	ADP
ma-179	436	24	tears	tear	NOUN
ma-179	436	25	,	,	PUNCT
ma-179	436	26	stat	stat	PROPN
ma-179	436	27	.	.	PUNCT
ma-179	437	1	prob	prob	PROPN
ma-179	437	2	.	.	PUNCT
ma-179	438	1	lett	lett	PROPN
ma-179	438	2	.	.	PUNCT
ma-179	439	1	123	123	NUM
ma-179	439	2	(	(	PUNCT
ma-179	439	3	2017)45	2017)45	NUM
ma-179	439	4	-	-	SYM
ma-179	439	5	55.[5	55.[5	NUM
ma-179	439	6	]	]	PUNCT
ma-179	439	7	j.p.n	j.p.n	PROPN
ma-179	439	8	.	.	PROPN
ma-179	439	9	bishwal	bishwal	PROPN
ma-179	439	10	,	,	PUNCT
ma-179	439	11	sharp	sharp	ADJ
ma-179	439	12	berry	berry	NOUN
ma-179	439	13	-	-	PUNCT
ma-179	439	14	esseen	esseen	PROPN
ma-179	439	15	bound	bind	VERB
ma-179	439	16	for	for	ADP
ma-179	439	17	the	the	DET
ma-179	439	18	maximum	maximum	ADJ
ma-179	439	19	likelihood	likelihood	NOUN
ma-179	439	20	estimator	estimator	NOUN
ma-179	439	21	in	in	ADP
ma-179	439	22	the	the	DET
ma-179	439	23	ornstein	ornstein	PROPN
ma-179	439	24	-	-	PUNCT
ma-179	439	25	uhlenbeck	uhlenbeck	PROPN
ma-179	439	26	process	process	NOUN
ma-179	439	27	,	,	PUNCT
ma-179	439	28	sankhya	sankhya	ADJ
ma-179	439	29	,	,	PUNCT
ma-179	439	30	ser	ser	NOUN
ma-179	439	31	.	.	PUNCT
ma-179	440	1	a.	a.	PROPN
ma-179	440	2	62	62	NUM
ma-179	440	3	(	(	PUNCT
ma-179	440	4	2000	2000	NUM
ma-179	440	5	)	)	PUNCT
ma-179	440	6	1	1	NUM
ma-179	440	7	-	-	SYM
ma-179	440	8	10.[6	10.[6	NUM
ma-179	440	9	]	]	PUNCT
ma-179	440	10	j.p.n	j.p.n	PROPN
ma-179	440	11	.	.	PROPN
ma-179	440	12	bishwal	bishwal	NOUN
ma-179	440	13	,	,	PUNCT
ma-179	440	14	rates	rate	NOUN
ma-179	440	15	of	of	ADP
ma-179	440	16	convergence	convergence	NOUN
ma-179	440	17	of	of	ADP
ma-179	440	18	the	the	DET
ma-179	440	19	posterior	posterior	ADJ
ma-179	440	20	distributions	distribution	NOUN
ma-179	440	21	and	and	CCONJ
ma-179	440	22	the	the	DET
ma-179	440	23	bayes	bayes	NOUN
ma-179	440	24	estimators	estimator	NOUN
ma-179	440	25	in	in	ADP
ma-179	440	26	the	the	DET
ma-179	440	27	ornstein	ornstein	PROPN
ma-179	440	28	-	-	PUNCT
ma-179	440	29	uhlenbeck	uhlenbeck	PROPN
ma-179	440	30	process	process	NOUN
ma-179	440	31	,	,	PUNCT
ma-179	440	32	rand	rand	NOUN
ma-179	440	33	.	.	PUNCT
ma-179	441	1	oper	oper	PROPN
ma-179	441	2	.	.	PROPN
ma-179	441	3	stoch	stoch	PROPN
ma-179	441	4	.	.	PUNCT
ma-179	442	1	equ	equ	PROPN
ma-179	442	2	.	.	PROPN
ma-179	442	3	8	8	NUM
ma-179	442	4	(	(	PUNCT
ma-179	442	5	2000b	2000b	NUM
ma-179	442	6	)	)	PUNCT
ma-179	442	7	51	51	NUM
ma-179	442	8	-	-	SYM
ma-179	442	9	70.[7	70.[7	NUM
ma-179	442	10	]	]	PUNCT
ma-179	442	11	j.p.n	j.p.n	PROPN
ma-179	442	12	.	.	PROPN
ma-179	442	13	bishwal	bishwal	PROPN
ma-179	442	14	,	,	PUNCT
ma-179	442	15	accuracy	accuracy	NOUN
ma-179	442	16	of	of	ADP
ma-179	442	17	normal	normal	ADJ
ma-179	442	18	approximation	approximation	NOUN
ma-179	442	19	for	for	ADP
ma-179	442	20	the	the	DET
ma-179	442	21	maximum	maximum	ADJ
ma-179	442	22	likelihood	likelihood	NOUN
ma-179	442	23	and	and	CCONJ
ma-179	442	24	the	the	DET
ma-179	442	25	bayes	bayes	NOUN
ma-179	442	26	estimators	estimator	NOUN
ma-179	442	27	in	in	ADP
ma-179	442	28	theornstein	theornstein	NOUN
ma-179	442	29	-	-	PUNCT
ma-179	442	30	uhlenbeck	uhlenbeck	NOUN
ma-179	442	31	process	process	NOUN
ma-179	442	32	using	use	VERB
ma-179	442	33	random	random	ADJ
ma-179	442	34	norming	norming	NOUN
ma-179	442	35	,	,	PUNCT
ma-179	442	36	stat	stat	PROPN
ma-179	442	37	.	.	PUNCT
ma-179	443	1	prob	prob	PROPN
ma-179	443	2	.	.	PUNCT
ma-179	444	1	lett	lett	PROPN
ma-179	444	2	.	.	PUNCT
ma-179	445	1	52	52	NUM
ma-179	445	2	(	(	PUNCT
ma-179	445	3	2001	2001	NUM
ma-179	445	4	)	)	PUNCT
ma-179	445	5	427	427	NUM
ma-179	445	6	-	-	SYM
ma-179	445	7	439.[8	439.[8	NUM
ma-179	445	8	]	]	PUNCT
ma-179	445	9	j.p.n	j.p.n	PROPN
ma-179	445	10	.	.	PROPN
ma-179	445	11	bishwal	bishwal	PROPN
ma-179	445	12	,	,	PUNCT
ma-179	445	13	parameter	parameter	NOUN
ma-179	445	14	estimation	estimation	NOUN
ma-179	445	15	in	in	ADP
ma-179	445	16	stochastic	stochastic	ADJ
ma-179	445	17	differential	differential	ADJ
ma-179	445	18	equations	equation	NOUN
ma-179	445	19	,	,	PUNCT
ma-179	445	20	lecture	lecture	NOUN
ma-179	445	21	notes	note	NOUN
ma-179	445	22	in	in	ADP
ma-179	445	23	mathematics	mathematic	NOUN
ma-179	445	24	,	,	PUNCT
ma-179	445	25	1923,springer	1923,springer	NUM
ma-179	445	26	-	-	PUNCT
ma-179	445	27	verlag	verlag	NOUN
ma-179	445	28	,	,	PUNCT
ma-179	445	29	(	(	PUNCT
ma-179	445	30	2008).[9	2008).[9	NOUN
ma-179	445	31	]	]	X
ma-179	445	32	j.p.n	j.p.n	PROPN
ma-179	445	33	.	.	PROPN
ma-179	445	34	bishwal	bishwal	NOUN
ma-179	445	35	,	,	PUNCT
ma-179	445	36	sequential	sequential	ADJ
ma-179	445	37	maximum	maximum	ADJ
ma-179	445	38	likelihood	likelihood	NOUN
ma-179	445	39	estimation	estimation	NOUN
ma-179	445	40	in	in	ADP
ma-179	445	41	nonlinear	nonlinear	ADJ
ma-179	445	42	non	non	ADJ
ma-179	445	43	-	-	ADJ
ma-179	445	44	markov	markov	ADJ
ma-179	445	45	diffusion	diffusion	NOUN
ma-179	445	46	type	type	NOUN
ma-179	445	47	processes	process	NOUN
ma-179	445	48	,	,	PUNCT
ma-179	445	49	dyn.syst	dyn.syst	NOUN
ma-179	445	50	.	.	PUNCT
ma-179	446	1	appl	appl	PROPN
ma-179	446	2	.	.	PROPN
ma-179	447	1	27	27	NUM
ma-179	447	2	(	(	PUNCT
ma-179	447	3	2018	2018	NUM
ma-179	447	4	)	)	PUNCT
ma-179	447	5	107	107	NUM
ma-179	447	6	-	-	SYM
ma-179	447	7	124.[10	124.[10	NUM
ma-179	447	8	]	]	PUNCT
ma-179	447	9	j.p.n	j.p.n	PROPN
ma-179	447	10	.	.	PROPN
ma-179	447	11	bishwal	bishwal	NOUN
ma-179	447	12	,	,	PUNCT
ma-179	447	13	berry	berry	NOUN
ma-179	447	14	-	-	PUNCT
ma-179	447	15	esseen	esseen	VERB
ma-179	447	16	bounds	bound	NOUN
ma-179	447	17	of	of	ADP
ma-179	447	18	approximate	approximate	ADJ
ma-179	447	19	bayes	bayes	PROPN
ma-179	447	20	estimators	estimator	NOUN
ma-179	447	21	for	for	ADP
ma-179	447	22	the	the	DET
ma-179	447	23	discretely	discretely	ADV
ma-179	447	24	observed	observe	VERB
ma-179	447	25	ornstein	ornstein	ADJ
ma-179	447	26	-	-	PUNCT
ma-179	447	27	uhlenbeck	uhlenbeck	PROPN
ma-179	447	28	process	process	NOUN
ma-179	447	29	,	,	PUNCT
ma-179	447	30	asian	asian	ADJ
ma-179	447	31	j.	j.	PROPN
ma-179	447	32	stat	stat	PROPN
ma-179	447	33	.	.	PUNCT
ma-179	448	1	sci	sci	PROPN
ma-179	448	2	.	.	PROPN
ma-179	448	3	1	1	NUM
ma-179	448	4	(	(	PUNCT
ma-179	448	5	2021	2021	NUM
ma-179	448	6	)	)	PUNCT
ma-179	448	7	83	83	NUM
ma-179	448	8	-	-	SYM
ma-179	448	9	122.[11	122.[11	NUM
ma-179	448	10	]	]	PUNCT
ma-179	448	11	j.p.n	j.p.n	PROPN
ma-179	448	12	.	.	PROPN
ma-179	448	13	bishwal	bishwal	PROPN
ma-179	448	14	,	,	PUNCT
ma-179	448	15	parameter	parameter	NOUN
ma-179	448	16	estimation	estimation	NOUN
ma-179	448	17	in	in	ADP
ma-179	448	18	stochastic	stochastic	ADJ
ma-179	448	19	volatility	volatility	NOUN
ma-179	448	20	models	model	NOUN
ma-179	448	21	,	,	PUNCT
ma-179	448	22	springer	springer	NOUN
ma-179	448	23	nature	nature	NOUN
ma-179	448	24	,	,	PUNCT
ma-179	448	25	cham	cham	PROPN
ma-179	448	26	,	,	PUNCT
ma-179	448	27	(	(	PUNCT
ma-179	448	28	2022).[12	2022).[12	NUM
ma-179	448	29	]	]	PUNCT
ma-179	448	30	j.p.n	j.p.n	PROPN
ma-179	448	31	.	.	PROPN
ma-179	448	32	bishwal	bishwal	PROPN
ma-179	448	33	,	,	PUNCT
ma-179	448	34	a.	a.	PROPN
ma-179	448	35	bose	bose	PROPN
ma-179	448	36	,	,	PUNCT
ma-179	448	37	speed	speed	NOUN
ma-179	448	38	of	of	ADP
ma-179	448	39	convergence	convergence	NOUN
ma-179	448	40	of	of	ADP
ma-179	448	41	the	the	DET
ma-179	448	42	maximum	maximum	ADJ
ma-179	448	43	likelihood	likelihood	NOUN
ma-179	448	44	estimator	estimator	NOUN
ma-179	448	45	in	in	ADP
ma-179	448	46	the	the	DET
ma-179	448	47	ornstein	ornstein	NOUN
ma-179	448	48	-	-	PUNCT
ma-179	448	49	uhlenbeckprocess	uhlenbeckprocess	NOUN
ma-179	448	50	,	,	PUNCT
ma-179	448	51	calcutta	calcutta	NOUN
ma-179	448	52	stat	stat	PROPN
ma-179	448	53	.	.	PUNCT
ma-179	449	1	assoc	assoc	PROPN
ma-179	449	2	.	.	PUNCT
ma-179	449	3	bull	bull	PROPN
ma-179	449	4	.	.	PUNCT
ma-179	450	1	45	45	NUM
ma-179	450	2	(	(	PUNCT
ma-179	450	3	1995	1995	NUM
ma-179	450	4	)	)	PUNCT
ma-179	450	5	,	,	PUNCT
ma-179	450	6	245	245	NUM
ma-179	450	7	-	-	SYM
ma-179	450	8	251.[13	251.[13	NUM
ma-179	450	9	]	]	PUNCT
ma-179	450	10	j.p.n	j.p.n	PROPN
ma-179	450	11	.	.	PROPN
ma-179	450	12	bishwal	bishwal	PROPN
ma-179	450	13	,	,	PUNCT
ma-179	450	14	a.	a.	PROPN
ma-179	450	15	bose	bose	PROPN
ma-179	450	16	,	,	PUNCT
ma-179	450	17	rates	rate	NOUN
ma-179	450	18	of	of	ADP
ma-179	450	19	convergence	convergence	NOUN
ma-179	450	20	of	of	ADP
ma-179	450	21	approximate	approximate	ADJ
ma-179	450	22	maximum	maximum	ADJ
ma-179	450	23	likelihood	likelihood	NOUN
ma-179	450	24	estimators	estimator	NOUN
ma-179	450	25	in	in	ADP
ma-179	450	26	the	the	DET
ma-179	450	27	ornstein	ornstein	PROPN
ma-179	450	28	-	-	PUNCT
ma-179	450	29	uhlenbeck	uhlenbeck	PROPN
ma-179	450	30	process	process	NOUN
ma-179	450	31	,	,	PUNCT
ma-179	450	32	comp	comp	PROPN
ma-179	450	33	.	.	PUNCT
ma-179	450	34	math	math	PROPN
ma-179	450	35	.	.	PUNCT
ma-179	451	1	appl	appl	PROPN
ma-179	451	2	.	.	PUNCT
ma-179	452	1	42	42	NUM
ma-179	452	2	(	(	PUNCT
ma-179	452	3	2001	2001	NUM
ma-179	452	4	)	)	PUNCT
ma-179	452	5	23	23	NUM
ma-179	452	6	-	-	SYM
ma-179	452	7	38.[14	38.[14	PROPN
ma-179	452	8	]	]	X
ma-179	452	9	a.a	a.a	PROPN
ma-179	452	10	.	.	PROPN
ma-179	452	11	borokov	borokov	PROPN
ma-179	452	12	,	,	PUNCT
ma-179	452	13	on	on	ADP
ma-179	452	14	the	the	DET
ma-179	452	15	rate	rate	NOUN
ma-179	452	16	of	of	ADP
ma-179	452	17	convergence	convergence	NOUN
ma-179	452	18	for	for	ADP
ma-179	452	19	the	the	DET
ma-179	452	20	invariance	invariance	NOUN
ma-179	452	21	principle	principle	NOUN
ma-179	452	22	,	,	PUNCT
ma-179	452	23	theory	theory	NOUN
ma-179	452	24	prob	prob	PROPN
ma-179	452	25	.	.	PUNCT
ma-179	452	26	appl	appl	PROPN
ma-179	452	27	.	.	PROPN
ma-179	453	1	18	18	NUM
ma-179	453	2	(	(	PUNCT
ma-179	453	3	1973	1973	NUM
ma-179	453	4	)	)	PUNCT
ma-179	453	5	217	217	NUM
ma-179	453	6	-	-	SYM
ma-179	453	7	234.[15	234.[15	PROPN
ma-179	453	8	]	]	X
ma-179	453	9	h.m	h.m	PROPN
ma-179	453	10	.	.	PROPN
ma-179	453	11	dietz	dietz	PROPN
ma-179	453	12	,	,	PUNCT
ma-179	453	13	y.a	y.a	PROPN
ma-179	453	14	.	.	PROPN
ma-179	453	15	kutoyants	kutoyant	NOUN
ma-179	453	16	,	,	PUNCT
ma-179	453	17	parameter	parameter	NOUN
ma-179	453	18	estimation	estimation	NOUN
ma-179	453	19	in	in	ADP
ma-179	453	20	some	some	DET
ma-179	453	21	non	non	ADJ
ma-179	453	22	-	-	ADJ
ma-179	453	23	recurrent	recurrent	ADJ
ma-179	453	24	solutions	solution	NOUN
ma-179	453	25	of	of	ADP
ma-179	453	26	sde	sde	PROPN
ma-179	453	27	,	,	PUNCT
ma-179	453	28	stat	stat	PROPN
ma-179	453	29	.	.	PUNCT
ma-179	454	1	decis	decis	PROPN
ma-179	454	2	.	.	PROPN
ma-179	454	3	21	21	NUM
ma-179	454	4	(	(	PUNCT
ma-179	454	5	2003)29	2003)29	NUM
ma-179	454	6	-	-	SYM
ma-179	454	7	45.[16	45.[16	PROPN
ma-179	454	8	]	]	X
ma-179	454	9	p.d	p.d	PROPN
ma-179	454	10	.	.	PROPN
ma-179	454	11	feigin	feigin	PROPN
ma-179	454	12	,	,	PUNCT
ma-179	454	13	maximum	maximum	ADJ
ma-179	454	14	likelihood	likelihood	NOUN
ma-179	454	15	estimation	estimation	NOUN
ma-179	454	16	for	for	ADP
ma-179	454	17	continuous	continuous	ADJ
ma-179	454	18	time	time	NOUN
ma-179	454	19	stochastic	stochastic	NOUN
ma-179	454	20	processes	process	NOUN
ma-179	454	21	,	,	PUNCT
ma-179	454	22	adv	adv	PROPN
ma-179	454	23	.	.	PUNCT
ma-179	454	24	appl	appl	PROPN
ma-179	454	25	.	.	PUNCT
ma-179	455	1	prob	prob	PROPN
ma-179	455	2	.	.	PROPN
ma-179	455	3	8	8	NUM
ma-179	455	4	(	(	PUNCT
ma-179	455	5	1976)712	1976)712	NOUN
ma-179	455	6	-	-	PUNCT
ma-179	455	7	736.[17	736.[17	PROPN
ma-179	455	8	]	]	PUNCT
ma-179	455	9	w.	w.	NOUN
ma-179	455	10	feller	feller	PROPN
ma-179	455	11	,	,	PUNCT
ma-179	455	12	an	an	DET
ma-179	455	13	introduction	introduction	NOUN
ma-179	455	14	to	to	ADP
ma-179	455	15	probability	probability	NOUN
ma-179	455	16	theory	theory	NOUN
ma-179	455	17	and	and	CCONJ
ma-179	455	18	its	its	PRON
ma-179	455	19	applications	application	NOUN
ma-179	455	20	,	,	PUNCT
ma-179	455	21	vol	vol	NOUN
ma-179	455	22	.	.	PUNCT
ma-179	456	1	i	i	PRON
ma-179	456	2	,	,	PUNCT
ma-179	456	3	wiley	wiley	PROPN
ma-179	456	4	,	,	PUNCT
ma-179	456	5	new	new	PROPN
ma-179	456	6	york	york	PROPN
ma-179	456	7	,	,	PUNCT
ma-179	456	8	(	(	PUNCT
ma-179	456	9	1957).[18	1957).[18	NUM
ma-179	456	10	]	]	X
ma-179	456	11	w.	w.	NOUN
ma-179	456	12	feller	feller	PROPN
ma-179	456	13	,	,	PUNCT
ma-179	456	14	an	an	DET
ma-179	456	15	introduction	introduction	NOUN
ma-179	456	16	to	to	ADP
ma-179	456	17	probability	probability	NOUN
ma-179	456	18	theory	theory	NOUN
ma-179	456	19	and	and	CCONJ
ma-179	456	20	its	its	PRON
ma-179	456	21	applications	application	NOUN
ma-179	456	22	,	,	PUNCT
ma-179	456	23	vol	vol	NOUN
ma-179	456	24	.	.	PUNCT
ma-179	456	25	ii	ii	PROPN
ma-179	456	26	,	,	PUNCT
ma-179	456	27	wiley	wiley	PROPN
ma-179	456	28	,	,	PUNCT
ma-179	456	29	new	new	PROPN
ma-179	456	30	york	york	PROPN
ma-179	456	31	,	,	PUNCT
ma-179	456	32	(	(	PUNCT
ma-179	456	33	1971).[19	1971).[19	NUM
ma-179	456	34	]	]	PUNCT
ma-179	456	35	a.	a.	NOUN
ma-179	456	36	friedman	friedman	PROPN
ma-179	456	37	,	,	PUNCT
ma-179	456	38	stochastic	stochastic	ADJ
ma-179	456	39	differential	differential	ADJ
ma-179	456	40	equations	equation	NOUN
ma-179	456	41	,	,	PUNCT
ma-179	456	42	vol	vol	NOUN
ma-179	456	43	.	.	PUNCT
ma-179	457	1	i	i	PRON
ma-179	457	2	,	,	PUNCT
ma-179	457	3	academic	academic	ADJ
ma-179	457	4	press	press	NOUN
ma-179	457	5	,	,	PUNCT
ma-179	457	6	new	new	PROPN
ma-179	457	7	york	york	PROPN
ma-179	457	8	,	,	PUNCT
ma-179	457	9	(	(	PUNCT
ma-179	457	10	1975).[20	1975).[20	X
ma-179	457	11	]	]	PUNCT
ma-179	457	12	p.	p.	PROPN
ma-179	457	13	hall	hall	PROPN
ma-179	457	14	,	,	PUNCT
ma-179	457	15	c.c	c.c	PROPN
ma-179	457	16	.	.	PROPN
ma-179	457	17	heyde	heyde	PROPN
ma-179	457	18	,	,	PUNCT
ma-179	457	19	martingale	martingale	ADJ
ma-179	457	20	limit	limit	NOUN
ma-179	457	21	theory	theory	NOUN
ma-179	457	22	and	and	CCONJ
ma-179	457	23	its	its	PRON
ma-179	457	24	applications	application	NOUN
ma-179	457	25	,	,	PUNCT
ma-179	457	26	academic	academic	ADJ
ma-179	457	27	press	press	NOUN
ma-179	457	28	,	,	PUNCT
ma-179	457	29	new	new	PROPN
ma-179	457	30	york	york	PROPN
ma-179	457	31	,	,	PUNCT
ma-179	457	32	(	(	PUNCT
ma-179	457	33	1980).[21	1980).[21	NUM
ma-179	457	34	]	]	X
ma-179	457	35	u.	u.	PROPN
ma-179	457	36	horst	horst	PROPN
ma-179	457	37	,	,	PUNCT
ma-179	457	38	j.	j.	PROPN
ma-179	457	39	wenzelburger	wenzelburger	PROPN
ma-179	457	40	,	,	PUNCT
ma-179	457	41	on	on	ADP
ma-179	457	42	non	non	ADJ
ma-179	457	43	-	-	ADJ
ma-179	457	44	ergodic	ergodic	ADJ
ma-179	457	45	asset	asset	NOUN
ma-179	457	46	prices	price	NOUN
ma-179	457	47	,	,	PUNCT
ma-179	457	48	econ	econ	PROPN
ma-179	457	49	.	.	PUNCT
ma-179	457	50	theory	theory	NOUN
ma-179	457	51	.	.	PUNCT
ma-179	458	1	34	34	NUM
ma-179	458	2	(	(	PUNCT
ma-179	458	3	2008	2008	NUM
ma-179	458	4	)	)	PUNCT
ma-179	458	5	207	207	NUM
ma-179	458	6	-	-	SYM
ma-179	458	7	234.[22	234.[22	PROPN
ma-179	458	8	]	]	X
ma-179	458	9	a.v	a.v	PROPN
ma-179	458	10	.	.	PROPN
ma-179	458	11	ivanov	ivanov	PROPN
ma-179	458	12	,	,	PUNCT
ma-179	458	13	the	the	DET
ma-179	458	14	berry	berry	NOUN
ma-179	458	15	-	-	PUNCT
ma-179	458	16	esseen	esseen	VERB
ma-179	458	17	inequality	inequality	NOUN
ma-179	458	18	for	for	ADP
ma-179	458	19	the	the	DET
ma-179	458	20	distribution	distribution	NOUN
ma-179	458	21	of	of	ADP
ma-179	458	22	the	the	DET
ma-179	458	23	least	least	ADJ
ma-179	458	24	squares	square	NOUN
ma-179	458	25	estimae	estimae	PROPN
ma-179	458	26	,	,	PUNCT
ma-179	458	27	math	math	NOUN
ma-179	458	28	.	.	PUNCT
ma-179	459	1	notes	note	NOUN
ma-179	459	2	.	.	PUNCT
ma-179	460	1	20	20	NUM
ma-179	460	2	(	(	PUNCT
ma-179	460	3	1976)721	1976)721	PROPN
ma-179	460	4	-	-	PUNCT
ma-179	460	5	727.[23	727.[23	PROPN
ma-179	460	6	]	]	X
ma-179	460	7	r.s	r.s	PROPN
ma-179	460	8	.	.	PROPN
ma-179	460	9	liptser	liptser	PROPN
ma-179	460	10	,	,	PUNCT
ma-179	460	11	a.n	a.n	PROPN
ma-179	460	12	.	.	PROPN
ma-179	460	13	shiryayev	shiryayev	PROPN
ma-179	460	14	,	,	PUNCT
ma-179	460	15	statistics	statistic	NOUN
ma-179	460	16	of	of	ADP
ma-179	460	17	random	random	ADJ
ma-179	460	18	processes	process	NOUN
ma-179	460	19	i	i	PRON
ma-179	460	20	:	:	PUNCT
ma-179	460	21	general	general	ADJ
ma-179	460	22	theory	theory	NOUN
ma-179	460	23	,	,	PUNCT
ma-179	460	24	springer	springer	NOUN
ma-179	460	25	-	-	PUNCT
ma-179	460	26	verlag	verlag	PROPN
ma-179	460	27	,	,	PUNCT
ma-179	460	28	berlin	berlin	PROPN
ma-179	460	29	,	,	PUNCT
ma-179	460	30	(	(	PUNCT
ma-179	460	31	1977).[24	1977).[24	PROPN
ma-179	460	32	]	]	PUNCT
ma-179	460	33	r.	r.	PROPN
ma-179	460	34	michel	michel	PROPN
ma-179	460	35	,	,	PUNCT
ma-179	460	36	j.	j.	PROPN
ma-179	460	37	pfanzagl	pfanzagl	PROPN
ma-179	460	38	,	,	PUNCT
ma-179	460	39	the	the	DET
ma-179	460	40	accuracy	accuracy	NOUN
ma-179	460	41	of	of	ADP
ma-179	460	42	the	the	DET
ma-179	460	43	normal	normal	ADJ
ma-179	460	44	approximation	approximation	NOUN
ma-179	460	45	for	for	ADP
ma-179	460	46	minimum	minimum	ADJ
ma-179	460	47	contrast	contrast	NOUN
ma-179	460	48	estimate	estimate	NOUN
ma-179	460	49	,	,	PUNCT
ma-179	460	50	zeit	zeit	PROPN
ma-179	460	51	wahr	wahr	PROPN
ma-179	460	52	.	.	PUNCT
ma-179	461	1	verw.gebiete	verw.gebiete	PROPN
ma-179	461	2	.	.	PUNCT
ma-179	462	1	18	18	NUM
ma-179	462	2	(	(	PUNCT
ma-179	462	3	1971	1971	NUM
ma-179	462	4	)	)	PUNCT
ma-179	462	5	73	73	NUM
ma-179	462	6	-	-	SYM
ma-179	462	7	84.[25	84.[25	NUM
ma-179	462	8	]	]	X
ma-179	462	9	i.	i.	NOUN
ma-179	462	10	nourdin	nourdin	PROPN
ma-179	462	11	,	,	PUNCT
ma-179	462	12	g.	g.	PROPN
ma-179	462	13	peccati	peccati	PROPN
ma-179	462	14	,	,	PUNCT
ma-179	462	15	stein	stein	PROPN
ma-179	462	16	’s	’s	PART
ma-179	462	17	method	method	NOUN
ma-179	462	18	on	on	ADP
ma-179	462	19	wiener	wiener	NOUN
ma-179	462	20	chaos	chaos	NOUN
ma-179	462	21	,	,	PUNCT
ma-179	462	22	prob	prob	PROPN
ma-179	462	23	.	.	PROPN
ma-179	462	24	theory	theory	NOUN
ma-179	462	25	related	relate	VERB
ma-179	462	26	fields	field	NOUN
ma-179	462	27	.	.	PUNCT
ma-179	463	1	145	145	NUM
ma-179	463	2	(	(	PUNCT
ma-179	463	3	2009	2009	NUM
ma-179	463	4	)	)	PUNCT
ma-179	463	5	75	75	NUM
ma-179	463	6	-	-	SYM
ma-179	463	7	118.[26	118.[26	NUM
ma-179	463	8	]	]	X
ma-179	463	9	i.	i.	NOUN
ma-179	463	10	nourdin	nourdin	PROPN
ma-179	463	11	,	,	PUNCT
ma-179	463	12	g.	g.	PROPN
ma-179	463	13	peccati	peccati	PROPN
ma-179	463	14	,	,	PUNCT
ma-179	463	15	normal	normal	ADJ
ma-179	463	16	approximation	approximation	NOUN
ma-179	463	17	with	with	ADP
ma-179	463	18	malliavin	malliavin	PROPN
ma-179	463	19	calculus	calculus	NOUN
ma-179	463	20	:	:	PUNCT
ma-179	463	21	from	from	ADP
ma-179	463	22	stein	stein	PROPN
ma-179	463	23	’s	’s	PART
ma-179	463	24	method	method	NOUN
ma-179	463	25	to	to	ADP
ma-179	463	26	universality	universality	NOUN
ma-179	463	27	,	,	PUNCT
ma-179	463	28	cambridgeuniversity	cambridgeuniversity	NOUN
ma-179	463	29	press	press	NOUN
ma-179	463	30	,	,	PUNCT
ma-179	463	31	cambridge	cambridge	PROPN
ma-179	463	32	,	,	PUNCT
ma-179	463	33	(	(	PUNCT
ma-179	463	34	2012).[27	2012).[27	NUM
ma-179	463	35	]	]	X
ma-179	463	36	v.v	v.v	PROPN
ma-179	463	37	.	.	PROPN
ma-179	463	38	petrov	petrov	PROPN
ma-179	463	39	,	,	PUNCT
ma-179	463	40	limit	limit	VERB
ma-179	463	41	theorems	theorem	NOUN
ma-179	463	42	of	of	ADP
ma-179	463	43	probability	probability	NOUN
ma-179	463	44	theory	theory	NOUN
ma-179	463	45	,	,	PUNCT
ma-179	463	46	oxford	oxford	PROPN
ma-179	463	47	university	university	PROPN
ma-179	463	48	press	press	NOUN
ma-179	463	49	,	,	PUNCT
ma-179	463	50	oxford	oxford	PROPN
ma-179	463	51	,	,	PUNCT
ma-179	463	52	(	(	PUNCT
ma-179	463	53	1995).[28	1995).[28	NUM
ma-179	463	54	]	]	X
ma-179	463	55	j.	j.	PROPN
ma-179	463	56	pfanzagl	pfanzagl	PROPN
ma-179	463	57	,	,	PUNCT
ma-179	463	58	the	the	DET
ma-179	463	59	berry	berry	NOUN
ma-179	463	60	-	-	PUNCT
ma-179	463	61	esseen	esseen	PROPN
ma-179	463	62	bound	bind	VERB
ma-179	463	63	for	for	ADP
ma-179	463	64	minimum	minimum	ADJ
ma-179	463	65	contrast	contrast	NOUN
ma-179	463	66	estimators	estimator	NOUN
ma-179	463	67	,	,	PUNCT
ma-179	463	68	metrika	metrika	NOUN
ma-179	463	69	.	.	PROPN
ma-179	463	70	17	17	NUM
ma-179	463	71	(	(	PUNCT
ma-179	463	72	1971	1971	NUM
ma-179	463	73	)	)	PUNCT
ma-179	463	74	82	82	NUM
ma-179	463	75	-	-	SYM
ma-179	463	76	91	91	NUM
ma-179	463	77	.	.	PUNCT
ma-179	464	1	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	PROPN
ma-179	464	2	eur	eur	PROPN
ma-179	464	3	.	.	PUNCT
ma-179	465	1	j.	j.	PROPN
ma-179	465	2	math	math	PROPN
ma-179	465	3	.	.	PUNCT
ma-179	466	1	anal	anal	PROPN
ma-179	466	2	.	.	PUNCT
ma-179	467	1	10.28924	10.28924	NUM
ma-179	467	2	/	/	SYM
ma-179	467	3	ada	ada	PROPN
ma-179	467	4	/	/	SYM
ma-179	467	5	ma.3.25	ma.3.25	NOUN
ma-179	467	6	17	17	NUM
ma-179	468	1	[	[	X
ma-179	468	2	29	29	NUM
ma-179	468	3	]	]	PUNCT
ma-179	468	4	p.	p.	NOUN
ma-179	468	5	protter	protter	NOUN
ma-179	468	6	,	,	PUNCT
ma-179	468	7	stochastic	stochastic	ADJ
ma-179	468	8	integration	integration	NOUN
ma-179	468	9	and	and	CCONJ
ma-179	468	10	differential	differential	ADJ
ma-179	468	11	equations	equation	NOUN
ma-179	468	12	:	:	PUNCT
ma-179	468	13	a	a	DET
ma-179	468	14	new	new	ADJ
ma-179	468	15	approach	approach	NOUN
ma-179	468	16	,	,	PUNCT
ma-179	468	17	springer	springer	NOUN
ma-179	468	18	-	-	PUNCT
ma-179	468	19	verlag	verlag	PROPN
ma-179	468	20	,	,	PUNCT
ma-179	468	21	berlin	berlin	PROPN
ma-179	468	22	,	,	PUNCT
ma-179	468	23	(	(	PUNCT
ma-179	468	24	1990).[30	1990).[30	NUM
ma-179	468	25	]	]	X
ma-179	468	26	y.	y.	PROPN
ma-179	468	27	shimizu	shimizu	PROPN
ma-179	468	28	,	,	PUNCT
ma-179	468	29	local	local	ADJ
ma-179	468	30	asymptotic	asymptotic	ADJ
ma-179	468	31	mixed	mixed	ADJ
ma-179	468	32	normality	normality	NOUN
ma-179	468	33	for	for	ADP
ma-179	468	34	discretely	discretely	ADV
ma-179	468	35	observed	observe	VERB
ma-179	468	36	non	non	ADJ
ma-179	468	37	-	-	ADJ
ma-179	468	38	recurrent	recurrent	ADJ
ma-179	468	39	ornstein	ornstein	PROPN
ma-179	468	40	-	-	PUNCT
ma-179	468	41	uhlenbeck	uhlenbeck	PROPN
ma-179	468	42	processes	process	NOUN
ma-179	468	43	,	,	PUNCT
ma-179	468	44	ann	ann	PROPN
ma-179	468	45	.	.	PROPN
ma-179	468	46	inst	inst	PROPN
ma-179	468	47	.	.	PUNCT
ma-179	469	1	stat	stat	PROPN
ma-179	469	2	.	.	PUNCT
ma-179	470	1	math	math	NOUN
ma-179	470	2	.	.	PUNCT
ma-179	471	1	64	64	NUM
ma-179	471	2	(	(	PUNCT
ma-179	471	3	2012	2012	NUM
ma-179	471	4	)	)	PUNCT
ma-179	471	5	193	193	NUM
ma-179	471	6	-	-	SYM
ma-179	471	7	211	211	NUM
ma-179	471	8	.	.	PUNCT
ma-179	472	1	https://doi.org/10.28924/ada/ma.3.25	https://doi.org/10.28924/ada/ma.3.25	NOUN
ma-179	472	2	references	reference	NOUN