id	sid	tid	token	lemma	pos
cana-6007	1	1	communications	communication	NOUN
cana-6007	1	2	on	on	ADP
cana-6007	1	3	applied	apply	VERB
cana-6007	1	4	nonlinear	nonlinear	ADJ
cana-6007	1	5	analysis	analysis	NOUN
cana-6007	1	6	issn	issn	NOUN
cana-6007	1	7	:	:	PUNCT
cana-6007	1	8	1074	1074	NUM
cana-6007	1	9	-	-	PUNCT
cana-6007	1	10	133x	133x	NUM
cana-6007	1	11	vol	vol	VERB
cana-6007	1	12	32	32	NUM
cana-6007	1	13	no	no	NOUN
cana-6007	1	14	.	.	PUNCT
cana-6007	2	1	10s	10	NOUN
cana-6007	2	2	(	(	PUNCT
cana-6007	2	3	2025	2025	NUM
cana-6007	2	4	)	)	PUNCT
cana-6007	2	5	3226	3226	NUM
cana-6007	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	2	7	numerical	numerical	ADJ
cana-6007	2	8	accuracy	accuracy	NOUN
cana-6007	2	9	of	of	ADP
cana-6007	2	10	euler	euler	NOUN
cana-6007	2	11	-	-	PUNCT
cana-6007	2	12	maruyama	maruyama	NOUN
cana-6007	2	13	and	and	CCONJ
cana-6007	2	14	milstein	milstein	ADJ
cana-6007	2	15	methods	method	NOUN
cana-6007	2	16	for	for	ADP
cana-6007	2	17	solving	solve	VERB
cana-6007	2	18	nonlinear	nonlinear	ADJ
cana-6007	2	19	stochastic	stochastic	ADJ
cana-6007	2	20	differential	differential	NOUN
cana-6007	2	21	equation	equation	NOUN
cana-6007	2	22	eram	eram	NOUN
cana-6007	2	23	naaz1	naaz1	PROPN
cana-6007	2	24	and	and	CCONJ
cana-6007	2	25	najmuddin	najmuddin	PROPN
cana-6007	2	26	ahmad2	ahmad2	PROPN
cana-6007	2	27	*	*	PROPN
cana-6007	2	28	1,2department	1,2department	NUM
cana-6007	2	29	of	of	ADP
cana-6007	2	30	mathematics	mathematics	PROPN
cana-6007	2	31	&	&	CCONJ
cana-6007	2	32	statistics	statistic	NOUN
cana-6007	2	33	,	,	PUNCT
cana-6007	2	34	integral	integral	ADJ
cana-6007	2	35	university	university	NOUN
cana-6007	2	36	,	,	PUNCT
cana-6007	2	37	lucknow226026	lucknow226026	PROPN
cana-6007	2	38	,	,	PUNCT
cana-6007	2	39	india	india	PROPN
cana-6007	2	40	.	.	PUNCT
cana-6007	3	1	*	*	PUNCT
cana-6007	3	2	coressponding	coressponde	VERB
cana-6007	3	3	author	author	NOUN
cana-6007	3	4	e	e	NOUN
cana-6007	3	5	-	-	NOUN
cana-6007	3	6	mail	mail	NOUN
cana-6007	3	7	:	:	PUNCT
cana-6007	3	8	najmuddinahmad33@gmail.com	najmuddinahmad33@gmail.com	X
cana-6007	3	9	2	2	NUM
cana-6007	3	10	author	author	NOUN
cana-6007	3	11	e	e	NOUN
cana-6007	3	12	-	-	NOUN
cana-6007	3	13	mail	mail	NOUN
cana-6007	3	14	:	:	PUNCT
cana-6007	4	1	eramphdiul@gmail.com	eramphdiul@gmail.com	X
cana-6007	4	2	1	1	NUM
cana-6007	4	3	article	article	NOUN
cana-6007	4	4	history	history	NOUN
cana-6007	4	5	:	:	PUNCT
cana-6007	4	6	received	receive	VERB
cana-6007	4	7	:	:	PUNCT
cana-6007	4	8	04/01/2025	04/01/2025	NUM
cana-6007	4	9	revised	revise	VERB
cana-6007	4	10	:	:	PUNCT
cana-6007	4	11	06/02/2025	06/02/2025	NUM
cana-6007	4	12	accepted	accept	VERB
cana-6007	4	13	:	:	PUNCT
cana-6007	4	14	11/03/2025	11/03/2025	NUM
cana-6007	4	15	abstract	abstract	NOUN
cana-6007	4	16	:	:	PUNCT
cana-6007	4	17	in	in	ADP
cana-6007	4	18	this	this	DET
cana-6007	4	19	paper	paper	NOUN
cana-6007	4	20	we	we	PRON
cana-6007	4	21	examine	examine	VERB
cana-6007	4	22	the	the	DET
cana-6007	4	23	numerical	numerical	ADJ
cana-6007	4	24	accuracy	accuracy	NOUN
cana-6007	4	25	of	of	ADP
cana-6007	4	26	two	two	NUM
cana-6007	4	27	widely	widely	ADV
cana-6007	4	28	used	use	VERB
cana-6007	4	29	methods	method	NOUN
cana-6007	4	30	-	-	PUNCT
cana-6007	4	31	the	the	DET
cana-6007	4	32	euler	euler	NOUN
cana-6007	4	33	–	–	PUNCT
cana-6007	4	34	maruyama	maruyama	NOUN
cana-6007	4	35	and	and	CCONJ
cana-6007	4	36	milstein	milstein	ADJ
cana-6007	4	37	methods	method	NOUN
cana-6007	4	38	for	for	ADP
cana-6007	4	39	solving	solve	VERB
cana-6007	4	40	stochastic	stochastic	ADJ
cana-6007	4	41	differential	differential	ADJ
cana-6007	4	42	equations	equation	NOUN
cana-6007	4	43	(	(	PUNCT
cana-6007	4	44	sdes	sde	NOUN
cana-6007	4	45	)	)	PUNCT
cana-6007	4	46	.	.	PUNCT
cana-6007	5	1	in	in	ADP
cana-6007	5	2	this	this	DET
cana-6007	5	3	study	study	NOUN
cana-6007	5	4	we	we	PRON
cana-6007	5	5	deal	deal	VERB
cana-6007	5	6	with	with	ADP
cana-6007	5	7	two	two	NUM
cana-6007	5	8	nonlinear	nonlinear	ADJ
cana-6007	5	9	sdes	sde	NOUN
cana-6007	5	10	,	,	PUNCT
cana-6007	5	11	whose	whose	DET
cana-6007	5	12	exact	exact	ADJ
cana-6007	5	13	solutions	solution	NOUN
cana-6007	5	14	are	be	AUX
cana-6007	5	15	derived	derive	VERB
cana-6007	5	16	using	use	VERB
cana-6007	5	17	itô	itô	PROPN
cana-6007	5	18	’s	’s	PART
cana-6007	5	19	calculus	calculus	NOUN
cana-6007	5	20	.	.	PUNCT
cana-6007	6	1	using	use	VERB
cana-6007	6	2	uniform	uniform	ADJ
cana-6007	6	3	discretization	discretization	NOUN
cana-6007	6	4	conditions	condition	NOUN
cana-6007	6	5	,	,	PUNCT
cana-6007	6	6	the	the	DET
cana-6007	6	7	comparative	comparative	ADJ
cana-6007	6	8	study	study	NOUN
cana-6007	6	9	is	be	AUX
cana-6007	6	10	made	make	VERB
cana-6007	6	11	on	on	ADP
cana-6007	6	12	the	the	DET
cana-6007	6	13	exact	exact	ADJ
cana-6007	6	14	solutions	solution	NOUN
cana-6007	6	15	,	,	PUNCT
cana-6007	6	16	approximate	approximate	ADJ
cana-6007	6	17	solutions	solution	NOUN
cana-6007	6	18	,	,	PUNCT
cana-6007	6	19	and	and	CCONJ
cana-6007	6	20	absolute	absolute	ADJ
cana-6007	6	21	errors	error	NOUN
cana-6007	6	22	,	,	PUNCT
cana-6007	6	23	supported	support	VERB
cana-6007	6	24	with	with	ADP
cana-6007	6	25	graphs	graph	NOUN
cana-6007	6	26	and	and	CCONJ
cana-6007	6	27	tables	table	NOUN
cana-6007	6	28	.	.	PUNCT
cana-6007	7	1	this	this	DET
cana-6007	7	2	study	study	NOUN
cana-6007	7	3	focuses	focus	VERB
cana-6007	7	4	on	on	ADP
cana-6007	7	5	selecting	select	VERB
cana-6007	7	6	reliable	reliable	ADJ
cana-6007	7	7	numerical	numerical	ADJ
cana-6007	7	8	methods	method	NOUN
cana-6007	7	9	for	for	ADP
cana-6007	7	10	accurately	accurately	ADV
cana-6007	7	11	solving	solve	VERB
cana-6007	7	12	nonlinear	nonlinear	ADJ
cana-6007	7	13	stochastic	stochastic	ADJ
cana-6007	7	14	systems	system	NOUN
cana-6007	7	15	.	.	PUNCT
cana-6007	8	1	keywords	keyword	NOUN
cana-6007	8	2	:	:	PUNCT
cana-6007	8	3	stochastic	stochastic	ADJ
cana-6007	8	4	differential	differential	ADJ
cana-6007	8	5	equations	equation	NOUN
cana-6007	8	6	,	,	PUNCT
cana-6007	8	7	itô	itô	PROPN
cana-6007	8	8	lemma	lemma	PROPN
cana-6007	8	9	,	,	PUNCT
cana-6007	8	10	eulermaruyama	eulermaruyama	NOUN
cana-6007	8	11	method	method	NOUN
cana-6007	8	12	,	,	PUNCT
cana-6007	8	13	milstein	milstein	NOUN
cana-6007	8	14	method	method	NOUN
cana-6007	8	15	.	.	PUNCT
cana-6007	9	1	ams	am	NOUN
cana-6007	9	2	subject	subject	ADJ
cana-6007	9	3	classification	classification	NOUN
cana-6007	9	4	:	:	PUNCT
cana-6007	9	5	65a05	65a05	NUM
cana-6007	9	6	,	,	PUNCT
cana-6007	9	7	65b15	65b15	NUM
cana-6007	9	8	1	1	NUM
cana-6007	9	9	.	.	PUNCT
cana-6007	9	10	introduction	introduction	NOUN
cana-6007	9	11	while	while	SCONJ
cana-6007	9	12	modeling	model	VERB
cana-6007	9	13	complex	complex	ADJ
cana-6007	9	14	real	real	ADJ
cana-6007	9	15	-	-	PUNCT
cana-6007	9	16	world	world	NOUN
cana-6007	9	17	systems	system	NOUN
cana-6007	9	18	that	that	PRON
cana-6007	9	19	have	have	VERB
cana-6007	9	20	randomness	randomness	NOUN
cana-6007	9	21	and	and	CCONJ
cana-6007	9	22	uncertainty	uncertainty	NOUN
cana-6007	9	23	,	,	PUNCT
cana-6007	9	24	like	like	ADP
cana-6007	9	25	stock	stock	NOUN
cana-6007	9	26	markets	market	NOUN
cana-6007	9	27	,	,	PUNCT
cana-6007	9	28	neurons	neuron	NOUN
cana-6007	9	29	,	,	PUNCT
cana-6007	9	30	and	and	CCONJ
cana-6007	9	31	ecosystems	ecosystem	NOUN
cana-6007	9	32	that	that	PRON
cana-6007	9	33	change	change	VERB
cana-6007	9	34	suddenly	suddenly	ADV
cana-6007	9	35	,	,	PUNCT
cana-6007	9	36	the	the	DET
cana-6007	9	37	traditional	traditional	ADJ
cana-6007	9	38	deterministic	deterministic	ADJ
cana-6007	9	39	models	model	NOUN
cana-6007	9	40	like	like	ADP
cana-6007	9	41	ordinary	ordinary	ADJ
cana-6007	9	42	differential	differential	ADJ
cana-6007	9	43	equations	equation	NOUN
cana-6007	9	44	are	be	AUX
cana-6007	9	45	insufficient	insufficient	ADJ
cana-6007	9	46	because	because	SCONJ
cana-6007	9	47	of	of	ADP
cana-6007	9	48	their	their	PRON
cana-6007	9	49	inability	inability	NOUN
cana-6007	9	50	to	to	PART
cana-6007	9	51	take	take	VERB
cana-6007	9	52	into	into	ADP
cana-6007	9	53	account	account	NOUN
cana-6007	9	54	stochastic	stochastic	NOUN
cana-6007	9	55	fluctuations	fluctuation	NOUN
cana-6007	9	56	and	and	CCONJ
cana-6007	9	57	unpredictable	unpredictable	ADJ
cana-6007	9	58	behaviors	behavior	NOUN
cana-6007	9	59	.	.	PUNCT
cana-6007	10	1	this	this	DET
cana-6007	10	2	gap	gap	NOUN
cana-6007	10	3	has	have	AUX
cana-6007	10	4	been	be	AUX
cana-6007	10	5	addressed	address	VERB
cana-6007	10	6	by	by	ADP
cana-6007	10	7	stochastic	stochastic	ADJ
cana-6007	10	8	differential	differential	ADJ
cana-6007	10	9	equations	equation	NOUN
cana-6007	10	10	(	(	PUNCT
cana-6007	10	11	sdes	sde	NOUN
cana-6007	10	12	)	)	PUNCT
cana-6007	10	13	by	by	ADP
cana-6007	10	14	capturing	capture	VERB
cana-6007	10	15	both	both	CCONJ
cana-6007	10	16	the	the	DET
cana-6007	10	17	deterministic	deterministic	ADJ
cana-6007	10	18	trends	trend	NOUN
cana-6007	10	19	and	and	CCONJ
cana-6007	10	20	the	the	DET
cana-6007	10	21	random	random	ADJ
cana-6007	10	22	noise	noise	NOUN
cana-6007	10	23	that	that	PRON
cana-6007	10	24	affects	affect	VERB
cana-6007	10	25	the	the	DET
cana-6007	10	26	system	system	NOUN
cana-6007	10	27	’s	’s	PART
cana-6007	10	28	behavior	behavior	NOUN
cana-6007	11	1	[	[	X
cana-6007	11	2	1	1	NUM
cana-6007	11	3	]	]	PUNCT
cana-6007	11	4	.	.	PUNCT
cana-6007	12	1	for	for	ADP
cana-6007	12	2	example	example	NOUN
cana-6007	12	3	,	,	PUNCT
cana-6007	12	4	in	in	ADP
cana-6007	12	5	quantitative	quantitative	ADJ
cana-6007	12	6	finance	finance	NOUN
cana-6007	12	7	,	,	PUNCT
cana-6007	12	8	sdes	sde	VERB
cana-6007	12	9	model	model	VERB
cana-6007	12	10	the	the	DET
cana-6007	12	11	uncertain	uncertain	ADJ
cana-6007	12	12	behavior	behavior	NOUN
cana-6007	12	13	of	of	ADP
cana-6007	12	14	stock	stock	NOUN
cana-6007	12	15	prices	price	NOUN
cana-6007	12	16	and	and	CCONJ
cana-6007	12	17	interest	interest	NOUN
cana-6007	12	18	rates	rate	NOUN
cana-6007	12	19	better	well	ADV
cana-6007	12	20	than	than	ADP
cana-6007	12	21	the	the	DET
cana-6007	12	22	traditional	traditional	ADJ
cana-6007	12	23	models	model	NOUN
cana-6007	12	24	[	[	X
cana-6007	12	25	1	1	NUM
cana-6007	12	26	]	]	PUNCT
cana-6007	12	27	,	,	PUNCT
cana-6007	12	28	[	[	X
cana-6007	12	29	13	13	NUM
cana-6007	12	30	]	]	PUNCT
cana-6007	12	31	.	.	PUNCT
cana-6007	13	1	similarly	similarly	ADV
cana-6007	13	2	,	,	PUNCT
cana-6007	13	3	sdes	sde	NOUN
cana-6007	13	4	help	help	VERB
cana-6007	13	5	to	to	PART
cana-6007	13	6	simulate	simulate	VERB
cana-6007	13	7	the	the	DET
cana-6007	13	8	effects	effect	NOUN
cana-6007	13	9	of	of	ADP
cana-6007	13	10	random	random	ADJ
cana-6007	13	11	outside	outside	ADJ
cana-6007	13	12	stimuli	stimulus	NOUN
cana-6007	13	13	and	and	CCONJ
cana-6007	13	14	mutations	mutation	NOUN
cana-6007	13	15	in	in	ADP
cana-6007	13	16	neuroscience	neuroscience	NOUN
cana-6007	13	17	and	and	CCONJ
cana-6007	13	18	epidemiology	epidemiology	NOUN
cana-6007	13	19	[	[	X
cana-6007	13	20	1	1	NUM
cana-6007	13	21	]	]	PUNCT
cana-6007	13	22	.	.	PUNCT
cana-6007	14	1	sdes	sde	NOUN
cana-6007	14	2	incorporate	incorporate	VERB
cana-6007	14	3	stochastic	stochastic	ADJ
cana-6007	14	4	elements	element	NOUN
cana-6007	14	5	like	like	ADP
cana-6007	14	6	brownian	brownian	ADJ
cana-6007	14	7	motion	motion	NOUN
cana-6007	14	8	,	,	PUNCT
cana-6007	14	9	making	make	VERB
cana-6007	14	10	them	they	PRON
cana-6007	14	11	more	more	ADV
cana-6007	14	12	realistic	realistic	ADJ
cana-6007	14	13	and	and	CCONJ
cana-6007	14	14	detailed	detailed	ADJ
cana-6007	14	15	for	for	ADP
cana-6007	14	16	the	the	DET
cana-6007	14	17	systems	system	NOUN
cana-6007	14	18	having	have	VERB
cana-6007	14	19	randomness	randomness	NOUN
cana-6007	14	20	or	or	CCONJ
cana-6007	14	21	uncertainty	uncertainty	NOUN
cana-6007	14	22	,	,	PUNCT
cana-6007	14	23	making	make	VERB
cana-6007	14	24	them	they	PRON
cana-6007	14	25	more	more	ADV
cana-6007	14	26	valuable	valuable	ADJ
cana-6007	14	27	across	across	ADP
cana-6007	14	28	various	various	ADJ
cana-6007	14	29	disciplines	discipline	NOUN
cana-6007	14	30	like	like	ADP
cana-6007	14	31	finance	finance	NOUN
cana-6007	14	32	,	,	PUNCT
cana-6007	14	33	physics	physics	NOUN
cana-6007	14	34	,	,	PUNCT
cana-6007	14	35	biology	biology	NOUN
cana-6007	14	36	,	,	PUNCT
cana-6007	14	37	engineering	engineering	NOUN
cana-6007	14	38	,	,	PUNCT
cana-6007	14	39	and	and	CCONJ
cana-6007	14	40	signal	signal	NOUN
cana-6007	14	41	processing	processing	NOUN
cana-6007	14	42	[	[	X
cana-6007	14	43	1	1	NUM
cana-6007	14	44	]	]	PUNCT
cana-6007	14	45	.	.	PUNCT
cana-6007	15	1	fundamental	fundamental	ADJ
cana-6007	15	2	research	research	NOUN
cana-6007	15	3	on	on	ADP
cana-6007	15	4	stochastic	stochastic	ADJ
cana-6007	15	5	processes	process	NOUN
cana-6007	15	6	was	be	AUX
cana-6007	15	7	driven	drive	VERB
cana-6007	15	8	by	by	ADP
cana-6007	15	9	einstein	einstein	PROPN
cana-6007	15	10	's	's	PART
cana-6007	15	11	1905	1905	NUM
cana-6007	15	12	analysis	analysis	NOUN
cana-6007	15	13	of	of	ADP
cana-6007	15	14	brownian	brownian	ADJ
cana-6007	15	15	motion	motion	NOUN
cana-6007	15	16	,	,	PUNCT
cana-6007	15	17	which	which	PRON
cana-6007	15	18	provided	provide	VERB
cana-6007	15	19	a	a	DET
cana-6007	15	20	probabilistic	probabilistic	ADJ
cana-6007	15	21	interpretation	interpretation	NOUN
cana-6007	15	22	of	of	ADP
cana-6007	15	23	diffusion	diffusion	NOUN
cana-6007	15	24	phenomena	phenomenon	NOUN
cana-6007	15	25	and	and	CCONJ
cana-6007	15	26	served	serve	VERB
cana-6007	15	27	as	as	ADP
cana-6007	15	28	the	the	DET
cana-6007	15	29	theoretical	theoretical	ADJ
cana-6007	15	30	foundation	foundation	NOUN
cana-6007	15	31	for	for	ADP
cana-6007	15	32	stochastic	stochastic	ADJ
cana-6007	15	33	differential	differential	ADJ
cana-6007	15	34	equations	equation	NOUN
cana-6007	15	35	(	(	PUNCT
cana-6007	15	36	sdes	sde	NOUN
cana-6007	15	37	)	)	PUNCT
cana-6007	16	1	[	[	X
cana-6007	16	2	1	1	NUM
cana-6007	16	3	]	]	PUNCT
cana-6007	16	4	.	.	PUNCT
cana-6007	17	1	norbert	norbert	PROPN
cana-6007	17	2	wiener	wiener	PROPN
cana-6007	17	3	made	make	VERB
cana-6007	17	4	this	this	DET
cana-6007	17	5	perspective	perspective	NOUN
cana-6007	17	6	very	very	ADV
cana-6007	17	7	formal	formal	ADJ
cana-6007	17	8	by	by	ADP
cana-6007	17	9	developing	develop	VERB
cana-6007	17	10	the	the	DET
cana-6007	17	11	wiener	wiener	NOUN
cana-6007	17	12	process	process	NOUN
cana-6007	17	13	,	,	PUNCT
cana-6007	17	14	which	which	PRON
cana-6007	17	15	provided	provide	VERB
cana-6007	17	16	a	a	DET
cana-6007	17	17	mathematical	mathematical	ADJ
cana-6007	17	18	model	model	NOUN
cana-6007	17	19	for	for	ADP
cana-6007	17	20	stochastic	stochastic	ADJ
cana-6007	17	21	perturbations	perturbation	NOUN
cana-6007	17	22	with	with	ADP
cana-6007	17	23	stationary	stationary	ADJ
cana-6007	17	24	and	and	CCONJ
cana-6007	17	25	independent	independent	ADJ
cana-6007	17	26	mailto:najmuddinahmad33@gmail.com	mailto:najmuddinahmad33@gmail.com	PROPN
cana-6007	17	27	mailto:eramphdiul@gmail.com	mailto:eramphdiul@gmail.com	PROPN
cana-6007	17	28	communications	communication	NOUN
cana-6007	17	29	on	on	ADP
cana-6007	17	30	applied	apply	VERB
cana-6007	17	31	nonlinear	nonlinear	ADJ
cana-6007	17	32	analysis	analysis	NOUN
cana-6007	17	33	issn	issn	NOUN
cana-6007	17	34	:	:	PUNCT
cana-6007	17	35	1074	1074	NUM
cana-6007	17	36	-	-	PUNCT
cana-6007	17	37	133x	133x	NUM
cana-6007	17	38	vol	vol	VERB
cana-6007	17	39	32	32	NUM
cana-6007	17	40	no	no	NOUN
cana-6007	17	41	.	.	PUNCT
cana-6007	18	1	10s	10	NOUN
cana-6007	18	2	(	(	PUNCT
cana-6007	18	3	2025	2025	NUM
cana-6007	18	4	)	)	PUNCT
cana-6007	18	5	3227	3227	NUM
cana-6007	18	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	18	7	increments	increment	NOUN
cana-6007	18	8	in	in	ADP
cana-6007	18	9	continuous	continuous	ADJ
cana-6007	18	10	time	time	NOUN
cana-6007	18	11	[	[	X
cana-6007	18	12	1	1	NUM
cana-6007	18	13	]	]	PUNCT
cana-6007	18	14	.	.	PUNCT
cana-6007	19	1	kiyosi	kiyosi	PROPN
cana-6007	19	2	itô	itô	PROPN
cana-6007	19	3	's	's	PART
cana-6007	19	4	contributions	contribution	NOUN
cana-6007	19	5	to	to	ADP
cana-6007	19	6	stochastic	stochastic	ADJ
cana-6007	19	7	calculus	calculus	NOUN
cana-6007	19	8	,	,	PUNCT
cana-6007	19	9	including	include	VERB
cana-6007	19	10	itô	itô	PROPN
cana-6007	19	11	's	's	PART
cana-6007	19	12	lemma	lemma	PROPN
cana-6007	19	13	and	and	CCONJ
cana-6007	19	14	itô	itô	PROPN
cana-6007	19	15	integral	integral	ADJ
cana-6007	19	16	,	,	PUNCT
cana-6007	19	17	enabled	enable	VERB
cana-6007	19	18	the	the	DET
cana-6007	19	19	differential	differential	ADJ
cana-6007	19	20	analysis	analysis	NOUN
cana-6007	19	21	of	of	ADP
cana-6007	19	22	non	non	ADJ
cana-6007	19	23	-	-	ADJ
cana-6007	19	24	deterministic	deterministic	ADJ
cana-6007	19	25	systems	system	NOUN
cana-6007	19	26	driven	drive	VERB
cana-6007	19	27	by	by	ADP
cana-6007	19	28	brownian	brownian	ADJ
cana-6007	19	29	motion	motion	NOUN
cana-6007	19	30	and	and	CCONJ
cana-6007	19	31	resulted	result	VERB
cana-6007	19	32	in	in	ADP
cana-6007	19	33	the	the	DET
cana-6007	19	34	modern	modern	ADJ
cana-6007	19	35	formulation	formulation	NOUN
cana-6007	19	36	of	of	ADP
cana-6007	19	37	sdes	sde	NOUN
cana-6007	19	38	[	[	X
cana-6007	19	39	1	1	NUM
cana-6007	19	40	]	]	PUNCT
cana-6007	19	41	.	.	PUNCT
cana-6007	20	1	paul	paul	PROPN
cana-6007	20	2	lévy	lévy	PROPN
cana-6007	20	3	added	add	VERB
cana-6007	20	4	to	to	ADP
cana-6007	20	5	this	this	DET
cana-6007	20	6	theory	theory	NOUN
cana-6007	20	7	by	by	ADP
cana-6007	20	8	introducing	introduce	VERB
cana-6007	20	9	lévy	lévy	ADJ
cana-6007	20	10	processes	process	NOUN
cana-6007	20	11	,	,	PUNCT
cana-6007	20	12	which	which	PRON
cana-6007	20	13	can	can	AUX
cana-6007	20	14	handle	handle	VERB
cana-6007	20	15	jump	jump	VERB
cana-6007	20	16	discontinuities	discontinuity	NOUN
cana-6007	20	17	and	and	CCONJ
cana-6007	20	18	extend	extend	VERB
cana-6007	20	19	brownian	brownian	ADJ
cana-6007	20	20	motion	motion	NOUN
cana-6007	20	21	to	to	ADP
cana-6007	20	22	a	a	DET
cana-6007	20	23	wider	wide	ADJ
cana-6007	20	24	range	range	NOUN
cana-6007	20	25	of	of	ADP
cana-6007	20	26	stochastic	stochastic	ADJ
cana-6007	20	27	drivers	driver	NOUN
cana-6007	20	28	[	[	X
cana-6007	20	29	1	1	NUM
cana-6007	20	30	]	]	PUNCT
cana-6007	20	31	.	.	PUNCT
cana-6007	21	1	these	these	DET
cana-6007	21	2	contributions	contribution	NOUN
cana-6007	21	3	together	together	ADV
cana-6007	21	4	formed	form	VERB
cana-6007	21	5	the	the	DET
cana-6007	21	6	theoretical	theoretical	ADJ
cana-6007	21	7	basis	basis	NOUN
cana-6007	21	8	of	of	ADP
cana-6007	21	9	sdes	sde	NOUN
cana-6007	21	10	,	,	PUNCT
cana-6007	21	11	which	which	PRON
cana-6007	21	12	let	let	VERB
cana-6007	21	13	us	we	PRON
cana-6007	21	14	model	model	NOUN
cana-6007	21	15	systems	system	NOUN
cana-6007	21	16	that	that	PRON
cana-6007	21	17	are	be	AUX
cana-6007	21	18	affected	affect	VERB
cana-6007	21	19	by	by	ADP
cana-6007	21	20	both	both	DET
cana-6007	21	21	jump	jump	NOUN
cana-6007	21	22	-	-	PUNCT
cana-6007	21	23	type	type	NOUN
cana-6007	21	24	and	and	CCONJ
cana-6007	21	25	continuous	continuous	ADJ
cana-6007	21	26	randomness	randomness	NOUN
cana-6007	21	27	.	.	PUNCT
cana-6007	22	1	in	in	ADP
cana-6007	22	2	various	various	ADJ
cana-6007	22	3	scientific	scientific	ADJ
cana-6007	22	4	and	and	CCONJ
cana-6007	22	5	engineering	engineering	NOUN
cana-6007	22	6	fields	field	NOUN
cana-6007	22	7	,	,	PUNCT
cana-6007	22	8	sdes	sde	NOUN
cana-6007	22	9	are	be	AUX
cana-6007	22	10	now	now	ADV
cana-6007	22	11	essential	essential	ADJ
cana-6007	22	12	for	for	ADP
cana-6007	22	13	the	the	DET
cana-6007	22	14	analysis	analysis	NOUN
cana-6007	22	15	and	and	CCONJ
cana-6007	22	16	simulation	simulation	NOUN
cana-6007	22	17	of	of	ADP
cana-6007	22	18	complex	complex	ADJ
cana-6007	22	19	systems	system	NOUN
cana-6007	23	1	[	[	X
cana-6007	23	2	1	1	NUM
cana-6007	23	3	]	]	PUNCT
cana-6007	23	4	,	,	PUNCT
cana-6007	23	5	[	[	X
cana-6007	23	6	13	13	NUM
cana-6007	23	7	]	]	PUNCT
cana-6007	23	8	.	.	PUNCT
cana-6007	24	1	2	2	X
cana-6007	24	2	.	.	X
cana-6007	24	3	stochastic	stochastic	ADJ
cana-6007	24	4	differential	differential	ADJ
cana-6007	24	5	equation	equation	NOUN
cana-6007	24	6	a	a	DET
cana-6007	24	7	crucial	crucial	ADJ
cana-6007	24	8	tool	tool	NOUN
cana-6007	24	9	for	for	ADP
cana-6007	24	10	simulating	simulate	VERB
cana-6007	24	11	systems	system	NOUN
cana-6007	24	12	with	with	ADP
cana-6007	24	13	inherent	inherent	ADJ
cana-6007	24	14	unpredictability	unpredictability	NOUN
cana-6007	24	15	is	be	AUX
cana-6007	24	16	the	the	DET
cana-6007	24	17	stochastic	stochastic	ADJ
cana-6007	24	18	differential	differential	ADJ
cana-6007	24	19	equation	equation	NOUN
cana-6007	24	20	(	(	PUNCT
cana-6007	24	21	sde	sde	PROPN
cana-6007	24	22	)	)	PUNCT
cana-6007	24	23	.	.	PUNCT
cana-6007	25	1	but	but	CCONJ
cana-6007	25	2	they	they	PRON
cana-6007	25	3	still	still	ADV
cana-6007	25	4	face	face	VERB
cana-6007	25	5	issues	issue	NOUN
cana-6007	25	6	like	like	ADP
cana-6007	25	7	analytical	analytical	ADJ
cana-6007	25	8	intractability	intractability	NOUN
cana-6007	25	9	,	,	PUNCT
cana-6007	25	10	especially	especially	ADV
cana-6007	25	11	with	with	ADP
cana-6007	25	12	nonlinear	nonlinear	ADJ
cana-6007	25	13	sdes	sde	NOUN
cana-6007	25	14	,	,	PUNCT
cana-6007	25	15	where	where	SCONJ
cana-6007	25	16	closed	close	VERB
cana-6007	25	17	-	-	PUNCT
cana-6007	25	18	form	form	NOUN
cana-6007	25	19	solutions	solution	NOUN
cana-6007	25	20	are	be	AUX
cana-6007	25	21	very	very	ADV
cana-6007	25	22	difficult	difficult	ADJ
cana-6007	25	23	to	to	PART
cana-6007	25	24	find	find	VERB
cana-6007	25	25	.	.	PUNCT
cana-6007	26	1	because	because	SCONJ
cana-6007	26	2	of	of	ADP
cana-6007	26	3	this	this	DET
cana-6007	26	4	limitation	limitation	NOUN
cana-6007	26	5	,	,	PUNCT
cana-6007	26	6	traditional	traditional	ADJ
cana-6007	26	7	stochastic	stochastic	ADJ
cana-6007	26	8	techniques	technique	NOUN
cana-6007	26	9	are	be	AUX
cana-6007	26	10	unable	unable	ADJ
cana-6007	26	11	to	to	PART
cana-6007	26	12	fully	fully	ADV
cana-6007	26	13	capture	capture	VERB
cana-6007	26	14	the	the	DET
cana-6007	26	15	complex	complex	ADJ
cana-6007	26	16	relationship	relationship	NOUN
cana-6007	26	17	between	between	ADP
cana-6007	26	18	stochastic	stochastic	ADJ
cana-6007	26	19	perturbations	perturbation	NOUN
cana-6007	26	20	and	and	CCONJ
cana-6007	26	21	deterministic	deterministic	ADJ
cana-6007	26	22	dynamics	dynamic	NOUN
cana-6007	26	23	that	that	PRON
cana-6007	26	24	happens	happen	VERB
cana-6007	26	25	in	in	ADP
cana-6007	26	26	the	the	DET
cana-6007	26	27	real	real	ADJ
cana-6007	26	28	-	-	PUNCT
cana-6007	26	29	world	world	NOUN
cana-6007	27	1	[	[	X
cana-6007	27	2	2	2	NUM
cana-6007	27	3	]	]	PUNCT
cana-6007	27	4	.	.	PUNCT
cana-6007	28	1	the	the	DET
cana-6007	28	2	importance	importance	NOUN
cana-6007	28	3	of	of	ADP
cana-6007	28	4	advanced	advanced	ADJ
cana-6007	28	5	numerical	numerical	ADJ
cana-6007	28	6	techniques	technique	NOUN
cana-6007	28	7	in	in	ADP
cana-6007	28	8	solving	solve	VERB
cana-6007	28	9	complicated	complicated	ADJ
cana-6007	28	10	mathematical	mathematical	ADJ
cana-6007	28	11	models	model	NOUN
cana-6007	28	12	is	be	AUX
cana-6007	28	13	further	far	ADV
cana-6007	28	14	illustrated	illustrate	VERB
cana-6007	28	15	by	by	ADP
cana-6007	28	16	the	the	DET
cana-6007	28	17	promising	promising	ADJ
cana-6007	28	18	results	result	NOUN
cana-6007	28	19	of	of	ADP
cana-6007	28	20	semi	semi	ADJ
cana-6007	28	21	-	-	ADJ
cana-6007	28	22	analytical	analytical	ADJ
cana-6007	28	23	approaches	approach	NOUN
cana-6007	28	24	like	like	ADP
cana-6007	28	25	the	the	DET
cana-6007	28	26	laplace	laplace	NOUN
cana-6007	28	27	–	–	PUNCT
cana-6007	28	28	adomian	adomian	NOUN
cana-6007	28	29	decomposition	decomposition	NOUN
cana-6007	28	30	method	method	NOUN
cana-6007	28	31	in	in	ADP
cana-6007	28	32	handling	handle	VERB
cana-6007	28	33	nonlinear	nonlinear	ADJ
cana-6007	28	34	integral	integral	ADJ
cana-6007	28	35	equations	equation	NOUN
cana-6007	28	36	[	[	X
cana-6007	28	37	10	10	NUM
cana-6007	28	38	]	]	PUNCT
cana-6007	28	39	.	.	PUNCT
cana-6007	29	1	as	as	ADP
cana-6007	29	2	a	a	DET
cana-6007	29	3	result	result	NOUN
cana-6007	29	4	of	of	ADP
cana-6007	29	5	this	this	PRON
cana-6007	29	6	,	,	PUNCT
cana-6007	29	7	the	the	DET
cana-6007	29	8	numerical	numerical	ADJ
cana-6007	29	9	approximation	approximation	NOUN
cana-6007	29	10	of	of	ADP
cana-6007	29	11	sdes	sde	NOUN
cana-6007	29	12	is	be	AUX
cana-6007	29	13	now	now	ADV
cana-6007	29	14	a	a	DET
cana-6007	29	15	crucial	crucial	ADJ
cana-6007	29	16	part	part	NOUN
cana-6007	29	17	of	of	ADP
cana-6007	29	18	stochastic	stochastic	ADJ
cana-6007	29	19	modeling	modeling	NOUN
cana-6007	29	20	.	.	PUNCT
cana-6007	30	1	the	the	DET
cana-6007	30	2	euler	euler	NOUN
cana-6007	30	3	–	–	PUNCT
cana-6007	30	4	maruyama	maruyama	NOUN
cana-6007	30	5	and	and	CCONJ
cana-6007	30	6	milstein	milstein	ADJ
cana-6007	30	7	methods	method	NOUN
cana-6007	30	8	are	be	AUX
cana-6007	30	9	renowned	renowned	ADJ
cana-6007	30	10	among	among	ADP
cana-6007	30	11	the	the	DET
cana-6007	30	12	developed	develop	VERB
cana-6007	30	13	numerical	numerical	ADJ
cana-6007	30	14	methods	method	NOUN
cana-6007	30	15	as	as	ADP
cana-6007	30	16	fundamental	fundamental	ADJ
cana-6007	30	17	first	first	ADJ
cana-6007	30	18	-	-	PUNCT
cana-6007	30	19	order	order	NOUN
cana-6007	30	20	approaches	approach	NOUN
cana-6007	30	21	[	[	X
cana-6007	30	22	3	3	NUM
cana-6007	30	23	]	]	PUNCT
cana-6007	30	24	,	,	PUNCT
cana-6007	30	25	[	[	X
cana-6007	30	26	7	7	NUM
cana-6007	30	27	]	]	PUNCT
cana-6007	30	28	,	,	PUNCT
cana-6007	30	29	[	[	X
cana-6007	30	30	13	13	NUM
cana-6007	30	31	]	]	PUNCT
cana-6007	30	32	.	.	PUNCT
cana-6007	31	1	the	the	DET
cana-6007	31	2	eulermaruyama	eulermaruyama	PROPN
cana-6007	31	3	method	method	NOUN
cana-6007	31	4	is	be	AUX
cana-6007	31	5	widely	widely	ADV
cana-6007	31	6	used	use	VERB
cana-6007	31	7	due	due	ADP
cana-6007	31	8	to	to	ADP
cana-6007	31	9	its	its	PRON
cana-6007	31	10	conceptual	conceptual	ADJ
cana-6007	31	11	simplicity	simplicity	NOUN
cana-6007	31	12	and	and	CCONJ
cana-6007	31	13	ease	ease	NOUN
cana-6007	31	14	of	of	ADP
cana-6007	31	15	use	use	NOUN
cana-6007	31	16	,	,	PUNCT
cana-6007	31	17	as	as	SCONJ
cana-6007	31	18	it	it	PRON
cana-6007	31	19	is	be	AUX
cana-6007	31	20	a	a	DET
cana-6007	31	21	natural	natural	ADJ
cana-6007	31	22	stochastic	stochastic	ADJ
cana-6007	31	23	analogue	analogue	NOUN
cana-6007	31	24	of	of	ADP
cana-6007	31	25	the	the	DET
cana-6007	31	26	classical	classical	ADJ
cana-6007	31	27	euler	euler	NOUN
cana-6007	31	28	method	method	NOUN
cana-6007	32	1	[	[	X
cana-6007	32	2	13	13	NUM
cana-6007	32	3	]	]	PUNCT
cana-6007	32	4	.	.	PUNCT
cana-6007	33	1	however	however	ADV
cana-6007	33	2	,	,	PUNCT
cana-6007	33	3	its	its	PRON
cana-6007	33	4	accuracy	accuracy	NOUN
cana-6007	33	5	in	in	ADP
cana-6007	33	6	finer	fine	ADJ
cana-6007	33	7	simulations	simulation	NOUN
cana-6007	33	8	is	be	AUX
cana-6007	33	9	limited	limit	VERB
cana-6007	33	10	by	by	ADP
cana-6007	33	11	its	its	PRON
cana-6007	33	12	relatively	relatively	ADV
cana-6007	33	13	low	low	ADJ
cana-6007	33	14	order	order	NOUN
cana-6007	33	15	of	of	ADP
cana-6007	33	16	strong	strong	ADJ
cana-6007	33	17	convergence	convergence	NOUN
cana-6007	33	18	[	[	X
cana-6007	33	19	3	3	NUM
cana-6007	33	20	]	]	PUNCT
cana-6007	33	21	.	.	PUNCT
cana-6007	34	1	this	this	DET
cana-6007	34	2	issue	issue	NOUN
cana-6007	34	3	is	be	AUX
cana-6007	34	4	solved	solve	VERB
cana-6007	34	5	by	by	ADP
cana-6007	34	6	the	the	DET
cana-6007	34	7	milstein	milstein	ADJ
cana-6007	34	8	method	method	NOUN
cana-6007	34	9	by	by	ADP
cana-6007	34	10	adding	add	VERB
cana-6007	34	11	an	an	DET
cana-6007	34	12	additional	additional	ADJ
cana-6007	34	13	term	term	NOUN
cana-6007	34	14	involving	involve	VERB
cana-6007	34	15	the	the	DET
cana-6007	34	16	diffusion	diffusion	NOUN
cana-6007	34	17	coefficient	coefficient	NOUN
cana-6007	34	18	's	's	PART
cana-6007	34	19	derivative	derivative	NOUN
cana-6007	34	20	,	,	PUNCT
cana-6007	34	21	improving	improve	VERB
cana-6007	34	22	the	the	DET
cana-6007	34	23	quality	quality	NOUN
cana-6007	34	24	of	of	ADP
cana-6007	34	25	the	the	DET
cana-6007	34	26	approximation	approximation	NOUN
cana-6007	34	27	,	,	PUNCT
cana-6007	34	28	particularly	particularly	ADV
cana-6007	34	29	in	in	ADP
cana-6007	34	30	systems	system	NOUN
cana-6007	34	31	with	with	ADP
cana-6007	34	32	multiplicative	multiplicative	ADJ
cana-6007	34	33	noise	noise	NOUN
cana-6007	34	34	or	or	CCONJ
cana-6007	34	35	non	non	ADJ
cana-6007	34	36	-	-	ADJ
cana-6007	34	37	trivial	trivial	ADJ
cana-6007	34	38	diffusion	diffusion	NOUN
cana-6007	34	39	structures	structure	NOUN
cana-6007	34	40	[	[	X
cana-6007	34	41	3	3	NUM
cana-6007	34	42	]	]	PUNCT
cana-6007	34	43	,	,	PUNCT
cana-6007	35	1	[	[	X
cana-6007	35	2	6	6	NUM
cana-6007	35	3	]	]	PUNCT
cana-6007	35	4	,	,	PUNCT
cana-6007	35	5	[	[	X
cana-6007	35	6	16	16	NUM
cana-6007	35	7	]	]	PUNCT
cana-6007	35	8	.	.	PUNCT
cana-6007	36	1	modified	modify	VERB
cana-6007	36	2	numerical	numerical	ADJ
cana-6007	36	3	methods	method	NOUN
cana-6007	36	4	have	have	AUX
cana-6007	36	5	been	be	AUX
cana-6007	36	6	researched	research	VERB
cana-6007	36	7	because	because	SCONJ
cana-6007	36	8	classical	classical	ADJ
cana-6007	36	9	methods	method	NOUN
cana-6007	36	10	like	like	ADP
cana-6007	36	11	euler	euler	NOUN
cana-6007	36	12	-	-	PUNCT
cana-6007	36	13	maruyama	maruyama	NOUN
cana-6007	36	14	and	and	CCONJ
cana-6007	36	15	milstein	milstein	NOUN
cana-6007	36	16	may	may	AUX
cana-6007	36	17	not	not	PART
cana-6007	36	18	be	be	AUX
cana-6007	36	19	able	able	ADJ
cana-6007	36	20	to	to	PART
cana-6007	36	21	hold	hold	VERB
cana-6007	36	22	important	important	ADJ
cana-6007	36	23	characteristics	characteristic	NOUN
cana-6007	36	24	like	like	ADP
cana-6007	36	25	positivity	positivity	NOUN
cana-6007	36	26	or	or	CCONJ
cana-6007	36	27	stability	stability	NOUN
cana-6007	36	28	in	in	ADP
cana-6007	36	29	situations	situation	NOUN
cana-6007	36	30	involving	involve	VERB
cana-6007	36	31	super	super	ADJ
cana-6007	36	32	-	-	ADJ
cana-6007	36	33	linear	linear	ADJ
cana-6007	36	34	growth	growth	NOUN
cana-6007	36	35	or	or	CCONJ
cana-6007	36	36	delay	delay	VERB
cana-6007	36	37	effects	effect	NOUN
cana-6007	36	38	[	[	X
cana-6007	36	39	9	9	NUM
cana-6007	36	40	]	]	PUNCT
cana-6007	36	41	,	,	PUNCT
cana-6007	36	42	[	[	X
cana-6007	36	43	14	14	NUM
cana-6007	36	44	]	]	PUNCT
cana-6007	36	45	.	.	PUNCT
cana-6007	37	1	the	the	DET
cana-6007	37	2	conceptual	conceptual	ADJ
cana-6007	37	3	basis	basis	NOUN
cana-6007	37	4	for	for	ADP
cana-6007	37	5	stochastic	stochastic	ADJ
cana-6007	37	6	numerical	numerical	ADJ
cana-6007	37	7	analysis	analysis	NOUN
cana-6007	37	8	was	be	AUX
cana-6007	37	9	established	establish	VERB
cana-6007	37	10	by	by	ADP
cana-6007	37	11	kloeden	kloeden	PROPN
cana-6007	37	12	and	and	CCONJ
cana-6007	37	13	platen	platen	ADJ
cana-6007	38	1	[	[	X
cana-6007	38	2	13	13	NUM
cana-6007	38	3	]	]	PUNCT
cana-6007	38	4	,	,	PUNCT
cana-6007	38	5	higham	higham	PROPN
cana-6007	39	1	[	[	X
cana-6007	39	2	3	3	NUM
cana-6007	39	3	]	]	PUNCT
cana-6007	39	4	,	,	PUNCT
cana-6007	39	5	burrage	burrage	NOUN
cana-6007	40	1	[	[	X
cana-6007	40	2	7	7	NUM
cana-6007	40	3	]	]	PUNCT
cana-6007	40	4	,	,	PUNCT
cana-6007	40	5	and	and	CCONJ
cana-6007	40	6	others	other	NOUN
cana-6007	40	7	in	in	ADP
cana-6007	40	8	their	their	PRON
cana-6007	40	9	seminal	seminal	ADJ
cana-6007	40	10	works	work	NOUN
cana-6007	41	1	[	[	X
cana-6007	41	2	3	3	NUM
cana-6007	41	3	]	]	PUNCT
cana-6007	41	4	,	,	PUNCT
cana-6007	42	1	[	[	X
cana-6007	42	2	7	7	NUM
cana-6007	42	3	]	]	PUNCT
cana-6007	42	4	,	,	PUNCT
cana-6007	42	5	[	[	X
cana-6007	42	6	13	13	NUM
cana-6007	42	7	]	]	PUNCT
cana-6007	42	8	,	,	PUNCT
cana-6007	42	9	which	which	PRON
cana-6007	42	10	thoroughly	thoroughly	ADV
cana-6007	42	11	investigated	investigate	VERB
cana-6007	42	12	the	the	DET
cana-6007	42	13	theoretical	theoretical	ADJ
cana-6007	42	14	foundations	foundation	NOUN
cana-6007	42	15	and	and	CCONJ
cana-6007	42	16	convergence	convergence	NOUN
cana-6007	42	17	analyses	analysis	NOUN
cana-6007	42	18	of	of	ADP
cana-6007	42	19	these	these	DET
cana-6007	42	20	methods	method	NOUN
cana-6007	42	21	.	.	PUNCT
cana-6007	43	1	after	after	ADP
cana-6007	43	2	these	these	DET
cana-6007	43	3	developments	development	NOUN
cana-6007	43	4	,	,	PUNCT
cana-6007	43	5	even	even	ADV
cana-6007	43	6	now	now	ADV
cana-6007	43	7	most	most	ADJ
cana-6007	43	8	of	of	ADP
cana-6007	43	9	the	the	DET
cana-6007	43	10	existing	exist	VERB
cana-6007	43	11	comparative	comparative	ADJ
cana-6007	43	12	literature	literature	NOUN
cana-6007	43	13	focuses	focus	VERB
cana-6007	43	14	mainly	mainly	ADV
cana-6007	43	15	on	on	ADP
cana-6007	43	16	linear	linear	ADJ
cana-6007	43	17	or	or	CCONJ
cana-6007	43	18	simplified	simplified	ADJ
cana-6007	43	19	sdes	sde	NOUN
cana-6007	43	20	,	,	PUNCT
cana-6007	43	21	frequently	frequently	ADV
cana-6007	43	22	without	without	ADP
cana-6007	43	23	access	access	NOUN
cana-6007	43	24	to	to	ADP
cana-6007	43	25	known	know	VERB
cana-6007	43	26	analytical	analytical	ADJ
cana-6007	43	27	solutions	solution	NOUN
cana-6007	43	28	.	.	PUNCT
cana-6007	44	1	this	this	PRON
cana-6007	44	2	makes	make	VERB
cana-6007	44	3	it	it	PRON
cana-6007	44	4	very	very	ADV
cana-6007	44	5	difficult	difficult	ADJ
cana-6007	44	6	to	to	PART
cana-6007	44	7	accurately	accurately	ADV
cana-6007	44	8	measure	measure	VERB
cana-6007	44	9	numerical	numerical	ADJ
cana-6007	44	10	error	error	NOUN
cana-6007	44	11	and	and	CCONJ
cana-6007	44	12	see	see	VERB
cana-6007	44	13	how	how	SCONJ
cana-6007	44	14	well	well	ADV
cana-6007	44	15	the	the	DET
cana-6007	44	16	methods	method	NOUN
cana-6007	44	17	work	work	VERB
cana-6007	44	18	in	in	ADP
cana-6007	44	19	more	more	ADV
cana-6007	44	20	complicated	complicated	ADJ
cana-6007	44	21	situations	situation	NOUN
cana-6007	44	22	[	[	X
cana-6007	44	23	4	4	NUM
cana-6007	44	24	]	]	PUNCT
cana-6007	44	25	,	,	PUNCT
cana-6007	44	26	[	[	X
cana-6007	44	27	15	15	NUM
cana-6007	44	28	]	]	PUNCT
cana-6007	44	29	.	.	PUNCT
cana-6007	45	1	identifying	identify	VERB
cana-6007	45	2	this	this	DET
cana-6007	45	3	gap	gap	NOUN
cana-6007	45	4	,	,	PUNCT
cana-6007	45	5	the	the	DET
cana-6007	45	6	current	current	ADJ
cana-6007	45	7	study	study	NOUN
cana-6007	45	8	conducts	conduct	VERB
cana-6007	45	9	a	a	DET
cana-6007	45	10	systematic	systematic	ADJ
cana-6007	45	11	comparison	comparison	NOUN
cana-6007	45	12	of	of	ADP
cana-6007	45	13	the	the	DET
cana-6007	45	14	euler	euler	NOUN
cana-6007	45	15	–	–	PUNCT
cana-6007	45	16	maruyama	maruyama	NOUN
cana-6007	45	17	and	and	CCONJ
cana-6007	45	18	milstein	milstein	ADJ
cana-6007	45	19	methods	method	NOUN
cana-6007	45	20	using	use	VERB
cana-6007	45	21	two	two	NUM
cana-6007	45	22	carefully	carefully	ADV
cana-6007	45	23	selected	select	VERB
cana-6007	45	24	nonlinear	nonlinear	ADJ
cana-6007	45	25	sdes	sde	NOUN
cana-6007	45	26	,	,	PUNCT
cana-6007	45	27	each	each	PRON
cana-6007	45	28	with	with	ADP
cana-6007	45	29	precise	precise	ADJ
cana-6007	45	30	closed	close	VERB
cana-6007	45	31	-	-	PUNCT
cana-6007	45	32	form	form	NOUN
cana-6007	45	33	solutions	solution	NOUN
cana-6007	45	34	obtained	obtain	VERB
cana-6007	45	35	via	via	ADP
cana-6007	45	36	itô	itô	PROPN
cana-6007	45	37	calculus	calculus	PROPN
cana-6007	45	38	[	[	X
cana-6007	45	39	1],[6	1],[6	NUM
cana-6007	45	40	]	]	PUNCT
cana-6007	45	41	.	.	PUNCT
cana-6007	46	1	these	these	DET
cana-6007	46	2	exact	exact	ADJ
cana-6007	46	3	solutions	solution	NOUN
cana-6007	46	4	are	be	AUX
cana-6007	46	5	not	not	PART
cana-6007	46	6	only	only	ADV
cana-6007	46	7	difficult	difficult	ADJ
cana-6007	46	8	to	to	PART
cana-6007	46	9	obtain	obtain	VERB
cana-6007	46	10	but	but	CCONJ
cana-6007	46	11	also	also	ADV
cana-6007	46	12	provide	provide	VERB
cana-6007	46	13	strict	strict	ADJ
cana-6007	46	14	criteria	criterion	NOUN
cana-6007	46	15	to	to	PART
cana-6007	46	16	determine	determine	VERB
cana-6007	46	17	the	the	DET
cana-6007	46	18	precision	precision	NOUN
cana-6007	46	19	,	,	PUNCT
cana-6007	46	20	stability	stability	NOUN
cana-6007	46	21	,	,	PUNCT
cana-6007	46	22	and	and	CCONJ
cana-6007	46	23	convergence	convergence	NOUN
cana-6007	46	24	behavior	behavior	NOUN
cana-6007	46	25	of	of	ADP
cana-6007	46	26	both	both	DET
cana-6007	46	27	approaches	approach	NOUN
cana-6007	46	28	under	under	ADP
cana-6007	46	29	uniform	uniform	ADJ
cana-6007	46	30	time	time	NOUN
cana-6007	46	31	steps	step	NOUN
cana-6007	46	32	.	.	PUNCT
cana-6007	47	1	this	this	DET
cana-6007	47	2	work	work	NOUN
cana-6007	47	3	contributes	contribute	VERB
cana-6007	47	4	to	to	ADP
cana-6007	47	5	a	a	DET
cana-6007	47	6	better	well	ADJ
cana-6007	47	7	understanding	understanding	NOUN
cana-6007	47	8	of	of	ADP
cana-6007	47	9	the	the	DET
cana-6007	47	10	performance	performance	NOUN
cana-6007	47	11	and	and	CCONJ
cana-6007	47	12	limitations	limitation	NOUN
cana-6007	47	13	of	of	ADP
cana-6007	47	14	these	these	DET
cana-6007	47	15	widely	widely	ADV
cana-6007	47	16	used	use	VERB
cana-6007	47	17	numerical	numerical	ADJ
cana-6007	47	18	methods	method	NOUN
cana-6007	47	19	by	by	ADP
cana-6007	47	20	concentrating	concentrate	VERB
cana-6007	47	21	on	on	ADP
cana-6007	47	22	systems	system	NOUN
cana-6007	47	23	where	where	SCONJ
cana-6007	47	24	both	both	DET
cana-6007	47	25	stochastic	stochastic	ADJ
cana-6007	47	26	effects	effect	NOUN
cana-6007	47	27	communications	communication	NOUN
cana-6007	47	28	on	on	ADP
cana-6007	47	29	applied	apply	VERB
cana-6007	47	30	nonlinear	nonlinear	ADJ
cana-6007	47	31	analysis	analysis	NOUN
cana-6007	47	32	issn	issn	NOUN
cana-6007	47	33	:	:	PUNCT
cana-6007	47	34	1074	1074	NUM
cana-6007	47	35	-	-	PUNCT
cana-6007	47	36	133x	133x	NUM
cana-6007	47	37	vol	vol	VERB
cana-6007	47	38	32	32	NUM
cana-6007	47	39	no	no	NOUN
cana-6007	47	40	.	.	PUNCT
cana-6007	48	1	10s	10	NOUN
cana-6007	48	2	(	(	PUNCT
cana-6007	48	3	2025	2025	NUM
cana-6007	48	4	)	)	PUNCT
cana-6007	48	5	3228	3228	NUM
cana-6007	48	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	48	7	and	and	CCONJ
cana-6007	48	8	nonlinearity	nonlinearity	NOUN
cana-6007	48	9	are	be	AUX
cana-6007	48	10	important	important	ADJ
cana-6007	48	11	.	.	PUNCT
cana-6007	49	1	thus	thus	ADV
cana-6007	49	2	,	,	PUNCT
cana-6007	49	3	provide	provide	VERB
cana-6007	49	4	a	a	DET
cana-6007	49	5	better	well	ADJ
cana-6007	49	6	understanding	understanding	NOUN
cana-6007	49	7	of	of	ADP
cana-6007	49	8	their	their	PRON
cana-6007	49	9	applicability	applicability	NOUN
cana-6007	49	10	in	in	ADP
cana-6007	49	11	real	real	ADJ
cana-6007	49	12	-	-	PUNCT
cana-6007	49	13	world	world	NOUN
cana-6007	49	14	modeling	modeling	NOUN
cana-6007	49	15	situations	situation	NOUN
cana-6007	50	1	[	[	X
cana-6007	50	2	2],[13	2],[13	NOUN
cana-6007	50	3	]	]	PUNCT
cana-6007	50	4	.	.	PUNCT
cana-6007	51	1	2.1	2.1	NUM
cana-6007	51	2	methods	method	NOUN
cana-6007	51	3	in	in	ADP
cana-6007	51	4	this	this	DET
cana-6007	51	5	paper	paper	NOUN
cana-6007	51	6	we	we	PRON
cana-6007	51	7	consider	consider	VERB
cana-6007	51	8	the	the	DET
cana-6007	51	9	general	general	ADJ
cana-6007	51	10	form	form	NOUN
cana-6007	51	11	of	of	ADP
cana-6007	51	12	a	a	DET
cana-6007	51	13	one	one	NUM
cana-6007	51	14	-	-	PUNCT
cana-6007	51	15	dimensional	dimensional	ADJ
cana-6007	51	16	sde	sde	NOUN
cana-6007	51	17	with	with	ADP
cana-6007	51	18	dx(t	dx(t	NOUN
cana-6007	51	19	)	)	PUNCT
cana-6007	51	20	=	=	SYM
cana-6007	51	21	α(x(t	α(x(t	PROPN
cana-6007	51	22	)	)	PUNCT
cana-6007	51	23	,	,	PUNCT
cana-6007	51	24	t	t	PROPN
cana-6007	51	25	)	)	PUNCT
cana-6007	51	26	 	 	SPACE
cana-6007	51	27	dt	dt	PUNCT
cana-6007	52	1	+	+	CCONJ
cana-6007	52	2	β(x(t	β(x(t	PROPN
cana-6007	52	3	)	)	PUNCT
cana-6007	52	4	,	,	PUNCT
cana-6007	52	5	t	t	PROPN
cana-6007	52	6	)	)	PUNCT
cana-6007	52	7	 	 	SPACE
cana-6007	52	8	dw(t	dw(t	NOUN
cana-6007	52	9	)	)	PUNCT
cana-6007	52	10	,	,	PUNCT
cana-6007	52	11	x(t0	x(t0	PROPN
cana-6007	52	12	)	)	PUNCT
cana-6007	53	1	=	=	PUNCT
cana-6007	53	2	x0	x0	PROPN
cana-6007	53	3	,	,	PUNCT
cana-6007	53	4	t0	t0	PROPN
cana-6007	53	5	≤	≤	PROPN
cana-6007	53	6	t	t	PROPN
cana-6007	53	7	≤	≤	PROPN
cana-6007	53	8	t	t	PROPN
cana-6007	53	9	(	(	PUNCT
cana-6007	53	10	1	1	NUM
cana-6007	53	11	)	)	PUNCT
cana-6007	53	12	where	where	SCONJ
cana-6007	53	13	:	:	PUNCT
cana-6007	53	14	x(t	x(t	PROPN
cana-6007	53	15	)	)	PUNCT
cana-6007	53	16	is	be	AUX
cana-6007	53	17	the	the	DET
cana-6007	53	18	unknown	unknown	ADJ
cana-6007	53	19	stochastic	stochastic	ADJ
cana-6007	53	20	process	process	NOUN
cana-6007	53	21	.	.	PUNCT
cana-6007	54	1	α(x(t	α(x(t	ADJ
cana-6007	54	2	)	)	PUNCT
cana-6007	54	3	,	,	PUNCT
cana-6007	54	4	t	t	PROPN
cana-6007	54	5	)	)	PUNCT
cana-6007	54	6	is	be	AUX
cana-6007	54	7	the	the	DET
cana-6007	54	8	drift	drift	NOUN
cana-6007	54	9	coefficient	coefficient	NOUN
cana-6007	54	10	.	.	PUNCT
cana-6007	55	1	β(x(t	β(x(t	PROPN
cana-6007	55	2	)	)	PUNCT
cana-6007	55	3	,	,	PUNCT
cana-6007	55	4	t	t	PROPN
cana-6007	55	5	)	)	PUNCT
cana-6007	55	6	is	be	AUX
cana-6007	55	7	the	the	DET
cana-6007	55	8	diffusion	diffusion	NOUN
cana-6007	55	9	coefficient	coefficient	NOUN
cana-6007	55	10	.	.	PUNCT
cana-6007	56	1	w(t	w(t	PROPN
cana-6007	56	2	)	)	PUNCT
cana-6007	56	3	is	be	AUX
cana-6007	56	4	the	the	DET
cana-6007	56	5	wiener	wiener	NOUN
cana-6007	56	6	process	process	NOUN
cana-6007	56	7	(	(	PUNCT
cana-6007	56	8	also	also	ADV
cana-6007	56	9	called	call	VERB
cana-6007	56	10	standard	standard	ADJ
cana-6007	56	11	brownian	brownian	ADJ
cana-6007	56	12	motion	motion	NOUN
cana-6007	56	13	)	)	PUNCT
cana-6007	56	14	,	,	PUNCT
cana-6007	56	15	representing	represent	VERB
cana-6007	56	16	the	the	DET
cana-6007	56	17	source	source	NOUN
cana-6007	56	18	of	of	ADP
cana-6007	56	19	randomness	randomness	NOUN
cana-6007	56	20	.	.	PUNCT
cana-6007	57	1	robert	robert	PROPN
cana-6007	57	2	brown	brown	PROPN
cana-6007	57	3	noticed	notice	VERB
cana-6007	57	4	the	the	DET
cana-6007	57	5	jittery	jittery	ADJ
cana-6007	57	6	motion	motion	NOUN
cana-6007	57	7	of	of	ADP
cana-6007	57	8	microscopic	microscopic	ADJ
cana-6007	57	9	particles	particle	NOUN
cana-6007	57	10	suspended	suspend	VERB
cana-6007	57	11	in	in	ADP
cana-6007	57	12	a	a	DET
cana-6007	57	13	fluid	fluid	NOUN
cana-6007	57	14	in	in	ADP
cana-6007	57	15	1827	1827	NUM
cana-6007	57	16	,	,	PUNCT
cana-6007	57	17	which	which	PRON
cana-6007	57	18	led	lead	VERB
cana-6007	57	19	to	to	ADP
cana-6007	57	20	the	the	DET
cana-6007	57	21	development	development	NOUN
cana-6007	57	22	of	of	ADP
cana-6007	57	23	the	the	DET
cana-6007	57	24	theory	theory	NOUN
cana-6007	57	25	of	of	ADP
cana-6007	57	26	brownian	brownian	ADJ
cana-6007	57	27	motion	motion	NOUN
cana-6007	57	28	.	.	PUNCT
cana-6007	58	1	later	later	ADV
cana-6007	58	2	,	,	PUNCT
cana-6007	58	3	norbert	norbert	PROPN
cana-6007	58	4	wiener	wiener	PROPN
cana-6007	58	5	's	's	PART
cana-6007	58	6	work	work	NOUN
cana-6007	58	7	gave	give	VERB
cana-6007	58	8	this	this	DET
cana-6007	58	9	physical	physical	ADJ
cana-6007	58	10	phenomenon	phenomenon	NOUN
cana-6007	58	11	a	a	DET
cana-6007	58	12	rigorous	rigorous	ADJ
cana-6007	58	13	mathematical	mathematical	ADJ
cana-6007	58	14	foundation	foundation	NOUN
cana-6007	58	15	by	by	ADP
cana-6007	58	16	constructing	construct	VERB
cana-6007	58	17	the	the	DET
cana-6007	58	18	wiener	wiener	NOUN
cana-6007	58	19	process	process	NOUN
cana-6007	58	20	,	,	PUNCT
cana-6007	58	21	which	which	PRON
cana-6007	58	22	served	serve	VERB
cana-6007	58	23	as	as	ADP
cana-6007	58	24	the	the	DET
cana-6007	58	25	basis	basis	NOUN
cana-6007	58	26	for	for	ADP
cana-6007	58	27	modern	modern	ADJ
cana-6007	58	28	stochastic	stochastic	ADJ
cana-6007	58	29	calculus	calculus	NOUN
cana-6007	58	30	[	[	X
cana-6007	58	31	1	1	NUM
cana-6007	58	32	]	]	PUNCT
cana-6007	58	33	.	.	PUNCT
cana-6007	59	1	the	the	DET
cana-6007	59	2	wiener	wiener	NOUN
cana-6007	59	3	process	process	NOUN
cana-6007	59	4	w(t	w(t	PROPN
cana-6007	59	5	)	)	PUNCT
cana-6007	59	6	on	on	ADP
cana-6007	59	7	[	[	X
cana-6007	59	8	0,t	0,t	X
cana-6007	59	9	]	]	X
cana-6007	59	10	is	be	AUX
cana-6007	59	11	characterized	characterize	VERB
cana-6007	59	12	by	by	ADP
cana-6007	59	13	three	three	NUM
cana-6007	59	14	essential	essential	ADJ
cana-6007	59	15	properties	property	NOUN
cana-6007	59	16	:	:	PUNCT
cana-6007	59	17	i.	i.	PROPN
cana-6007	59	18	w(0)=0	w(0)=0	PROPN
cana-6007	59	19	,	,	PUNCT
cana-6007	59	20	which	which	PRON
cana-6007	59	21	means	mean	VERB
cana-6007	59	22	that	that	SCONJ
cana-6007	59	23	it	it	PRON
cana-6007	59	24	begins	begin	VERB
cana-6007	59	25	deterministically	deterministically	ADV
cana-6007	59	26	at	at	ADP
cana-6007	59	27	zero	zero	NUM
cana-6007	59	28	(	(	PUNCT
cana-6007	59	29	with	with	ADP
cana-6007	59	30	probability	probability	NOUN
cana-6007	59	31	1	1	NUM
cana-6007	59	32	)	)	PUNCT
cana-6007	59	33	.	.	PUNCT
cana-6007	60	1	ii	ii	PROPN
cana-6007	60	2	.	.	PUNCT
cana-6007	61	1	for	for	ADP
cana-6007	61	2	any	any	DET
cana-6007	61	3	0	0	NUM
cana-6007	61	4	≤	≤	NOUN
cana-6007	61	5	s	s	PART
cana-6007	61	6	<	<	X
cana-6007	61	7	t	t	X
cana-6007	61	8	≤	≤	PROPN
cana-6007	61	9	t	t	PROPN
cana-6007	61	10	,	,	PUNCT
cana-6007	61	11	the	the	DET
cana-6007	61	12	increment	increment	NOUN
cana-6007	61	13	w(t)−w(s	w(t)−w(s	NOUN
cana-6007	61	14	)	)	PUNCT
cana-6007	61	15	is	be	AUX
cana-6007	61	16	n(0	n(0	PROPN
cana-6007	61	17	,	,	PUNCT
cana-6007	61	18	t	t	PROPN
cana-6007	61	19	-	-	PUNCT
cana-6007	61	20	s	s	NOUN
cana-6007	61	21	)	)	PUNCT
cana-6007	61	22	distributed	distribute	VERB
cana-6007	61	23	.	.	PUNCT
cana-6007	62	1	iii	iii	X
cana-6007	62	2	.	.	PUNCT
cana-6007	63	1	the	the	DET
cana-6007	63	2	increments	increment	NOUN
cana-6007	63	3	w(t	w(t	PROPN
cana-6007	63	4	)	)	PUNCT
cana-6007	63	5	−	−	PROPN
cana-6007	63	6	w(s	w(s	PROPN
cana-6007	63	7	)	)	PUNCT
cana-6007	63	8	and	and	CCONJ
cana-6007	63	9	w(v	w(v	NOUN
cana-6007	63	10	)	)	PUNCT
cana-6007	63	11	−	−	PROPN
cana-6007	63	12	w(u	w(u	PROPN
cana-6007	63	13	)	)	PUNCT
cana-6007	63	14	are	be	AUX
cana-6007	63	15	statistically	statistically	ADV
cana-6007	63	16	independent	independent	ADJ
cana-6007	63	17	for	for	ADP
cana-6007	63	18	disjoint	disjoint	NOUN
cana-6007	63	19	intervals	interval	NOUN
cana-6007	63	20	[	[	X
cana-6007	63	21	s	s	X
cana-6007	63	22	,	,	PUNCT
cana-6007	63	23	t	t	PROPN
cana-6007	63	24	]	]	PUNCT
cana-6007	63	25	and	and	CCONJ
cana-6007	63	26	[	[	X
cana-6007	63	27	u	u	NOUN
cana-6007	63	28	,	,	PUNCT
cana-6007	63	29	v	v	NOUN
cana-6007	63	30	]	]	PUNCT
cana-6007	63	31	respectively	respectively	ADV
cana-6007	63	32	,	,	PUNCT
cana-6007	63	33	where	where	SCONJ
cana-6007	63	34	0	0	NUM
cana-6007	63	35	≤	≤	NOUN
cana-6007	63	36	s	s	X
cana-6007	63	37	<	<	X
cana-6007	63	38	t	t	X
cana-6007	63	39	<	<	X
cana-6007	63	40	u	u	X
cana-6007	63	41	<	<	X
cana-6007	63	42	v	v	NOUN
cana-6007	63	43	≤	≤	ADJ
cana-6007	63	44	t.	t.	NOUN
cana-6007	63	45	researchers	researcher	NOUN
cana-6007	63	46	like	like	ADP
cana-6007	63	47	xuerong	xuerong	PROPN
cana-6007	63	48	mao	mao	PROPN
cana-6007	63	49	and	and	CCONJ
cana-6007	63	50	chenggui	chenggui	PROPN
cana-6007	63	51	yuan	yuan	PROPN
cana-6007	63	52	have	have	AUX
cana-6007	63	53	made	make	VERB
cana-6007	63	54	significant	significant	ADJ
cana-6007	63	55	contributions	contribution	NOUN
cana-6007	63	56	to	to	ADP
cana-6007	63	57	the	the	DET
cana-6007	63	58	study	study	NOUN
cana-6007	63	59	of	of	ADP
cana-6007	63	60	stochastic	stochastic	ADJ
cana-6007	63	61	systems	system	NOUN
cana-6007	63	62	.	.	PUNCT
cana-6007	64	1	for	for	ADP
cana-6007	64	2	instance	instance	NOUN
cana-6007	64	3	,	,	PUNCT
cana-6007	64	4	they	they	PRON
cana-6007	64	5	have	have	AUX
cana-6007	64	6	created	create	VERB
cana-6007	64	7	theoretical	theoretical	ADJ
cana-6007	64	8	frameworks	framework	NOUN
cana-6007	64	9	for	for	ADP
cana-6007	64	10	stochastic	stochastic	ADJ
cana-6007	64	11	differential	differential	ADJ
cana-6007	64	12	equations	equation	NOUN
cana-6007	64	13	(	(	PUNCT
cana-6007	64	14	sdes	sde	NOUN
cana-6007	64	15	)	)	PUNCT
cana-6007	64	16	with	with	ADP
cana-6007	64	17	markovian	markovian	ADJ
cana-6007	64	18	switching	switching	NOUN
cana-6007	64	19	and	and	CCONJ
cana-6007	64	20	nonlinear	nonlinear	ADJ
cana-6007	64	21	dynamics	dynamic	NOUN
cana-6007	64	22	[	[	X
cana-6007	64	23	17	17	NUM
cana-6007	64	24	]	]	PUNCT
cana-6007	64	25	and	and	CCONJ
cana-6007	64	26	also	also	ADV
cana-6007	64	27	developed	develop	VERB
cana-6007	64	28	numerical	numerical	ADJ
cana-6007	64	29	methods	method	NOUN
cana-6007	64	30	that	that	PRON
cana-6007	64	31	preserve	preserve	VERB
cana-6007	64	32	structural	structural	ADJ
cana-6007	64	33	properties	property	NOUN
cana-6007	64	34	in	in	ADP
cana-6007	64	35	financial	financial	ADJ
cana-6007	64	36	sdes	sde	NOUN
cana-6007	64	37	with	with	ADP
cana-6007	64	38	superlinear	superlinear	ADJ
cana-6007	64	39	coefficients	coefficient	NOUN
cana-6007	64	40	[	[	X
cana-6007	64	41	14	14	NUM
cana-6007	64	42	]	]	PUNCT
cana-6007	64	43	.	.	PUNCT
cana-6007	65	1	integrating	integrate	VERB
cana-6007	65	2	equation	equation	NOUN
cana-6007	65	3	(	(	PUNCT
cana-6007	65	4	1	1	NUM
cana-6007	65	5	)	)	PUNCT
cana-6007	65	6	from	from	ADP
cana-6007	65	7	t0	t0	PROPN
cana-6007	65	8	to	to	ADP
cana-6007	65	9	t	t	PROPN
cana-6007	65	10	,	,	PUNCT
cana-6007	65	11	we	we	PRON
cana-6007	65	12	have	have	VERB
cana-6007	65	13	the	the	DET
cana-6007	65	14	following	follow	VERB
cana-6007	65	15	integral	integral	ADJ
cana-6007	65	16	form	form	NOUN
cana-6007	65	17	:	:	PUNCT
cana-6007	65	18	x(t	x(t	PROPN
cana-6007	65	19	)	)	PUNCT
cana-6007	65	20	=	=	SYM
cana-6007	65	21	x(t0	x(t0	PROPN
cana-6007	65	22	)	)	PUNCT
cana-6007	66	1	+	+	CCONJ
cana-6007	67	1	∫t0	∫t0	PROPN
cana-6007	67	2	t	t	PROPN
cana-6007	67	3	α(s	α(s	PROPN
cana-6007	67	4	,	,	PUNCT
cana-6007	67	5	x(s))ds	x(s))ds	PROPN
cana-6007	68	1	+	+	CCONJ
cana-6007	68	2	∫t0	∫t0	PROPN
cana-6007	68	3	t	t	PROPN
cana-6007	68	4	β(s	β(s	PROPN
cana-6007	68	5	,	,	PUNCT
cana-6007	68	6	x(s))dw(s	x(s))dw(s	PROPN
cana-6007	68	7	)	)	PUNCT
cana-6007	68	8	the	the	DET
cana-6007	68	9	first	first	ADJ
cana-6007	68	10	integral	integral	ADJ
cana-6007	68	11	∫t0	∫t0	PROPN
cana-6007	68	12	t	t	PROPN
cana-6007	68	13	α(s	α(s	PROPN
cana-6007	68	14	,	,	PUNCT
cana-6007	68	15	x(s))ds	x(s))ds	PROPN
cana-6007	68	16	is	be	AUX
cana-6007	68	17	a	a	DET
cana-6007	68	18	standard	standard	NOUN
cana-6007	68	19	(	(	PUNCT
cana-6007	68	20	riemann	riemann	PROPN
cana-6007	68	21	or	or	CCONJ
cana-6007	68	22	lebesgue	lebesgue	NOUN
cana-6007	68	23	)	)	PUNCT
cana-6007	68	24	integral	integral	NOUN
cana-6007	68	25	that	that	PRON
cana-6007	68	26	represent	represent	VERB
cana-6007	68	27	the	the	DET
cana-6007	68	28	deterministic	deterministic	ADJ
cana-6007	68	29	part	part	NOUN
cana-6007	68	30	(	(	PUNCT
cana-6007	68	31	drift	drift	NOUN
cana-6007	68	32	)	)	PUNCT
cana-6007	68	33	.	.	PUNCT
cana-6007	69	1	the	the	DET
cana-6007	69	2	second	second	ADJ
cana-6007	69	3	integral	integral	ADJ
cana-6007	69	4	∫t0	∫t0	PROPN
cana-6007	69	5	t	t	PROPN
cana-6007	69	6	β(s	β(s	PROPN
cana-6007	69	7	,	,	PUNCT
cana-6007	69	8	x(s))dw(s	x(s))dw(s	PROPN
cana-6007	69	9	)	)	PUNCT
cana-6007	69	10	is	be	AUX
cana-6007	69	11	a	a	DET
cana-6007	69	12	stochastic	stochastic	ADJ
cana-6007	69	13	(	(	PUNCT
cana-6007	69	14	itô	itô	ADJ
cana-6007	69	15	)	)	PUNCT
cana-6007	69	16	integral	integral	ADJ
cana-6007	69	17	,	,	PUNCT
cana-6007	69	18	that	that	PRON
cana-6007	69	19	represents	represent	VERB
cana-6007	69	20	the	the	DET
cana-6007	69	21	random	random	ADJ
cana-6007	69	22	fluctuations	fluctuation	NOUN
cana-6007	69	23	introduced	introduce	VERB
cana-6007	69	24	by	by	ADP
cana-6007	69	25	the	the	DET
cana-6007	69	26	brownian	brownian	ADJ
cana-6007	69	27	motion	motion	NOUN
cana-6007	69	28	w(t	w(t	PROPN
cana-6007	69	29	)	)	PUNCT
cana-6007	69	30	.	.	PUNCT
cana-6007	70	1	the	the	DET
cana-6007	70	2	last	last	ADJ
cana-6007	70	3	term	term	NOUN
cana-6007	70	4	in	in	ADP
cana-6007	70	5	the	the	DET
cana-6007	70	6	integral	integral	ADJ
cana-6007	70	7	formulation	formulation	NOUN
cana-6007	70	8	of	of	ADP
cana-6007	70	9	a	a	DET
cana-6007	70	10	stochastic	stochastic	ADJ
cana-6007	70	11	differential	differential	NOUN
cana-6007	70	12	equation	equation	NOUN
cana-6007	70	13	is	be	AUX
cana-6007	70	14	known	know	VERB
cana-6007	70	15	as	as	ADP
cana-6007	70	16	the	the	DET
cana-6007	70	17	itô	itô	PROPN
cana-6007	70	18	integral	integral	ADJ
cana-6007	70	19	;	;	PUNCT
cana-6007	70	20	it	it	PRON
cana-6007	70	21	is	be	AUX
cana-6007	70	22	a	a	DET
cana-6007	70	23	key	key	ADJ
cana-6007	70	24	idea	idea	NOUN
cana-6007	70	25	in	in	ADP
cana-6007	70	26	stochastic	stochastic	ADJ
cana-6007	70	27	calculus	calculus	NOUN
cana-6007	70	28	.	.	PUNCT
cana-6007	71	1	the	the	DET
cana-6007	71	2	itô	itô	PROPN
cana-6007	71	3	formula	formula	NOUN
cana-6007	71	4	is	be	AUX
cana-6007	71	5	a	a	DET
cana-6007	71	6	stochastic	stochastic	ADJ
cana-6007	71	7	variant	variant	NOUN
cana-6007	71	8	of	of	ADP
cana-6007	71	9	communications	communication	NOUN
cana-6007	71	10	on	on	ADP
cana-6007	71	11	applied	apply	VERB
cana-6007	71	12	nonlinear	nonlinear	ADJ
cana-6007	71	13	analysis	analysis	NOUN
cana-6007	71	14	issn	issn	NOUN
cana-6007	71	15	:	:	PUNCT
cana-6007	71	16	1074	1074	NUM
cana-6007	71	17	-	-	PUNCT
cana-6007	71	18	133x	133x	NUM
cana-6007	71	19	vol	vol	VERB
cana-6007	71	20	32	32	NUM
cana-6007	71	21	no	no	NOUN
cana-6007	71	22	.	.	PUNCT
cana-6007	72	1	10s	10	NOUN
cana-6007	72	2	(	(	PUNCT
cana-6007	72	3	2025	2025	NUM
cana-6007	72	4	)	)	PUNCT
cana-6007	72	5	3229	3229	NUM
cana-6007	72	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	73	1	the	the	DET
cana-6007	73	2	classical	classical	ADJ
cana-6007	73	3	calculus	calculus	NOUN
cana-6007	73	4	chain	chain	NOUN
cana-6007	73	5	rule	rule	NOUN
cana-6007	73	6	;	;	PUNCT
cana-6007	73	7	it	it	PRON
cana-6007	73	8	is	be	AUX
cana-6007	73	9	used	use	VERB
cana-6007	73	10	to	to	PART
cana-6007	73	11	analytically	analytically	ADV
cana-6007	73	12	examine	examine	VERB
cana-6007	73	13	such	such	ADJ
cana-6007	73	14	equations	equation	NOUN
cana-6007	73	15	,	,	PUNCT
cana-6007	73	16	especially	especially	ADV
cana-6007	73	17	when	when	SCONJ
cana-6007	73	18	transforming	transform	VERB
cana-6007	73	19	functions	function	NOUN
cana-6007	73	20	of	of	ADP
cana-6007	73	21	stochastic	stochastic	ADJ
cana-6007	73	22	processes	process	NOUN
cana-6007	73	23	[	[	X
cana-6007	73	24	1	1	NUM
cana-6007	73	25	]	]	PUNCT
cana-6007	73	26	,	,	PUNCT
cana-6007	73	27	[	[	X
cana-6007	73	28	13	13	NUM
cana-6007	73	29	]	]	PUNCT
cana-6007	73	30	.	.	PUNCT
cana-6007	74	1	we	we	PRON
cana-6007	74	2	create	create	VERB
cana-6007	74	3	a	a	DET
cana-6007	74	4	new	new	ADJ
cana-6007	74	5	process	process	NOUN
cana-6007	74	6	.	.	PUNCT
cana-6007	75	1	u	u	NOUN
cana-6007	75	2	=	=	PUNCT
cana-6007	75	3	f(t	f(t	NOUN
cana-6007	75	4	,	,	PUNCT
cana-6007	75	5	xt	xt	NUM
cana-6007	75	6	)	)	PUNCT
cana-6007	75	7	,	,	PUNCT
cana-6007	75	8	where	where	SCONJ
cana-6007	75	9	,	,	PUNCT
cana-6007	75	10	f	f	PROPN
cana-6007	75	11	is	be	AUX
cana-6007	75	12	a	a	DET
cana-6007	75	13	smooth	smooth	ADJ
cana-6007	75	14	function	function	NOUN
cana-6007	75	15	and	and	CCONJ
cana-6007	75	16	the	the	DET
cana-6007	75	17	differential	differential	NOUN
cana-6007	75	18	of	of	ADP
cana-6007	75	19	u	u	NOUN
cana-6007	75	20	is	be	AUX
cana-6007	75	21	given	give	VERB
cana-6007	75	22	by	by	ADP
cana-6007	75	23	:	:	PUNCT
cana-6007	75	24	du	du	X
cana-6007	75	25	=	=	PUNCT
cana-6007	75	26	(	(	PUNCT
cana-6007	75	27	∂f/∂t)dt	∂f/∂t)dt	PROPN
cana-6007	75	28	+	+	CCONJ
cana-6007	75	29	(	(	PUNCT
cana-6007	75	30	∂f/∂x)dxt	∂f/∂x)dxt	NOUN
cana-6007	75	31	+	+	CCONJ
cana-6007	75	32	1/2(∂2f/∂x2)(dxt)^2	1/2(∂2f/∂x2)(dxt)^2	NUM
cana-6007	75	33	substituting	substitute	VERB
cana-6007	75	34	the	the	DET
cana-6007	75	35	expression	expression	NOUN
cana-6007	75	36	for	for	ADP
cana-6007	75	37	dxt	dxt	PROPN
cana-6007	75	38	into	into	ADP
cana-6007	75	39	this	this	DET
cana-6007	75	40	expansion	expansion	NOUN
cana-6007	75	41	and	and	CCONJ
cana-6007	75	42	applying	apply	VERB
cana-6007	75	43	itô	itô	PROPN
cana-6007	75	44	’s	’s	PART
cana-6007	75	45	product	product	NOUN
cana-6007	75	46	rules	rule	NOUN
cana-6007	75	47	—	—	PUNCT
cana-6007	75	48	itô	itô	ADJ
cana-6007	75	49	multiplication	multiplication	NOUN
cana-6007	75	50	table	table	NOUN
cana-6007	75	51	we	we	PRON
cana-6007	75	52	have	have	VERB
cana-6007	75	53	,	,	PUNCT
cana-6007	75	54	du	du	PROPN
cana-6007	75	55	=[	=[	X
cana-6007	75	56	(	(	PUNCT
cana-6007	75	57	∂f/∂t	∂f/∂t	NOUN
cana-6007	75	58	)	)	PUNCT
cana-6007	75	59	+	+	NUM
cana-6007	75	60	α(∂f/∂x	α(∂f/∂x	NUM
cana-6007	75	61	)	)	PUNCT
cana-6007	76	1	+	+	CCONJ
cana-6007	76	2	(	(	PUNCT
cana-6007	76	3	1/2)β2(∂2f/∂x2)]dt	1/2)β2(∂2f/∂x2)]dt	NUM
cana-6007	76	4	+	+	NUM
cana-6007	76	5	β(∂f/∂x)dwt	β(∂f/∂x)dwt	NOUN
cana-6007	76	6	this	this	DET
cana-6007	76	7	formulation	formulation	NOUN
cana-6007	76	8	is	be	AUX
cana-6007	76	9	the	the	DET
cana-6007	76	10	basis	basis	NOUN
cana-6007	76	11	for	for	ADP
cana-6007	76	12	itô	itô	PROPN
cana-6007	76	13	–	–	PUNCT
cana-6007	76	14	taylor	taylor	PROPN
cana-6007	76	15	expansions	expansion	NOUN
cana-6007	76	16	,	,	PUNCT
cana-6007	76	17	which	which	PRON
cana-6007	76	18	are	be	AUX
cana-6007	76	19	fundamental	fundamental	ADJ
cana-6007	76	20	in	in	ADP
cana-6007	76	21	developing	develop	VERB
cana-6007	76	22	high	high	ADJ
cana-6007	76	23	-	-	PUNCT
cana-6007	76	24	precision	precision	NOUN
cana-6007	76	25	numerical	numerical	ADJ
cana-6007	76	26	approaches	approach	NOUN
cana-6007	76	27	for	for	ADP
cana-6007	76	28	solving	solve	VERB
cana-6007	76	29	stochastic	stochastic	ADJ
cana-6007	76	30	differential	differential	ADJ
cana-6007	76	31	equations	equation	NOUN
cana-6007	76	32	[	[	X
cana-6007	76	33	3	3	NUM
cana-6007	76	34	]	]	PUNCT
cana-6007	76	35	,	,	PUNCT
cana-6007	76	36	[	[	X
cana-6007	76	37	13	13	NUM
cana-6007	76	38	]	]	PUNCT
cana-6007	76	39	.	.	PUNCT
cana-6007	77	1	over	over	ADP
cana-6007	77	2	the	the	DET
cana-6007	77	3	years	year	NOUN
cana-6007	77	4	,	,	PUNCT
cana-6007	77	5	various	various	ADJ
cana-6007	77	6	studies	study	NOUN
cana-6007	77	7	have	have	AUX
cana-6007	77	8	been	be	AUX
cana-6007	77	9	done	do	VERB
cana-6007	77	10	comparing	compare	VERB
cana-6007	77	11	the	the	DET
cana-6007	77	12	effectiveness	effectiveness	NOUN
cana-6007	77	13	of	of	ADP
cana-6007	77	14	numerical	numerical	ADJ
cana-6007	77	15	techniques	technique	NOUN
cana-6007	77	16	in	in	ADP
cana-6007	77	17	solving	solve	VERB
cana-6007	77	18	ordinary	ordinary	ADJ
cana-6007	77	19	differential	differential	ADJ
cana-6007	77	20	equations	equation	NOUN
cana-6007	77	21	with	with	ADP
cana-6007	77	22	initial	initial	ADJ
cana-6007	77	23	value	value	NOUN
cana-6007	77	24	problems	problem	NOUN
cana-6007	77	25	[	[	X
cana-6007	77	26	11	11	NUM
cana-6007	77	27	]	]	PUNCT
cana-6007	77	28	.	.	PUNCT
cana-6007	78	1	these	these	DET
cana-6007	78	2	basic	basic	ADJ
cana-6007	78	3	ideas	idea	NOUN
cana-6007	78	4	continue	continue	VERB
cana-6007	78	5	to	to	PART
cana-6007	78	6	influence	influence	VERB
cana-6007	78	7	the	the	DET
cana-6007	78	8	development	development	NOUN
cana-6007	78	9	and	and	CCONJ
cana-6007	78	10	assessment	assessment	NOUN
cana-6007	78	11	of	of	ADP
cana-6007	78	12	more	more	ADV
cana-6007	78	13	advanced	advanced	ADJ
cana-6007	78	14	methods	method	NOUN
cana-6007	78	15	such	such	ADJ
cana-6007	78	16	as	as	ADP
cana-6007	78	17	euler	euler	NOUN
cana-6007	78	18	–	–	PUNCT
cana-6007	78	19	maruyama	maruyama	NOUN
cana-6007	78	20	and	and	CCONJ
cana-6007	78	21	milstein	milstein	ADJ
cana-6007	78	22	for	for	ADP
cana-6007	78	23	stochastic	stochastic	ADJ
cana-6007	78	24	systems	system	NOUN
cana-6007	78	25	.	.	PUNCT
cana-6007	79	1	2.2	2.2	NUM
cana-6007	79	2	euler	euler	NOUN
cana-6007	79	3	maruyama	maruyama	PROPN
cana-6007	79	4	method	method	VERB
cana-6007	79	5	a	a	DET
cana-6007	79	6	simple	simple	ADJ
cana-6007	79	7	technique	technique	NOUN
cana-6007	79	8	to	to	PART
cana-6007	79	9	get	get	VERB
cana-6007	79	10	approximate	approximate	ADJ
cana-6007	79	11	answers	answer	NOUN
cana-6007	79	12	to	to	ADP
cana-6007	79	13	stochastic	stochastic	ADJ
cana-6007	79	14	differential	differential	ADJ
cana-6007	79	15	equations	equation	NOUN
cana-6007	79	16	is	be	AUX
cana-6007	79	17	the	the	DET
cana-6007	79	18	euler	euler	NOUN
cana-6007	79	19	–	–	PUNCT
cana-6007	79	20	maruyama	maruyama	NOUN
cana-6007	79	21	method	method	NOUN
cana-6007	79	22	.	.	PUNCT
cana-6007	80	1	it	it	PRON
cana-6007	80	2	is	be	AUX
cana-6007	80	3	like	like	ADP
cana-6007	80	4	a	a	DET
cana-6007	80	5	traditional	traditional	ADJ
cana-6007	80	6	euler	euler	NOUN
cana-6007	80	7	method	method	NOUN
cana-6007	80	8	for	for	ADP
cana-6007	80	9	solving	solve	VERB
cana-6007	80	10	deterministic	deterministic	ADJ
cana-6007	80	11	ordinary	ordinary	ADJ
cana-6007	80	12	differential	differential	ADJ
cana-6007	80	13	equations	equation	NOUN
cana-6007	80	14	(	(	PUNCT
cana-6007	80	15	odes	ode	VERB
cana-6007	80	16	)	)	PUNCT
cana-6007	81	1	[	[	X
cana-6007	81	2	3	3	NUM
cana-6007	81	3	]	]	PUNCT
cana-6007	81	4	,	,	PUNCT
cana-6007	81	5	[	[	X
cana-6007	81	6	13	13	NUM
cana-6007	81	7	]	]	PUNCT
cana-6007	81	8	.	.	PUNCT
cana-6007	82	1	this	this	DET
cana-6007	82	2	method	method	NOUN
cana-6007	82	3	extends	extend	VERB
cana-6007	82	4	the	the	DET
cana-6007	82	5	concept	concept	NOUN
cana-6007	82	6	of	of	ADP
cana-6007	82	7	taylor	taylor	PROPN
cana-6007	82	8	expansion	expansion	NOUN
cana-6007	82	9	to	to	PART
cana-6007	82	10	incorporate	incorporate	VERB
cana-6007	82	11	stochastic	stochastic	ADJ
cana-6007	82	12	processes	process	NOUN
cana-6007	82	13	,	,	PUNCT
cana-6007	82	14	forming	form	VERB
cana-6007	82	15	the	the	DET
cana-6007	82	16	basis	basis	NOUN
cana-6007	82	17	for	for	ADP
cana-6007	82	18	simulating	simulate	VERB
cana-6007	82	19	itô	itô	ADJ
cana-6007	82	20	-	-	PUNCT
cana-6007	82	21	type	type	NOUN
cana-6007	82	22	sdes	sde	NOUN
cana-6007	82	23	in	in	ADP
cana-6007	82	24	real	real	ADJ
cana-6007	82	25	-	-	PUNCT
cana-6007	82	26	world	world	NOUN
cana-6007	82	27	situations	situation	NOUN
cana-6007	82	28	where	where	SCONJ
cana-6007	82	29	analytical	analytical	ADJ
cana-6007	82	30	solutions	solution	NOUN
cana-6007	82	31	are	be	AUX
cana-6007	82	32	hard	hard	ADJ
cana-6007	82	33	or	or	CCONJ
cana-6007	82	34	impossible	impossible	ADJ
cana-6007	82	35	to	to	PART
cana-6007	82	36	find	find	VERB
cana-6007	82	37	[	[	X
cana-6007	82	38	13	13	NUM
cana-6007	82	39	]	]	PUNCT
cana-6007	82	40	.	.	PUNCT
cana-6007	83	1	as	as	SCONJ
cana-6007	83	2	explained	explain	VERB
cana-6007	83	3	in	in	ADP
cana-6007	83	4	[	[	PUNCT
cana-6007	83	5	13	13	NUM
cana-6007	83	6	]	]	PUNCT
cana-6007	83	7	the	the	DET
cana-6007	83	8	scheme	scheme	NOUN
cana-6007	83	9	is	be	AUX
cana-6007	83	10	obtained	obtain	VERB
cana-6007	83	11	by	by	ADP
cana-6007	83	12	truncating	truncate	VERB
cana-6007	83	13	the	the	DET
cana-6007	83	14	itô	itô	PROPN
cana-6007	83	15	-	-	PUNCT
cana-6007	83	16	taylor	taylor	PROPN
cana-6007	83	17	expansion	expansion	NOUN
cana-6007	83	18	after	after	ADP
cana-6007	83	19	the	the	DET
cana-6007	83	20	firstorder	firstorder	NOUN
cana-6007	83	21	terms	term	NOUN
cana-6007	83	22	(	(	PUNCT
cana-6007	83	23	drift	drift	NOUN
cana-6007	83	24	and	and	CCONJ
cana-6007	83	25	diffusion	diffusion	NOUN
cana-6007	83	26	)	)	PUNCT
cana-6007	83	27	.	.	PUNCT
cana-6007	84	1	let	let	VERB
cana-6007	84	2	us	we	PRON
cana-6007	84	3	consider	consider	VERB
cana-6007	84	4	the	the	DET
cana-6007	84	5	itô	itô	PROPN
cana-6007	84	6	stochastic	stochastic	ADJ
cana-6007	84	7	differential	differential	ADJ
cana-6007	84	8	equation	equation	NOUN
cana-6007	84	9	of	of	ADP
cana-6007	84	10	the	the	DET
cana-6007	84	11	form	form	NOUN
cana-6007	84	12	:	:	PUNCT
cana-6007	84	13	dxt	dxt	PROPN
cana-6007	84	14	=	=	SYM
cana-6007	84	15	α(xt	α(xt	PROPN
cana-6007	84	16	,	,	PUNCT
cana-6007	84	17	t	t	PROPN
cana-6007	84	18	)	)	PUNCT
cana-6007	84	19	 	 	SPACE
cana-6007	84	20	dt	dt	PUNCT
cana-6007	85	1	+	+	CCONJ
cana-6007	85	2	β(xt	β(xt	PROPN
cana-6007	85	3	,	,	PUNCT
cana-6007	85	4	t)dwt	t)dwt	PRON
cana-6007	85	5	,	,	PUNCT
cana-6007	85	6	xt0	xt0	PROPN
cana-6007	85	7	=	=	SYM
cana-6007	85	8	x0	x0	PROPN
cana-6007	85	9	,	,	PUNCT
cana-6007	85	10	.	.	PUNCT
cana-6007	86	1	dt	dt	PUNCT
cana-6007	87	1	dwt	dwt	INTJ
cana-6007	87	2	dt	dt	NOUN
cana-6007	87	3	0	0	NUM
cana-6007	87	4	0	0	NUM
cana-6007	87	5	dwt	dwt	NOUN
cana-6007	87	6	0	0	NUM
cana-6007	87	7	dt	dt	NOUN
cana-6007	87	8	communications	communication	NOUN
cana-6007	87	9	on	on	ADP
cana-6007	87	10	applied	apply	VERB
cana-6007	87	11	nonlinear	nonlinear	ADJ
cana-6007	87	12	analysis	analysis	NOUN
cana-6007	87	13	issn	issn	NOUN
cana-6007	87	14	:	:	PUNCT
cana-6007	87	15	1074	1074	NUM
cana-6007	87	16	-	-	PUNCT
cana-6007	87	17	133x	133x	NUM
cana-6007	87	18	vol	vol	VERB
cana-6007	87	19	32	32	NUM
cana-6007	87	20	no	no	NOUN
cana-6007	87	21	.	.	PUNCT
cana-6007	88	1	10s	10	NOUN
cana-6007	88	2	(	(	PUNCT
cana-6007	88	3	2025	2025	NUM
cana-6007	88	4	)	)	PUNCT
cana-6007	88	5	3230	3230	NUM
cana-6007	88	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	88	7	where	where	SCONJ
cana-6007	88	8	α(xt	α(xt	NOUN
cana-6007	88	9	,	,	PUNCT
cana-6007	88	10	t	t	PROPN
cana-6007	88	11	)	)	PUNCT
cana-6007	88	12	is	be	AUX
cana-6007	88	13	the	the	DET
cana-6007	88	14	drift	drift	NOUN
cana-6007	88	15	coefficient	coefficient	NOUN
cana-6007	88	16	,	,	PUNCT
cana-6007	88	17	β(xt	β(xt	PROPN
cana-6007	88	18	,	,	PUNCT
cana-6007	88	19	t	t	PROPN
cana-6007	88	20	)	)	PUNCT
cana-6007	88	21	is	be	AUX
cana-6007	88	22	the	the	DET
cana-6007	88	23	diffusion	diffusion	NOUN
cana-6007	88	24	coefficient	coefficient	NOUN
cana-6007	88	25	,	,	PUNCT
cana-6007	88	26	and	and	CCONJ
cana-6007	88	27	wt	wt	PROPN
cana-6007	88	28	is	be	AUX
cana-6007	88	29	the	the	DET
cana-6007	88	30	wiener	wiener	NOUN
cana-6007	88	31	process	process	NOUN
cana-6007	88	32	or	or	CCONJ
cana-6007	88	33	brownian	brownian	ADJ
cana-6007	88	34	motion	motion	NOUN
cana-6007	88	35	.	.	PUNCT
cana-6007	89	1	to	to	PART
cana-6007	89	2	numerically	numerically	ADV
cana-6007	89	3	approximate	approximate	VERB
cana-6007	89	4	this	this	DET
cana-6007	89	5	sde	sde	NOUN
cana-6007	89	6	,	,	PUNCT
cana-6007	89	7	we	we	PRON
cana-6007	89	8	divide	divide	VERB
cana-6007	89	9	the	the	DET
cana-6007	89	10	time	time	NOUN
cana-6007	89	11	interval	interval	NOUN
cana-6007	89	12	[	[	X
cana-6007	89	13	t0	t0	PROPN
cana-6007	89	14	,	,	PUNCT
cana-6007	89	15	t	t	X
cana-6007	89	16	]	]	PUNCT
cana-6007	89	17	into	into	ADP
cana-6007	89	18	n	n	CCONJ
cana-6007	89	19	equal	equal	ADJ
cana-6007	89	20	steps	step	NOUN
cana-6007	89	21	of	of	ADP
cana-6007	89	22	size	size	NOUN
cana-6007	89	23	δt	δt	PROPN
cana-6007	89	24	.	.	PUNCT
cana-6007	90	1	we	we	PRON
cana-6007	90	2	define	define	VERB
cana-6007	90	3	the	the	DET
cana-6007	90	4	euler	euler	NOUN
cana-6007	90	5	–	–	PUNCT
cana-6007	90	6	maruyama	maruyama	NOUN
cana-6007	90	7	iteration	iteration	NOUN
cana-6007	90	8	scheme	scheme	NOUN
cana-6007	90	9	using	use	VERB
cana-6007	90	10	the	the	DET
cana-6007	90	11	formula	formula	NOUN
cana-6007	90	12	:	:	PUNCT
cana-6007	90	13	yn+1	yn+1	PROPN
cana-6007	90	14	=	=	SYM
cana-6007	90	15	yn	yn	PROPN
cana-6007	90	16	+	+	CCONJ
cana-6007	90	17	α(yn	α(yn	PROPN
cana-6007	90	18	,	,	PUNCT
cana-6007	90	19	tn)δt	tn)δt	PUNCT
cana-6007	90	20	+	+	CCONJ
cana-6007	90	21	β(yn	β(yn	NUM
cana-6007	90	22	,	,	PUNCT
cana-6007	90	23	tn)δwn	tn)δwn	NOUN
cana-6007	90	24	,	,	PUNCT
cana-6007	90	25	where	where	SCONJ
cana-6007	90	26	δwn	δwn	NOUN
cana-6007	90	27	=	=	SYM
cana-6007	90	28	wtn+1	wtn+1	NOUN
cana-6007	90	29	−	−	NOUN
cana-6007	90	30	wtn	wtn	NOUN
cana-6007	90	31	is	be	AUX
cana-6007	90	32	the	the	DET
cana-6007	90	33	brownian	brownian	ADJ
cana-6007	90	34	increment	increment	NOUN
cana-6007	90	35	over	over	ADP
cana-6007	90	36	the	the	DET
cana-6007	90	37	interval	interval	NOUN
cana-6007	90	38	,	,	PUNCT
cana-6007	90	39	and	and	CCONJ
cana-6007	90	40	e[δwn	e[δwn	VERB
cana-6007	90	41	]	]	X
cana-6007	91	1	=	=	SYM
cana-6007	91	2	0	0	NUM
cana-6007	91	3	and	and	CCONJ
cana-6007	91	4	var(δwn	var(δwn	PROPN
cana-6007	91	5	)	)	PUNCT
cana-6007	92	1	=	=	SYM
cana-6007	92	2	δt	δt	X
cana-6007	92	3	.	.	PUNCT
cana-6007	93	1	this	this	DET
cana-6007	93	2	scheme	scheme	NOUN
cana-6007	93	3	is	be	AUX
cana-6007	93	4	derived	derive	VERB
cana-6007	93	5	by	by	ADP
cana-6007	93	6	reducing	reduce	VERB
cana-6007	93	7	the	the	DET
cana-6007	93	8	stochastic	stochastic	ADJ
cana-6007	93	9	taylor	taylor	NOUN
cana-6007	93	10	expansion	expansion	NOUN
cana-6007	93	11	at	at	ADP
cana-6007	93	12	the	the	DET
cana-6007	93	13	lowest	low	ADJ
cana-6007	93	14	-	-	PUNCT
cana-6007	93	15	order	order	NOUN
cana-6007	93	16	terms	term	NOUN
cana-6007	93	17	[	[	X
cana-6007	93	18	2	2	NUM
cana-6007	93	19	]	]	PUNCT
cana-6007	93	20	.	.	PUNCT
cana-6007	94	1	the	the	DET
cana-6007	94	2	deterministic	deterministic	ADJ
cana-6007	94	3	part	part	NOUN
cana-6007	94	4	,	,	PUNCT
cana-6007	94	5	α(tn	α(tn	NUM
cana-6007	94	6	,	,	PUNCT
cana-6007	94	7	yn)δt	yn)δt	PRON
cana-6007	94	8	,	,	PUNCT
cana-6007	94	9	is	be	AUX
cana-6007	94	10	derived	derive	VERB
cana-6007	94	11	from	from	ADP
cana-6007	94	12	the	the	DET
cana-6007	94	13	standard	standard	PROPN
cana-6007	94	14	euler	euler	NOUN
cana-6007	94	15	method	method	NOUN
cana-6007	94	16	,	,	PUNCT
cana-6007	94	17	while	while	SCONJ
cana-6007	94	18	the	the	DET
cana-6007	94	19	stochastic	stochastic	ADJ
cana-6007	94	20	term	term	NOUN
cana-6007	94	21	β(tn	β(tn	NOUN
cana-6007	94	22	,	,	PUNCT
cana-6007	94	23	yn)δwn	yn)δwn	NOUN
cana-6007	94	24	accounts	account	VERB
cana-6007	94	25	for	for	ADP
cana-6007	94	26	the	the	DET
cana-6007	94	27	random	random	ADJ
cana-6007	94	28	fluctuations	fluctuation	NOUN
cana-6007	94	29	.	.	PUNCT
cana-6007	95	1	the	the	DET
cana-6007	95	2	euler	euler	NOUN
cana-6007	95	3	–	–	PUNCT
cana-6007	95	4	maruyama	maruyama	NOUN
cana-6007	95	5	method	method	NOUN
cana-6007	95	6	achieves	achieve	VERB
cana-6007	95	7	a	a	DET
cana-6007	95	8	strong	strong	ADJ
cana-6007	95	9	convergence	convergence	NOUN
cana-6007	95	10	of	of	ADP
cana-6007	95	11	order	order	NOUN
cana-6007	95	12	0.5	0.5	NUM
cana-6007	95	13	,	,	PUNCT
cana-6007	95	14	as	as	SCONJ
cana-6007	95	15	evidenced	evidence	VERB
cana-6007	95	16	by	by	ADP
cana-6007	95	17	the	the	DET
cana-6007	95	18	decreasing	decrease	VERB
cana-6007	95	19	expected	expect	VERB
cana-6007	95	20	error	error	NOUN
cana-6007	95	21	between	between	ADP
cana-6007	95	22	the	the	DET
cana-6007	95	23	exact	exact	ADJ
cana-6007	95	24	and	and	CCONJ
cana-6007	95	25	numerical	numerical	ADJ
cana-6007	95	26	solutions	solution	NOUN
cana-6007	95	27	with	with	ADP
cana-6007	95	28	√δt	√δt	PROPN
cana-6007	95	29	.	.	PROPN
cana-6007	95	30	on	on	ADP
cana-6007	95	31	the	the	DET
cana-6007	95	32	other	other	ADJ
cana-6007	95	33	hand	hand	NOUN
cana-6007	95	34	,	,	PUNCT
cana-6007	95	35	as	as	SCONJ
cana-6007	95	36	discussed	discuss	VERB
cana-6007	95	37	in	in	ADP
cana-6007	95	38	[	[	X
cana-6007	95	39	3	3	NUM
cana-6007	95	40	]	]	PUNCT
cana-6007	95	41	,	,	PUNCT
cana-6007	95	42	[	[	X
cana-6007	95	43	13	13	NUM
cana-6007	95	44	]	]	PUNCT
cana-6007	95	45	,	,	PUNCT
cana-6007	95	46	its	its	PRON
cana-6007	95	47	weak	weak	ADJ
cana-6007	95	48	convergence	convergence	NOUN
cana-6007	95	49	(	(	PUNCT
cana-6007	95	50	for	for	ADP
cana-6007	95	51	expectation	expectation	NOUN
cana-6007	95	52	errors	error	NOUN
cana-6007	95	53	)	)	PUNCT
cana-6007	95	54	is	be	AUX
cana-6007	95	55	of	of	ADP
cana-6007	95	56	order	order	NOUN
cana-6007	95	57	1	1	NUM
cana-6007	95	58	.	.	PUNCT
cana-6007	96	1	when	when	SCONJ
cana-6007	96	2	the	the	DET
cana-6007	96	3	diffusion	diffusion	NOUN
cana-6007	96	4	term	term	NOUN
cana-6007	96	5	β	β	PROPN
cana-6007	96	6	≡	≡	PROPN
cana-6007	96	7	0	0	NUM
cana-6007	96	8	,	,	PUNCT
cana-6007	96	9	the	the	DET
cana-6007	96	10	method	method	NOUN
cana-6007	96	11	reduces	reduce	VERB
cana-6007	96	12	to	to	ADP
cana-6007	96	13	the	the	DET
cana-6007	96	14	deterministic	deterministic	PROPN
cana-6007	96	15	euler	euler	NOUN
cana-6007	96	16	scheme	scheme	NOUN
cana-6007	96	17	with	with	ADP
cana-6007	96	18	a	a	DET
cana-6007	96	19	stronger	strong	ADJ
cana-6007	96	20	convergence	convergence	NOUN
cana-6007	96	21	rate	rate	NOUN
cana-6007	96	22	of	of	ADP
cana-6007	96	23	order	order	NOUN
cana-6007	96	24	1	1	NUM
cana-6007	96	25	[	[	X
cana-6007	96	26	1	1	NUM
cana-6007	96	27	]	]	PUNCT
cana-6007	96	28	,	,	PUNCT
cana-6007	96	29	[	[	X
cana-6007	96	30	3	3	NUM
cana-6007	96	31	]	]	PUNCT
cana-6007	96	32	,	,	PUNCT
cana-6007	96	33	[	[	X
cana-6007	96	34	13	13	NUM
cana-6007	96	35	]	]	PUNCT
cana-6007	96	36	.	.	PUNCT
cana-6007	97	1	despite	despite	SCONJ
cana-6007	97	2	its	its	PRON
cana-6007	97	3	limitations	limitation	NOUN
cana-6007	97	4	,	,	PUNCT
cana-6007	97	5	the	the	DET
cana-6007	97	6	euler	euler	NOUN
cana-6007	97	7	–	–	PUNCT
cana-6007	97	8	maruyama	maruyama	NOUN
cana-6007	97	9	method	method	NOUN
cana-6007	97	10	remains	remain	VERB
cana-6007	97	11	popular	popular	ADJ
cana-6007	97	12	for	for	ADP
cana-6007	97	13	modeling	model	VERB
cana-6007	97	14	systems	system	NOUN
cana-6007	97	15	with	with	ADP
cana-6007	97	16	randomness	randomness	NOUN
cana-6007	97	17	.	.	PUNCT
cana-6007	98	1	because	because	SCONJ
cana-6007	98	2	of	of	ADP
cana-6007	98	3	its	its	PRON
cana-6007	98	4	simplicity	simplicity	NOUN
cana-6007	98	5	and	and	CCONJ
cana-6007	98	6	ease	ease	NOUN
cana-6007	98	7	of	of	ADP
cana-6007	98	8	use	use	NOUN
cana-6007	98	9	,	,	PUNCT
cana-6007	98	10	it	it	PRON
cana-6007	98	11	is	be	AUX
cana-6007	98	12	widely	widely	ADV
cana-6007	98	13	used	use	VERB
cana-6007	98	14	in	in	ADP
cana-6007	98	15	finance	finance	NOUN
cana-6007	98	16	,	,	PUNCT
cana-6007	98	17	physics	physics	NOUN
cana-6007	98	18	,	,	PUNCT
cana-6007	98	19	biology	biology	NOUN
cana-6007	98	20	,	,	PUNCT
cana-6007	98	21	and	and	CCONJ
cana-6007	98	22	other	other	ADJ
cana-6007	98	23	applied	apply	VERB
cana-6007	98	24	areas	area	NOUN
cana-6007	98	25	[	[	X
cana-6007	98	26	1	1	NUM
cana-6007	98	27	]	]	PUNCT
cana-6007	98	28	,	,	PUNCT
cana-6007	98	29	[	[	X
cana-6007	98	30	8	8	NUM
cana-6007	98	31	]	]	PUNCT
cana-6007	98	32	,	,	PUNCT
cana-6007	98	33	[	[	X
cana-6007	98	34	13	13	NUM
cana-6007	98	35	]	]	PUNCT
cana-6007	98	36	.	.	PUNCT
cana-6007	99	1	2.3	2.3	NUM
cana-6007	99	2	milstein	milstein	ADP
cana-6007	99	3	method	method	NOUN
cana-6007	99	4	the	the	DET
cana-6007	99	5	milstein	milstein	ADJ
cana-6007	99	6	method	method	NOUN
cana-6007	99	7	is	be	AUX
cana-6007	99	8	an	an	DET
cana-6007	99	9	advanced	advanced	ADJ
cana-6007	99	10	numerical	numerical	ADJ
cana-6007	99	11	method	method	NOUN
cana-6007	99	12	developed	develop	VERB
cana-6007	99	13	to	to	PART
cana-6007	99	14	improve	improve	VERB
cana-6007	99	15	upon	upon	SCONJ
cana-6007	99	16	the	the	DET
cana-6007	99	17	euler	euler	NOUN
cana-6007	99	18	–	–	PUNCT
cana-6007	99	19	maruyama	maruyama	NOUN
cana-6007	99	20	method	method	NOUN
cana-6007	99	21	by	by	ADP
cana-6007	99	22	adding	add	VERB
cana-6007	99	23	an	an	DET
cana-6007	99	24	additional	additional	ADJ
cana-6007	99	25	correction	correction	NOUN
cana-6007	99	26	term	term	NOUN
cana-6007	99	27	from	from	ADP
cana-6007	99	28	the	the	DET
cana-6007	99	29	second	second	ADJ
cana-6007	99	30	-	-	PUNCT
cana-6007	99	31	order	order	NOUN
cana-6007	99	32	itôtaylor	itôtaylor	NOUN
cana-6007	99	33	expansion	expansion	NOUN
cana-6007	99	34	for	for	ADP
cana-6007	99	35	approximating	approximate	VERB
cana-6007	99	36	solutions	solution	NOUN
cana-6007	99	37	of	of	ADP
cana-6007	99	38	stochastic	stochastic	ADJ
cana-6007	99	39	differential	differential	ADJ
cana-6007	99	40	equations	equation	NOUN
cana-6007	99	41	(	(	PUNCT
cana-6007	99	42	sdes	sde	NOUN
cana-6007	99	43	)	)	PUNCT
cana-6007	99	44	,	,	PUNCT
cana-6007	99	45	hence	hence	ADV
cana-6007	99	46	achieving	achieve	VERB
cana-6007	99	47	a	a	DET
cana-6007	99	48	strong	strong	ADJ
cana-6007	99	49	convergence	convergence	NOUN
cana-6007	99	50	order	order	NOUN
cana-6007	99	51	of	of	ADP
cana-6007	99	52	1	1	NUM
cana-6007	99	53	[	[	X
cana-6007	99	54	3	3	NUM
cana-6007	99	55	]	]	PUNCT
cana-6007	99	56	,	,	PUNCT
cana-6007	99	57	[	[	X
cana-6007	99	58	6	6	NUM
cana-6007	99	59	]	]	PUNCT
cana-6007	99	60	,	,	PUNCT
cana-6007	99	61	[	[	X
cana-6007	99	62	13	13	NUM
cana-6007	99	63	]	]	PUNCT
cana-6007	99	64	.	.	PUNCT
cana-6007	100	1	the	the	DET
cana-6007	100	2	euler	euler	NOUN
cana-6007	100	3	–	–	PUNCT
cana-6007	100	4	maruyama	maruyama	NOUN
cana-6007	100	5	method	method	NOUN
cana-6007	100	6	approximates	approximate	VERB
cana-6007	100	7	the	the	DET
cana-6007	100	8	sde	sde	PROPN
cana-6007	100	9	dxt	dxt	PROPN
cana-6007	100	10	=	=	PUNCT
cana-6007	100	11	α(xt	α(xt	PROPN
cana-6007	100	12	,	,	PUNCT
cana-6007	100	13	t	t	PROPN
cana-6007	100	14	)	)	PUNCT
cana-6007	100	15	 	 	SPACE
cana-6007	100	16	dt	dt	PUNCT
cana-6007	101	1	+	+	CCONJ
cana-6007	101	2	β(xt	β(xt	PROPN
cana-6007	101	3	,	,	PUNCT
cana-6007	101	4	t	t	PROPN
cana-6007	101	5	)	)	PUNCT
cana-6007	101	6	 	 	SPACE
cana-6007	101	7	dwt	dwt	NOUN
cana-6007	101	8	by	by	ADP
cana-6007	101	9	discretizing	discretize	VERB
cana-6007	101	10	the	the	DET
cana-6007	101	11	drift	drift	NOUN
cana-6007	101	12	and	and	CCONJ
cana-6007	101	13	diffusion	diffusion	NOUN
cana-6007	101	14	terms	term	NOUN
cana-6007	101	15	,	,	PUNCT
cana-6007	101	16	while	while	SCONJ
cana-6007	101	17	the	the	DET
cana-6007	101	18	milstein	milstein	ADJ
cana-6007	101	19	method	method	NOUN
cana-6007	101	20	improves	improve	VERB
cana-6007	101	21	this	this	PRON
cana-6007	101	22	by	by	ADP
cana-6007	101	23	adding	add	VERB
cana-6007	101	24	the	the	DET
cana-6007	101	25	derivative	derivative	NOUN
cana-6007	101	26	of	of	ADP
cana-6007	101	27	the	the	DET
cana-6007	101	28	diffusion	diffusion	NOUN
cana-6007	101	29	term	term	NOUN
cana-6007	101	30	.	.	PUNCT
cana-6007	102	1	the	the	DET
cana-6007	102	2	milstein	milstein	ADJ
cana-6007	102	3	approximation	approximation	NOUN
cana-6007	102	4	for	for	ADP
cana-6007	102	5	this	this	DET
cana-6007	102	6	sde	sde	PROPN
cana-6007	102	7	,	,	PUNCT
cana-6007	102	8	over	over	ADP
cana-6007	102	9	a	a	DET
cana-6007	102	10	uniform	uniform	ADJ
cana-6007	102	11	discretization	discretization	NOUN
cana-6007	102	12	tn	tn	NOUN
cana-6007	102	13	=	=	SYM
cana-6007	102	14	nδt	nδt	PROPN
cana-6007	102	15	,	,	PUNCT
cana-6007	102	16	is	be	AUX
cana-6007	102	17	given	give	VERB
cana-6007	102	18	by	by	ADP
cana-6007	102	19	:	:	PUNCT
cana-6007	102	20	xn+1	xn+1	PROPN
cana-6007	102	21	=	=	SYM
cana-6007	102	22	xn	xn	PROPN
cana-6007	103	1	+	+	CCONJ
cana-6007	103	2	α(xn)δt	α(xn)δt	ADJ
cana-6007	103	3	+	+	PROPN
cana-6007	103	4	β(xn)δwn	β(xn)δwn	NOUN
cana-6007	103	5	+	+	CCONJ
cana-6007	103	6	(	(	PUNCT
cana-6007	103	7	1/2)β(xn)β'(xn)[(δwn)2	1/2)β(xn)β'(xn)[(δwn)2	NUM
cana-6007	103	8	−	−	NOUN
cana-6007	103	9	δt	δt	X
cana-6007	103	10	]	]	PUNCT
cana-6007	103	11	,	,	PUNCT
cana-6007	103	12	where	where	SCONJ
cana-6007	103	13	δwn	δwn	NOUN
cana-6007	103	14	=	=	SYM
cana-6007	103	15	wtn+1	wtn+1	PROPN
cana-6007	103	16	−	−	PROPN
cana-6007	103	17	wtn	wtn	NOUN
cana-6007	103	18	and	and	CCONJ
cana-6007	103	19	β′(xn	β′(xn	PROPN
cana-6007	103	20	)	)	PUNCT
cana-6007	103	21	is	be	AUX
cana-6007	103	22	the	the	DET
cana-6007	103	23	partial	partial	ADJ
cana-6007	103	24	derivative	derivative	NOUN
cana-6007	103	25	of	of	ADP
cana-6007	103	26	β	β	NOUN
cana-6007	103	27	with	with	ADP
cana-6007	103	28	respect	respect	NOUN
cana-6007	103	29	to	to	ADP
cana-6007	103	30	the	the	DET
cana-6007	103	31	spatial	spatial	ADJ
cana-6007	103	32	variable	variable	NOUN
cana-6007	103	33	x.	x.	NOUN
cana-6007	104	1	the	the	DET
cana-6007	104	2	additional	additional	ADJ
cana-6007	104	3	term	term	NOUN
cana-6007	104	4	,	,	PUNCT
cana-6007	104	5	(	(	PUNCT
cana-6007	104	6	1/2)β(xn)β'(xn)[(δwn)2	1/2)β(xn)β'(xn)[(δwn)2	NUM
cana-6007	104	7	−	−	NOUN
cana-6007	104	8	δt	δt	NOUN
cana-6007	104	9	]	]	PUNCT
cana-6007	104	10	,	,	PUNCT
cana-6007	104	11	captures	capture	VERB
cana-6007	104	12	the	the	DET
cana-6007	104	13	random	random	ADJ
cana-6007	104	14	variations	variation	NOUN
cana-6007	104	15	of	of	ADP
cana-6007	104	16	brownian	brownian	ADJ
cana-6007	104	17	motion	motion	NOUN
cana-6007	104	18	more	more	ADV
cana-6007	104	19	accurately	accurately	ADV
cana-6007	104	20	by	by	ADP
cana-6007	104	21	including	include	VERB
cana-6007	104	22	the	the	DET
cana-6007	104	23	itô	itô	PROPN
cana-6007	104	24	–	–	PUNCT
cana-6007	104	25	stratonovich	stratonovich	NOUN
cana-6007	104	26	adjustment	adjustment	NOUN
cana-6007	104	27	that	that	SCONJ
cana-6007	104	28	the	the	DET
cana-6007	104	29	euler	euler	NOUN
cana-6007	104	30	–	–	PUNCT
cana-6007	104	31	maruyama	maruyama	NOUN
cana-6007	104	32	method	method	NOUN
cana-6007	104	33	ignores	ignore	VERB
cana-6007	104	34	.	.	PUNCT
cana-6007	105	1	when	when	SCONJ
cana-6007	105	2	dealing	deal	VERB
cana-6007	105	3	with	with	ADP
cana-6007	105	4	nonlinear	nonlinear	ADJ
cana-6007	105	5	stochastic	stochastic	ADJ
cana-6007	105	6	systems	system	NOUN
cana-6007	105	7	(	(	PUNCT
cana-6007	105	8	where	where	SCONJ
cana-6007	105	9	β	β	PROPN
cana-6007	105	10	depends	depend	VERB
cana-6007	105	11	on	on	ADP
cana-6007	105	12	xt	xt	PROPN
cana-6007	105	13	)	)	PUNCT
cana-6007	105	14	,	,	PUNCT
cana-6007	105	15	the	the	DET
cana-6007	105	16	milstein	milstein	ADJ
cana-6007	105	17	method	method	NOUN
cana-6007	105	18	performs	perform	VERB
cana-6007	105	19	significantly	significantly	ADV
cana-6007	105	20	better	well	ADV
cana-6007	105	21	than	than	ADP
cana-6007	105	22	euler	euler	NOUN
cana-6007	105	23	–	–	PUNCT
cana-6007	105	24	maruyama	maruyama	NOUN
cana-6007	105	25	[	[	X
cana-6007	105	26	6	6	NUM
cana-6007	105	27	]	]	PUNCT
cana-6007	105	28	,	,	PUNCT
cana-6007	105	29	[	[	X
cana-6007	105	30	13	13	NUM
cana-6007	105	31	]	]	PUNCT
cana-6007	105	32	,	,	PUNCT
cana-6007	105	33	[	[	X
cana-6007	105	34	16	16	NUM
cana-6007	105	35	]	]	PUNCT
cana-6007	105	36	.	.	PUNCT
cana-6007	106	1	when	when	SCONJ
cana-6007	106	2	the	the	DET
cana-6007	106	3	noise	noise	NOUN
cana-6007	106	4	is	be	AUX
cana-6007	106	5	additive	additive	ADJ
cana-6007	106	6	(	(	PUNCT
cana-6007	106	7	β	β	NOUN
cana-6007	106	8	'	'	PUNCT
cana-6007	106	9	=	=	NOUN
cana-6007	106	10	0	0	NUM
cana-6007	106	11	)	)	PUNCT
cana-6007	106	12	,	,	PUNCT
cana-6007	106	13	both	both	CCONJ
cana-6007	106	14	the	the	DET
cana-6007	106	15	methods	method	NOUN
cana-6007	106	16	give	give	VERB
cana-6007	106	17	the	the	DET
cana-6007	106	18	same	same	ADJ
cana-6007	106	19	result	result	NOUN
cana-6007	106	20	.	.	PUNCT
cana-6007	107	1	due	due	ADP
cana-6007	107	2	to	to	ADP
cana-6007	107	3	its	its	PRON
cana-6007	107	4	ability	ability	NOUN
cana-6007	107	5	to	to	PART
cana-6007	107	6	capture	capture	VERB
cana-6007	107	7	higher	high	ADJ
cana-6007	107	8	-	-	PUNCT
cana-6007	107	9	order	order	NOUN
cana-6007	107	10	stochastic	stochastic	ADJ
cana-6007	107	11	dynamics	dynamic	NOUN
cana-6007	107	12	,	,	PUNCT
cana-6007	107	13	it	it	PRON
cana-6007	107	14	is	be	AUX
cana-6007	107	15	considered	consider	VERB
cana-6007	107	16	a	a	DET
cana-6007	107	17	better	well	ADJ
cana-6007	107	18	option	option	NOUN
cana-6007	107	19	in	in	ADP
cana-6007	107	20	applications	application	NOUN
cana-6007	107	21	where	where	SCONJ
cana-6007	107	22	fine	fine	ADV
cana-6007	107	23	-	-	PUNCT
cana-6007	107	24	grained	grain	VERB
cana-6007	107	25	statistical	statistical	ADJ
cana-6007	107	26	simulation	simulation	NOUN
cana-6007	107	27	,	,	PUNCT
cana-6007	107	28	strong	strong	ADJ
cana-6007	107	29	convergence	convergence	NOUN
cana-6007	107	30	,	,	PUNCT
cana-6007	107	31	and	and	CCONJ
cana-6007	107	32	path	path	NOUN
cana-6007	107	33	accuracy	accuracy	NOUN
cana-6007	107	34	communications	communication	NOUN
cana-6007	107	35	on	on	ADP
cana-6007	107	36	applied	apply	VERB
cana-6007	107	37	nonlinear	nonlinear	ADJ
cana-6007	107	38	analysis	analysis	NOUN
cana-6007	107	39	issn	issn	NOUN
cana-6007	107	40	:	:	PUNCT
cana-6007	107	41	1074	1074	NUM
cana-6007	107	42	-	-	PUNCT
cana-6007	107	43	133x	133x	NUM
cana-6007	107	44	vol	vol	VERB
cana-6007	107	45	32	32	NUM
cana-6007	107	46	no	no	NOUN
cana-6007	107	47	.	.	PUNCT
cana-6007	108	1	10s	10	NOUN
cana-6007	108	2	(	(	PUNCT
cana-6007	108	3	2025	2025	NUM
cana-6007	108	4	)	)	PUNCT
cana-6007	108	5	3231	3231	NUM
cana-6007	108	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	108	7	are	be	AUX
cana-6007	108	8	essential	essential	ADJ
cana-6007	108	9	.	.	PUNCT
cana-6007	109	1	this	this	PRON
cana-6007	109	2	makes	make	VERB
cana-6007	109	3	it	it	PRON
cana-6007	109	4	valuable	valuable	ADJ
cana-6007	109	5	in	in	ADP
cana-6007	109	6	fields	field	NOUN
cana-6007	109	7	like	like	ADP
cana-6007	109	8	quantitative	quantitative	ADJ
cana-6007	109	9	finance	finance	NOUN
cana-6007	109	10	,	,	PUNCT
cana-6007	109	11	stochastic	stochastic	ADJ
cana-6007	109	12	physics	physics	NOUN
cana-6007	109	13	,	,	PUNCT
cana-6007	109	14	and	and	CCONJ
cana-6007	109	15	computational	computational	ADJ
cana-6007	109	16	biology	biology	NOUN
cana-6007	109	17	,	,	PUNCT
cana-6007	109	18	where	where	SCONJ
cana-6007	109	19	capturing	capture	VERB
cana-6007	109	20	complex	complex	ADJ
cana-6007	109	21	stochastic	stochastic	ADJ
cana-6007	109	22	behavior	behavior	NOUN
cana-6007	109	23	is	be	AUX
cana-6007	109	24	essential	essential	ADJ
cana-6007	109	25	[	[	X
cana-6007	109	26	6	6	NUM
cana-6007	109	27	]	]	PUNCT
cana-6007	109	28	,	,	PUNCT
cana-6007	110	1	[	[	X
cana-6007	110	2	13	13	NUM
cana-6007	110	3	]	]	PUNCT
cana-6007	110	4	.	.	PUNCT
cana-6007	111	1	3	3	X
cana-6007	111	2	.	.	X
cana-6007	111	3	numerical	numerical	ADJ
cana-6007	111	4	implementation	implementation	NOUN
cana-6007	111	5	and	and	CCONJ
cana-6007	111	6	comparative	comparative	ADJ
cana-6007	111	7	analysis	analysis	NOUN
cana-6007	111	8	for	for	ADP
cana-6007	111	9	the	the	DET
cana-6007	111	10	numerical	numerical	ADJ
cana-6007	111	11	implementation	implementation	NOUN
cana-6007	111	12	and	and	CCONJ
cana-6007	111	13	comparative	comparative	ADJ
cana-6007	111	14	analysis	analysis	NOUN
cana-6007	111	15	,	,	PUNCT
cana-6007	111	16	we	we	PRON
cana-6007	111	17	consider	consider	VERB
cana-6007	111	18	two	two	NUM
cana-6007	111	19	distinct	distinct	ADJ
cana-6007	111	20	nonlinear	nonlinear	ADJ
cana-6007	111	21	stochastic	stochastic	ADJ
cana-6007	111	22	differential	differential	ADJ
cana-6007	111	23	equations	equation	NOUN
cana-6007	111	24	(	(	PUNCT
cana-6007	111	25	sdes	sde	NOUN
cana-6007	111	26	)	)	PUNCT
cana-6007	111	27	with	with	ADP
cana-6007	111	28	known	know	VERB
cana-6007	111	29	exact	exact	ADJ
cana-6007	111	30	solutions	solution	NOUN
cana-6007	111	31	.	.	PUNCT
cana-6007	112	1	this	this	PRON
cana-6007	112	2	is	be	AUX
cana-6007	112	3	done	do	VERB
cana-6007	112	4	to	to	PART
cana-6007	112	5	evaluate	evaluate	VERB
cana-6007	112	6	the	the	DET
cana-6007	112	7	accuracy	accuracy	NOUN
cana-6007	112	8	and	and	CCONJ
cana-6007	112	9	convergence	convergence	NOUN
cana-6007	112	10	behavior	behavior	NOUN
cana-6007	112	11	of	of	ADP
cana-6007	112	12	the	the	DET
cana-6007	112	13	euler	euler	NOUN
cana-6007	112	14	–	–	PUNCT
cana-6007	112	15	maruyama	maruyama	NOUN
cana-6007	112	16	and	and	CCONJ
cana-6007	112	17	milstein	milstein	ADJ
cana-6007	112	18	methods	method	NOUN
cana-6007	112	19	when	when	SCONJ
cana-6007	112	20	applied	apply	VERB
cana-6007	112	21	to	to	ADP
cana-6007	112	22	systems	system	NOUN
cana-6007	112	23	with	with	ADP
cana-6007	112	24	nonlinear	nonlinear	ADJ
cana-6007	112	25	drift	drift	NOUN
cana-6007	112	26	and	and	CCONJ
cana-6007	112	27	diffusion	diffusion	NOUN
cana-6007	112	28	structures	structure	NOUN
cana-6007	112	29	[	[	X
cana-6007	112	30	4	4	NUM
cana-6007	112	31	]	]	PUNCT
cana-6007	112	32	,	,	PUNCT
cana-6007	112	33	[	[	X
cana-6007	112	34	15	15	NUM
cana-6007	112	35	]	]	PUNCT
cana-6007	112	36	.	.	PUNCT
cana-6007	113	1	the	the	DET
cana-6007	113	2	selected	select	VERB
cana-6007	113	3	sdes	sde	NOUN
cana-6007	113	4	are	be	AUX
cana-6007	113	5	:	:	PUNCT
cana-6007	113	6	example	example	NOUN
cana-6007	113	7	1	1	NUM
cana-6007	113	8	:	:	PUNCT
cana-6007	113	9	dx(t	dx(t	X
cana-6007	113	10	)	)	PUNCT
cana-6007	113	11	=	=	SYM
cana-6007	113	12	axt	axt	PROPN
cana-6007	113	13	(	(	PUNCT
cana-6007	113	14	1	1	NUM
cana-6007	113	15	xt	xt	ADP
cana-6007	113	16	2)dt	2)dt	PROPN
cana-6007	113	17	+	+	CCONJ
cana-6007	113	18	b(1	b(1	PROPN
cana-6007	113	19	xt	xt	ADP
cana-6007	113	20	2)dwt	2)dwt	NUM
cana-6007	113	21	where	where	SCONJ
cana-6007	113	22	,	,	PUNCT
cana-6007	113	23	a	a	DET
cana-6007	113	24	=	=	SYM
cana-6007	113	25	1	1	NUM
cana-6007	113	26	,	,	PUNCT
cana-6007	113	27	b	b	NOUN
cana-6007	113	28	=	=	SYM
cana-6007	113	29	1.5	1.5	NUM
cana-6007	113	30	,	,	PUNCT
cana-6007	113	31	t	t	NOUN
cana-6007	113	32	=	=	SYM
cana-6007	113	33	1	1	NUM
cana-6007	113	34	,	,	PUNCT
cana-6007	113	35	x0	x0	PROPN
cana-6007	113	36	=	=	PUNCT
cana-6007	113	37	0.5	0.5	NUM
cana-6007	113	38	,	,	PUNCT
cana-6007	113	39	t	t	NOUN
cana-6007	113	40	ϵ	ϵ	X
cana-6007	114	1	[	[	X
cana-6007	114	2	0	0	NUM
cana-6007	114	3	,	,	PUNCT
cana-6007	114	4	t	t	PROPN
cana-6007	114	5	]	]	X
cana-6007	114	6	the	the	DET
cana-6007	114	7	exact	exact	ADJ
cana-6007	114	8	solution	solution	NOUN
cana-6007	114	9	given	give	VERB
cana-6007	114	10	by	by	ADP
cana-6007	114	11	:	:	PUNCT
cana-6007	114	12	x(t	x(t	PROPN
cana-6007	114	13	)	)	PUNCT
cana-6007	114	14	=	=	SYM
cana-6007	114	15	tanh(tanh⁻¹(x0	tanh(tanh⁻¹(x0	NOUN
cana-6007	114	16	)	)	PUNCT
cana-6007	115	1	+	+	CCONJ
cana-6007	115	2	(	(	PUNCT
cana-6007	115	3	a	a	DET
cana-6007	115	4	+	+	CCONJ
cana-6007	115	5	b²)t	b²)t	NOUN
cana-6007	115	6	+	+	CCONJ
cana-6007	115	7	bwt	bwt	PROPN
cana-6007	115	8	)	)	PUNCT
cana-6007	115	9	example	example	NOUN
cana-6007	115	10	2	2	NUM
cana-6007	115	11	:	:	PUNCT
cana-6007	115	12	dx(t	dx(t	X
cana-6007	115	13	)	)	PUNCT
cana-6007	115	14	=	=	SYM
cana-6007	116	1	[	[	X
cana-6007	116	2	(	(	PUNCT
cana-6007	116	3	2/5)xt^(3/5	2/5)xt^(3/5	NUM
cana-6007	116	4	)	)	PUNCT
cana-6007	116	5	+	+	CCONJ
cana-6007	117	1	5xt^(4/5)]dt	5xt^(4/5)]dt	NUM
cana-6007	117	2	+	+	CCONJ
cana-6007	117	3	xt^(4/5)dwt	xt^(4/5)dwt	NUM
cana-6007	117	4	where	where	SCONJ
cana-6007	117	5	,	,	PUNCT
cana-6007	117	6	t	t	PROPN
cana-6007	117	7	=	=	SYM
cana-6007	117	8	1	1	NUM
cana-6007	117	9	,	,	PUNCT
cana-6007	117	10	x0	x0	PROPN
cana-6007	117	11	=	=	SYM
cana-6007	117	12	1	1	NUM
cana-6007	117	13	,	,	PUNCT
cana-6007	117	14	t	t	NOUN
cana-6007	117	15	ϵ	ϵ	X
cana-6007	118	1	[	[	X
cana-6007	118	2	0	0	NUM
cana-6007	118	3	,	,	PUNCT
cana-6007	118	4	t	t	PROPN
cana-6007	118	5	]	]	X
cana-6007	118	6	the	the	DET
cana-6007	118	7	exact	exact	ADJ
cana-6007	118	8	solution	solution	NOUN
cana-6007	118	9	given	give	VERB
cana-6007	118	10	by	by	ADP
cana-6007	118	11	:	:	PUNCT
cana-6007	118	12	x(t	x(t	PROPN
cana-6007	118	13	)	)	PUNCT
cana-6007	118	14	=	=	PUNCT
cana-6007	119	1	(	(	PUNCT
cana-6007	119	2	1	1	NUM
cana-6007	119	3	+	+	NUM
cana-6007	119	4	t	t	NOUN
cana-6007	119	5	+	+	CCONJ
cana-6007	119	6	(	(	PUNCT
cana-6007	119	7	1/5)wt	1/5)wt	NUM
cana-6007	119	8	)	)	PUNCT
cana-6007	120	1	[	[	X
cana-6007	120	2	8	8	NUM
cana-6007	120	3	]	]	PUNCT
cana-6007	120	4	euler	euler	NOUN
cana-6007	120	5	–	–	PUNCT
cana-6007	120	6	maruyama	maruyama	NOUN
cana-6007	120	7	and	and	CCONJ
cana-6007	120	8	milstein	milstein	ADJ
cana-6007	120	9	schemes	scheme	NOUN
cana-6007	120	10	are	be	AUX
cana-6007	120	11	used	use	VERB
cana-6007	120	12	to	to	PART
cana-6007	120	13	numerically	numerically	ADV
cana-6007	120	14	integrate	integrate	VERB
cana-6007	120	15	both	both	DET
cana-6007	120	16	sdes	sde	NOUN
cana-6007	120	17	over	over	ADP
cana-6007	120	18	a	a	DET
cana-6007	120	19	uniform	uniform	ADJ
cana-6007	120	20	time	time	NOUN
cana-6007	120	21	grid	grid	NOUN
cana-6007	120	22	.	.	PUNCT
cana-6007	121	1	the	the	DET
cana-6007	121	2	computed	compute	VERB
cana-6007	121	3	results	result	NOUN
cana-6007	121	4	are	be	AUX
cana-6007	121	5	compared	compare	VERB
cana-6007	121	6	with	with	ADP
cana-6007	121	7	the	the	DET
cana-6007	121	8	exact	exact	ADJ
cana-6007	121	9	solution	solution	NOUN
cana-6007	121	10	at	at	ADP
cana-6007	121	11	various	various	ADJ
cana-6007	121	12	time	time	NOUN
cana-6007	121	13	points	point	NOUN
cana-6007	121	14	,	,	PUNCT
cana-6007	121	15	and	and	CCONJ
cana-6007	121	16	the	the	DET
cana-6007	121	17	results	result	NOUN
cana-6007	121	18	are	be	AUX
cana-6007	121	19	compiled	compile	VERB
cana-6007	121	20	in	in	ADP
cana-6007	121	21	tabular	tabular	NOUN
cana-6007	121	22	form	form	NOUN
cana-6007	121	23	to	to	PART
cana-6007	121	24	quantitatively	quantitatively	ADV
cana-6007	121	25	evaluate	evaluate	VERB
cana-6007	121	26	the	the	DET
cana-6007	121	27	performance	performance	NOUN
cana-6007	121	28	of	of	ADP
cana-6007	121	29	both	both	DET
cana-6007	121	30	methods	method	NOUN
cana-6007	121	31	.	.	PUNCT
cana-6007	122	1	this	this	DET
cana-6007	122	2	comparison	comparison	NOUN
cana-6007	122	3	enables	enable	VERB
cana-6007	122	4	a	a	DET
cana-6007	122	5	deeper	deep	ADJ
cana-6007	122	6	understanding	understanding	NOUN
cana-6007	122	7	of	of	ADP
cana-6007	122	8	the	the	DET
cana-6007	122	9	methods	method	NOUN
cana-6007	122	10	’	'	PUNCT
cana-6007	122	11	accuracy	accuracy	NOUN
cana-6007	122	12	in	in	ADP
cana-6007	122	13	handling	handle	VERB
cana-6007	122	14	nonlinear	nonlinear	ADJ
cana-6007	122	15	dynamics	dynamic	NOUN
cana-6007	122	16	and	and	CCONJ
cana-6007	122	17	their	their	PRON
cana-6007	122	18	responsiveness	responsiveness	NOUN
cana-6007	122	19	to	to	ADP
cana-6007	122	20	the	the	DET
cana-6007	122	21	structure	structure	NOUN
cana-6007	122	22	of	of	ADP
cana-6007	122	23	the	the	DET
cana-6007	122	24	diffusion	diffusion	NOUN
cana-6007	122	25	term	term	NOUN
cana-6007	122	26	.	.	PUNCT
cana-6007	123	1	along	along	ADP
cana-6007	123	2	with	with	ADP
cana-6007	123	3	the	the	DET
cana-6007	123	4	tabulated	tabulate	VERB
cana-6007	123	5	data	datum	NOUN
cana-6007	123	6	,	,	PUNCT
cana-6007	123	7	graphical	graphical	ADJ
cana-6007	123	8	comparisons	comparison	NOUN
cana-6007	123	9	are	be	AUX
cana-6007	123	10	presented	present	VERB
cana-6007	123	11	to	to	PART
cana-6007	123	12	show	show	VERB
cana-6007	123	13	the	the	DET
cana-6007	123	14	exact	exact	ADJ
cana-6007	123	15	solution	solution	NOUN
cana-6007	123	16	and	and	CCONJ
cana-6007	123	17	the	the	DET
cana-6007	123	18	trajectories	trajectory	NOUN
cana-6007	123	19	generated	generate	VERB
cana-6007	123	20	by	by	ADP
cana-6007	123	21	each	each	DET
cana-6007	123	22	numerical	numerical	ADJ
cana-6007	123	23	method	method	NOUN
cana-6007	123	24	.	.	PUNCT
cana-6007	124	1	these	these	DET
cana-6007	124	2	plots	plot	NOUN
cana-6007	124	3	show	show	VERB
cana-6007	124	4	how	how	SCONJ
cana-6007	124	5	accurately	accurately	ADV
cana-6007	124	6	the	the	DET
cana-6007	124	7	milstein	milstein	NOUN
cana-6007	124	8	and	and	CCONJ
cana-6007	124	9	euler	euler	PROPN
cana-6007	124	10	–	–	PUNCT
cana-6007	124	11	maruyama	maruyama	NOUN
cana-6007	124	12	approximations	approximation	NOUN
cana-6007	124	13	follow	follow	VERB
cana-6007	124	14	the	the	DET
cana-6007	124	15	exact	exact	ADJ
cana-6007	124	16	solution	solution	NOUN
cana-6007	124	17	over	over	ADP
cana-6007	124	18	time	time	NOUN
cana-6007	124	19	.	.	PUNCT
cana-6007	125	1	by	by	ADP
cana-6007	125	2	including	include	VERB
cana-6007	125	3	both	both	CCONJ
cana-6007	125	4	individual	individual	ADJ
cana-6007	125	5	and	and	CCONJ
cana-6007	125	6	combined	combined	ADJ
cana-6007	125	7	trajectories	trajectory	NOUN
cana-6007	125	8	,	,	PUNCT
cana-6007	125	9	the	the	DET
cana-6007	125	10	figures	figure	NOUN
cana-6007	125	11	effectively	effectively	ADV
cana-6007	125	12	illustrate	illustrate	VERB
cana-6007	125	13	variations	variation	NOUN
cana-6007	125	14	in	in	ADP
cana-6007	125	15	pathwise	pathwise	NOUN
cana-6007	125	16	behavior	behavior	NOUN
cana-6007	125	17	and	and	CCONJ
cana-6007	125	18	provide	provide	VERB
cana-6007	125	19	insightful	insightful	ADJ
cana-6007	125	20	information	information	NOUN
cana-6007	125	21	about	about	ADP
cana-6007	125	22	the	the	DET
cana-6007	125	23	relative	relative	ADJ
cana-6007	125	24	accuracy	accuracy	NOUN
cana-6007	125	25	of	of	ADP
cana-6007	125	26	each	each	DET
cana-6007	125	27	scheme	scheme	NOUN
cana-6007	125	28	.	.	PUNCT
cana-6007	126	1	previous	previous	ADJ
cana-6007	126	2	research	research	NOUN
cana-6007	126	3	on	on	ADP
cana-6007	126	4	ordinary	ordinary	ADJ
cana-6007	126	5	differential	differential	ADJ
cana-6007	126	6	equations	equation	NOUN
cana-6007	126	7	has	have	AUX
cana-6007	126	8	shown	show	VERB
cana-6007	126	9	that	that	SCONJ
cana-6007	126	10	increasing	increase	VERB
cana-6007	126	11	the	the	DET
cana-6007	126	12	algorithmic	algorithmic	ADJ
cana-6007	126	13	order	order	NOUN
cana-6007	126	14	of	of	ADP
cana-6007	126	15	fifth	fifth	ADJ
cana-6007	126	16	-	-	PUNCT
cana-6007	126	17	order	order	NOUN
cana-6007	126	18	runge	runge	NOUN
cana-6007	126	19	-	-	PUNCT
cana-6007	126	20	kutta	kutta	NOUN
cana-6007	126	21	methods	method	NOUN
cana-6007	126	22	can	can	AUX
cana-6007	126	23	enhance	enhance	VERB
cana-6007	126	24	the	the	DET
cana-6007	126	25	accuracy	accuracy	NOUN
cana-6007	126	26	of	of	ADP
cana-6007	126	27	numerical	numerical	ADJ
cana-6007	126	28	results	result	NOUN
cana-6007	126	29	[	[	X
cana-6007	126	30	12	12	NUM
cana-6007	126	31	]	]	PUNCT
cana-6007	126	32	.	.	PUNCT
cana-6007	127	1	these	these	DET
cana-6007	127	2	classical	classical	ADJ
cana-6007	127	3	results	result	NOUN
cana-6007	127	4	provide	provide	VERB
cana-6007	127	5	conceptual	conceptual	ADJ
cana-6007	127	6	understanding	understanding	NOUN
cana-6007	127	7	of	of	ADP
cana-6007	127	8	numerical	numerical	ADJ
cana-6007	127	9	analysis	analysis	NOUN
cana-6007	127	10	.	.	PUNCT
cana-6007	128	1	due	due	ADP
cana-6007	128	2	to	to	ADP
cana-6007	128	3	the	the	DET
cana-6007	128	4	non	non	ADJ
cana-6007	128	5	-	-	ADJ
cana-6007	128	6	differentiable	differentiable	ADJ
cana-6007	128	7	nature	nature	NOUN
cana-6007	128	8	of	of	ADP
cana-6007	128	9	brownian	brownian	ADJ
cana-6007	128	10	motion	motion	NOUN
cana-6007	128	11	,	,	PUNCT
cana-6007	128	12	the	the	DET
cana-6007	128	13	stochastic	stochastic	ADJ
cana-6007	128	14	differential	differential	ADJ
cana-6007	128	15	equations	equation	NOUN
cana-6007	128	16	(	(	PUNCT
cana-6007	128	17	sdes	sde	NOUN
cana-6007	128	18	)	)	PUNCT
cana-6007	128	19	present	present	ADJ
cana-6007	128	20	fundamentally	fundamentally	ADV
cana-6007	128	21	different	different	ADJ
cana-6007	128	22	challenges	challenge	NOUN
cana-6007	128	23	.	.	PUNCT
cana-6007	129	1	as	as	ADP
cana-6007	129	2	a	a	DET
cana-6007	129	3	result	result	NOUN
cana-6007	129	4	,	,	PUNCT
cana-6007	129	5	even	even	ADV
cana-6007	129	6	the	the	DET
cana-6007	129	7	most	most	ADV
cana-6007	129	8	advanced	advanced	ADJ
cana-6007	129	9	methods	method	NOUN
cana-6007	129	10	,	,	PUNCT
cana-6007	129	11	like	like	ADP
cana-6007	129	12	euler	euler	NOUN
cana-6007	129	13	maruyama	maruyama	PROPN
cana-6007	129	14	and	and	CCONJ
cana-6007	129	15	milstein	milstein	ADV
cana-6007	129	16	achieve	achieve	VERB
cana-6007	129	17	significantly	significantly	ADV
cana-6007	129	18	lower	low	ADJ
cana-6007	129	19	convergence	convergence	NOUN
cana-6007	129	20	orders	order	NOUN
cana-6007	129	21	communications	communication	NOUN
cana-6007	129	22	on	on	ADP
cana-6007	129	23	applied	apply	VERB
cana-6007	129	24	nonlinear	nonlinear	ADJ
cana-6007	129	25	analysis	analysis	NOUN
cana-6007	129	26	issn	issn	NOUN
cana-6007	129	27	:	:	PUNCT
cana-6007	129	28	1074	1074	NUM
cana-6007	129	29	-	-	PUNCT
cana-6007	129	30	133x	133x	NUM
cana-6007	129	31	vol	vol	VERB
cana-6007	129	32	32	32	NUM
cana-6007	129	33	no	no	NOUN
cana-6007	129	34	.	.	PUNCT
cana-6007	130	1	10s	10	NOUN
cana-6007	130	2	(	(	PUNCT
cana-6007	130	3	2025	2025	NUM
cana-6007	130	4	)	)	PUNCT
cana-6007	130	5	3232	3232	NUM
cana-6007	130	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	130	7	than	than	ADP
cana-6007	130	8	their	their	PRON
cana-6007	130	9	ode	ode	PROPN
cana-6007	130	10	counterparts	counterpart	NOUN
cana-6007	130	11	[	[	X
cana-6007	130	12	3	3	NUM
cana-6007	130	13	]	]	PUNCT
cana-6007	130	14	,	,	PUNCT
cana-6007	130	15	[	[	X
cana-6007	130	16	13	13	NUM
cana-6007	130	17	]	]	PUNCT
cana-6007	130	18	.	.	PUNCT
cana-6007	131	1	the	the	DET
cana-6007	131	2	result	result	NOUN
cana-6007	131	3	of	of	ADP
cana-6007	131	4	odes	ode	NOUN
cana-6007	131	5	[	[	X
cana-6007	131	6	12	12	NUM
cana-6007	131	7	]	]	PUNCT
cana-6007	131	8	remain	remain	VERB
cana-6007	131	9	valuable	valuable	ADJ
cana-6007	131	10	for	for	ADP
cana-6007	131	11	understanding	understanding	NOUN
cana-6007	131	12	and	and	CCONJ
cana-6007	131	13	comparing	compare	VERB
cana-6007	131	14	how	how	SCONJ
cana-6007	131	15	different	different	ADJ
cana-6007	131	16	numerical	numerical	ADJ
cana-6007	131	17	methods	method	NOUN
cana-6007	131	18	perform	perform	VERB
cana-6007	131	19	in	in	ADP
cana-6007	131	20	stochastic	stochastic	ADJ
cana-6007	131	21	situations	situation	NOUN
cana-6007	131	22	.	.	PUNCT
cana-6007	132	1	the	the	DET
cana-6007	132	2	table	table	NOUN
cana-6007	132	3	below	below	ADV
cana-6007	132	4	shows	show	VERB
cana-6007	132	5	the	the	DET
cana-6007	132	6	computed	compute	VERB
cana-6007	132	7	solutions	solution	NOUN
cana-6007	132	8	for	for	ADP
cana-6007	132	9	example	example	NOUN
cana-6007	132	10	1	1	NUM
cana-6007	132	11	and	and	CCONJ
cana-6007	132	12	example	example	NOUN
cana-6007	132	13	2	2	NUM
cana-6007	132	14	,	,	PUNCT
cana-6007	132	15	obtained	obtain	VERB
cana-6007	132	16	using	use	VERB
cana-6007	132	17	matlab	matlab	PROPN
cana-6007	132	18	.	.	PUNCT
cana-6007	132	19	table	table	NOUN
cana-6007	132	20	1	1	NUM
cana-6007	132	21	comparative	comparative	ADJ
cana-6007	132	22	evaluation	evaluation	NOUN
cana-6007	132	23	of	of	ADP
cana-6007	132	24	euler	euler	NOUN
cana-6007	132	25	–	–	PUNCT
cana-6007	132	26	maruyama	maruyama	NOUN
cana-6007	132	27	and	and	CCONJ
cana-6007	132	28	milstein	milstein	ADJ
cana-6007	132	29	methods	method	NOUN
cana-6007	132	30	for	for	ADP
cana-6007	132	31	example	example	NOUN
cana-6007	132	32	1	1	NUM
cana-6007	132	33	figure	figure	NOUN
cana-6007	132	34	1	1	NUM
cana-6007	132	35	exact	exact	NOUN
cana-6007	132	36	vs	vs	ADP
cana-6007	132	37	euler	euler	NOUN
cana-6007	132	38	maruyama	maruyama	PROPN
cana-6007	132	39	vs	vs	ADP
cana-6007	132	40	milstein	milstein	NOUN
cana-6007	132	41	approximation	approximation	NOUN
cana-6007	132	42	time	time	NOUN
cana-6007	132	43	exact	exact	ADJ
cana-6007	132	44	solution	solution	NOUN
cana-6007	132	45	euler	euler	NOUN
cana-6007	132	46	maruyama	maruyama	PROPN
cana-6007	132	47	milstein	milstein	ADP
cana-6007	132	48	0.0020	0.0020	NUM
cana-6007	132	49	0.523426969817	0.523426969817	NUM
cana-6007	132	50	0.520918917534	0.520918917534	NUM
cana-6007	132	51	0.521053465775	0.521053465775	NUM
cana-6007	132	52	0.1020	0.1020	NUM
cana-6007	132	53	0.548354657801	0.548354657801	NUM
cana-6007	132	54	0.390362133547	0.390362133547	NUM
cana-6007	132	55	0.392628655112	0.392628655112	NUM
cana-6007	132	56	0.2020	0.2020	NUM
cana-6007	132	57	0.667506138063	0.667506138063	NUM
cana-6007	132	58	0.356521561587	0.356521561587	NUM
cana-6007	132	59	0.361200653554	0.361200653554	NUM
cana-6007	132	60	0.3020	0.3020	NUM
cana-6007	132	61	0.945028337189	0.945028337189	NUM
cana-6007	133	1	0.832924520116	0.832924520116	NUM
cana-6007	133	2	0.847678837873	0.847678837873	NUM
cana-6007	133	3	0.4020	0.4020	NUM
cana-6007	133	4	0.964242605866	0.964242605866	NUM
cana-6007	133	5	0.876321176132	0.876321176132	NUM
cana-6007	133	6	0.891026800035	0.891026800035	NUM
cana-6007	133	7	0.5020	0.5020	NUM
cana-6007	133	8	0.983133376703	0.983133376703	NUM
cana-6007	133	9	0.948884254395	0.948884254395	NUM
cana-6007	133	10	0.944217419428	0.944217419428	NUM
cana-6007	133	11	0.6020	0.6020	NUM
cana-6007	133	12	0.978290012959	0.978290012959	NUM
cana-6007	133	13	0.928645239899	0.928645239899	NUM
cana-6007	133	14	0.926191258282	0.926191258282	NUM
cana-6007	133	15	0.7020	0.7020	NUM
cana-6007	133	16	0.988486234074	0.988486234074	NUM
cana-6007	133	17	0.960326979129	0.960326979129	NUM
cana-6007	133	18	0.958629463677	0.958629463677	NUM
cana-6007	133	19	0.8020	0.8020	NUM
cana-6007	133	20	0.998297123373	0.998297123373	NUM
cana-6007	133	21	0.994057619480	0.994057619480	NUM
cana-6007	133	22	0.993773765945	0.993773765945	NUM
cana-6007	133	23	0.9020	0.9020	NUM
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cana-6007	133	26	0.995504785803	0.995504785803	NUM
cana-6007	133	27	communications	communication	NOUN
cana-6007	133	28	on	on	ADP
cana-6007	133	29	applied	apply	VERB
cana-6007	133	30	nonlinear	nonlinear	ADJ
cana-6007	133	31	analysis	analysis	NOUN
cana-6007	133	32	issn	issn	NOUN
cana-6007	133	33	:	:	PUNCT
cana-6007	133	34	1074	1074	NUM
cana-6007	133	35	-	-	PUNCT
cana-6007	133	36	133x	133x	NUM
cana-6007	133	37	vol	vol	VERB
cana-6007	133	38	32	32	NUM
cana-6007	133	39	no	no	NOUN
cana-6007	133	40	.	.	PUNCT
cana-6007	134	1	10s	10	NOUN
cana-6007	134	2	(	(	PUNCT
cana-6007	134	3	2025	2025	NUM
cana-6007	134	4	)	)	PUNCT
cana-6007	134	5	3233	3233	NUM
cana-6007	134	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	134	7	table	table	NOUN
cana-6007	134	8	2	2	NUM
cana-6007	134	9	a	a	DET
cana-6007	134	10	comparative	comparative	ADJ
cana-6007	134	11	error	error	NOUN
cana-6007	134	12	study	study	NOUN
cana-6007	134	13	of	of	ADP
cana-6007	134	14	euler	euler	PROPN
cana-6007	134	15	–	–	PUNCT
cana-6007	134	16	maruyama	maruyama	NOUN
cana-6007	134	17	and	and	CCONJ
cana-6007	134	18	milstein	milstein	ADJ
cana-6007	134	19	methods	method	NOUN
cana-6007	134	20	for	for	ADP
cana-6007	134	21	example	example	NOUN
cana-6007	134	22	1	1	NUM
cana-6007	134	23	the	the	DET
cana-6007	134	24	mean	mean	ADJ
cana-6007	134	25	absolute	absolute	ADJ
cana-6007	134	26	error	error	NOUN
cana-6007	134	27	for	for	ADP
cana-6007	134	28	euler	euler	PROPN
cana-6007	134	29	maruyama	maruyama	PROPN
cana-6007	134	30	is	be	AUX
cana-6007	134	31	0.079092207934	0.079092207934	NUM
cana-6007	134	32	and	and	CCONJ
cana-6007	134	33	mean	mean	VERB
cana-6007	134	34	absolute	absolute	ADJ
cana-6007	134	35	error	error	NOUN
cana-6007	134	36	for	for	ADP
cana-6007	134	37	milstein	milstein	NOUN
cana-6007	134	38	is	be	AUX
cana-6007	134	39	0.076363830162	0.076363830162	NUM
cana-6007	134	40	.	.	PUNCT
cana-6007	135	1	figure	figure	NOUN
cana-6007	135	2	2	2	NUM
cana-6007	135	3	absolute	absolute	ADJ
cana-6007	135	4	error	error	NOUN
cana-6007	135	5	comparison	comparison	NOUN
cana-6007	135	6	time	time	NOUN
cana-6007	135	7	exact	exact	ADJ
cana-6007	135	8	solution	solution	NOUN
cana-6007	135	9	absolute	absolute	ADJ
cana-6007	135	10	error	error	NOUN
cana-6007	135	11	(	(	PUNCT
cana-6007	135	12	euler	euler	NOUN
cana-6007	135	13	m.	m.	NOUN
cana-6007	135	14	)	)	PUNCT
cana-6007	135	15	absolute	absolute	ADJ
cana-6007	135	16	error	error	NOUN
cana-6007	135	17	(	(	PUNCT
cana-6007	135	18	milstein	milstein	ADJ
cana-6007	135	19	)	)	PUNCT
cana-6007	136	1	0.0020	0.0020	NUM
cana-6007	136	2	0.523426969817	0.523426969817	NUM
cana-6007	136	3	0.002508052283	0.002508052283	NUM
cana-6007	136	4	0.002373504042	0.002373504042	NUM
cana-6007	136	5	0.1020	0.1020	NUM
cana-6007	136	6	0.548354657801	0.548354657801	NUM
cana-6007	136	7	0.157992524254	0.157992524254	NUM
cana-6007	136	8	0.155726002689	0.155726002689	NUM
cana-6007	136	9	0.2020	0.2020	NUM
cana-6007	136	10	0.667506138063	0.667506138063	NUM
cana-6007	136	11	0.310984576476	0.310984576476	NUM
cana-6007	136	12	0.306305484509	0.306305484509	NUM
cana-6007	136	13	0.3020	0.3020	NUM
cana-6007	136	14	0.945028337189	0.945028337189	NUM
cana-6007	136	15	0.112103817073	0.112103817073	NUM
cana-6007	136	16	0.097349499316	0.097349499316	NUM
cana-6007	136	17	0.4020	0.4020	NUM
cana-6007	136	18	0.964242605866	0.964242605866	NUM
cana-6007	137	1	0.087921429734	0.087921429734	NUM
cana-6007	137	2	0.073215805831	0.073215805831	NUM
cana-6007	137	3	0.5020	0.5020	NUM
cana-6007	137	4	0.983133376703	0.983133376703	NUM
cana-6007	137	5	0.034249122308	0.034249122308	NUM
cana-6007	137	6	0.038915957275	0.038915957275	NUM
cana-6007	137	7	0.6020	0.6020	NUM
cana-6007	137	8	0.978290012959	0.978290012959	NUM
cana-6007	137	9	0.049644773060	0.049644773060	NUM
cana-6007	137	10	0.052098754677	0.052098754677	NUM
cana-6007	137	11	0.7020	0.7020	NUM
cana-6007	137	12	0.988486234074	0.988486234074	NUM
cana-6007	137	13	0.028159254945	0.028159254945	NUM
cana-6007	137	14	0.029856770397	0.029856770397	NUM
cana-6007	137	15	0.8020	0.8020	NUM
cana-6007	137	16	0.998297123373	0.998297123373	NUM
cana-6007	137	17	0.004239503893	0.004239503893	NUM
cana-6007	137	18	0.004523357428	0.004523357428	NUM
cana-6007	137	19	0.9020	0.9020	NUM
cana-6007	137	20	0.998777951262	0.998777951262	NUM
cana-6007	137	21	0.003119025316	0.003119025316	NUM
cana-6007	137	22	0.003273165459	0.003273165459	NUM
cana-6007	137	23	communications	communication	NOUN
cana-6007	137	24	on	on	ADP
cana-6007	137	25	applied	apply	VERB
cana-6007	137	26	nonlinear	nonlinear	ADJ
cana-6007	137	27	analysis	analysis	NOUN
cana-6007	137	28	issn	issn	NOUN
cana-6007	137	29	:	:	PUNCT
cana-6007	137	30	1074	1074	NUM
cana-6007	137	31	-	-	PUNCT
cana-6007	137	32	133x	133x	NUM
cana-6007	137	33	vol	vol	VERB
cana-6007	137	34	32	32	NUM
cana-6007	137	35	no	no	NOUN
cana-6007	137	36	.	.	PUNCT
cana-6007	138	1	10s	10	NOUN
cana-6007	138	2	(	(	PUNCT
cana-6007	138	3	2025	2025	NUM
cana-6007	138	4	)	)	PUNCT
cana-6007	138	5	3234	3234	NUM
cana-6007	138	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	138	7	table	table	NOUN
cana-6007	138	8	3	3	NUM
cana-6007	138	9	comparative	comparative	ADJ
cana-6007	138	10	evaluation	evaluation	NOUN
cana-6007	138	11	of	of	ADP
cana-6007	138	12	euler	euler	NOUN
cana-6007	138	13	–	–	PUNCT
cana-6007	138	14	maruyama	maruyama	NOUN
cana-6007	138	15	and	and	CCONJ
cana-6007	138	16	milstein	milstein	ADJ
cana-6007	138	17	methods	method	NOUN
cana-6007	138	18	for	for	ADP
cana-6007	138	19	example	example	NOUN
cana-6007	138	20	2	2	NUM
cana-6007	138	21	figure	figure	NOUN
cana-6007	138	22	3	3	NUM
cana-6007	138	23	exact	exact	NOUN
cana-6007	138	24	vs	vs	ADP
cana-6007	138	25	euler	euler	NOUN
cana-6007	138	26	maruyama	maruyama	PROPN
cana-6007	138	27	vs	vs	ADP
cana-6007	138	28	milstein	milstein	NOUN
cana-6007	138	29	approximation	approximation	NOUN
cana-6007	138	30	time	time	NOUN
cana-6007	138	31	exact	exact	ADJ
cana-6007	138	32	solution	solution	NOUN
cana-6007	138	33	euler	euler	NOUN
cana-6007	138	34	maruyama	maruyama	PROPN
cana-6007	138	35	milstein	milstein	ADP
cana-6007	138	36	0.0020	0.0020	NUM
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cana-6007	139	5	3.990556304959	3.990556304959	NUM
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cana-6007	139	8	0.3020	0.3020	NUM
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cana-6007	140	4	0.4020	0.4020	NUM
cana-6007	140	5	7.377947326403	7.377947326403	NUM
cana-6007	140	6	7.357715839617	7.357715839617	NUM
cana-6007	140	7	7.375795333862	7.375795333862	NUM
cana-6007	140	8	0.5020	0.5020	NUM
cana-6007	140	9	9.418679276993	9.418679276993	NUM
cana-6007	140	10	9.397619125580	9.397619125580	NUM
cana-6007	140	11	9.415924333430	9.415924333430	NUM
cana-6007	140	12	0.6020	0.6020	NUM
cana-6007	140	13	15.557996089632	15.557996089632	NUM
cana-6007	140	14	15.535273112617	15.535273112617	NUM
cana-6007	140	15	15.552684640900	15.552684640900	NUM
cana-6007	140	16	0.7020	0.7020	NUM
cana-6007	140	17	13.898007189249	13.898007189249	NUM
cana-6007	140	18	13.863297287643	13.863297287643	NUM
cana-6007	140	19	13.894091286272	13.894091286272	NUM
cana-6007	140	20	0.8020	0.8020	NUM
cana-6007	140	21	17.085661386138	17.085661386138	NUM
cana-6007	140	22	17.051310284758	17.051310284758	NUM
cana-6007	140	23	17.080860625168	17.080860625168	NUM
cana-6007	140	24	0.9020	0.9020	NUM
cana-6007	140	25	14.892091213402	14.892091213402	NUM
cana-6007	140	26	14.859788368000	14.859788368000	NUM
cana-6007	140	27	14.888848395348	14.888848395348	NUM
cana-6007	140	28	communications	communication	NOUN
cana-6007	140	29	on	on	ADP
cana-6007	140	30	applied	apply	VERB
cana-6007	140	31	nonlinear	nonlinear	ADJ
cana-6007	140	32	analysis	analysis	NOUN
cana-6007	140	33	issn	issn	NOUN
cana-6007	140	34	:	:	PUNCT
cana-6007	140	35	1074	1074	NUM
cana-6007	140	36	-	-	PUNCT
cana-6007	140	37	133x	133x	NUM
cana-6007	140	38	vol	vol	VERB
cana-6007	140	39	32	32	NUM
cana-6007	140	40	no	no	NOUN
cana-6007	140	41	.	.	PUNCT
cana-6007	141	1	10s	10	NOUN
cana-6007	141	2	(	(	PUNCT
cana-6007	141	3	2025	2025	NUM
cana-6007	141	4	)	)	PUNCT
cana-6007	141	5	3235	3235	NUM
cana-6007	141	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	141	7	table	table	NOUN
cana-6007	141	8	4	4	NUM
cana-6007	141	9	a	a	DET
cana-6007	141	10	comparative	comparative	ADJ
cana-6007	141	11	error	error	NOUN
cana-6007	141	12	study	study	NOUN
cana-6007	141	13	of	of	ADP
cana-6007	141	14	euler	euler	PROPN
cana-6007	141	15	–	–	PUNCT
cana-6007	141	16	maruyama	maruyama	NOUN
cana-6007	141	17	and	and	CCONJ
cana-6007	141	18	milstein	milstein	ADJ
cana-6007	141	19	methods	method	NOUN
cana-6007	141	20	for	for	ADP
cana-6007	141	21	sde	sde	PROPN
cana-6007	141	22	2	2	NUM
cana-6007	141	23	the	the	DET
cana-6007	141	24	mean	mean	ADJ
cana-6007	141	25	absolute	absolute	ADJ
cana-6007	141	26	error	error	NOUN
cana-6007	141	27	for	for	ADP
cana-6007	141	28	euler	euler	PROPN
cana-6007	141	29	maruyama	maruyama	PROPN
cana-6007	141	30	is	be	AUX
cana-6007	141	31	0.019507283937	0.019507283937	NUM
cana-6007	141	32	and	and	CCONJ
cana-6007	141	33	mean	mean	VERB
cana-6007	141	34	absolute	absolute	ADJ
cana-6007	141	35	error	error	NOUN
cana-6007	141	36	for	for	ADP
cana-6007	141	37	milstein	milstein	NOUN
cana-6007	141	38	is	be	AUX
cana-6007	141	39	0.002451743439	0.002451743439	NUM
cana-6007	141	40	.	.	PUNCT
cana-6007	142	1	figure	figure	VERB
cana-6007	142	2	4	4	NUM
cana-6007	142	3	absolute	absolute	ADJ
cana-6007	142	4	error	error	NOUN
cana-6007	142	5	comparison	comparison	NOUN
cana-6007	142	6	time	time	NOUN
cana-6007	142	7	exact	exact	ADJ
cana-6007	142	8	solution	solution	NOUN
cana-6007	142	9	absolute	absolute	ADJ
cana-6007	142	10	error	error	NOUN
cana-6007	142	11	(	(	PUNCT
cana-6007	142	12	euler	euler	NOUN
cana-6007	142	13	m.	m.	NOUN
cana-6007	142	14	)	)	PUNCT
cana-6007	142	15	absolute	absolute	ADJ
cana-6007	142	16	error	error	NOUN
cana-6007	142	17	(	(	PUNCT
cana-6007	142	18	milstein	milstein	ADJ
cana-6007	142	19	)	)	PUNCT
cana-6007	142	20	0.0020	0.0020	NUM
cana-6007	142	21	0.974885356941	0.974885356941	NUM
cana-6007	142	22	0.000022368456	0.000022368456	NUM
cana-6007	142	23	0.000012580666	0.000012580666	NUM
cana-6007	142	24	0.1020	0.1020	NUM
cana-6007	142	25	1.471179176072	1.471179176072	NUM
cana-6007	142	26	0.000526432254	0.000526432254	NUM
cana-6007	142	27	0.000055181741	0.000055181741	NUM
cana-6007	143	1	0.2020	0.2020	NUM
cana-6007	143	2	3.990556304959	3.990556304959	NUM
cana-6007	143	3	0.013125643594	0.013125643594	NUM
cana-6007	143	4	0.001069334192	0.001069334192	NUM
cana-6007	143	5	0.3020	0.3020	NUM
cana-6007	143	6	4.799183231921	4.799183231921	NUM
cana-6007	143	7	0.016019931463	0.016019931463	NUM
cana-6007	143	8	0.001202470956	0.001202470956	NUM
cana-6007	143	9	0.4020	0.4020	NUM
cana-6007	143	10	7.377947326403	7.377947326403	NUM
cana-6007	143	11	0.020231486786	0.020231486786	NUM
cana-6007	143	12	0.002151992541	0.002151992541	NUM
cana-6007	143	13	0.5020	0.5020	NUM
cana-6007	143	14	9.418679276993	9.418679276993	NUM
cana-6007	143	15	0.021060151413	0.021060151413	NUM
cana-6007	143	16	0.002754943563	0.002754943563	NUM
cana-6007	143	17	0.6020	0.6020	NUM
cana-6007	143	18	15.557996089632	15.557996089632	NUM
cana-6007	143	19	0.022722977015	0.022722977015	NUM
cana-6007	143	20	0.005311448732	0.005311448732	NUM
cana-6007	143	21	0.7020	0.7020	NUM
cana-6007	143	22	13.898007189249	13.898007189249	NUM
cana-6007	143	23	0.034709901606	0.034709901606	NUM
cana-6007	143	24	0.003915902977	0.003915902977	NUM
cana-6007	143	25	0.8020	0.8020	NUM
cana-6007	143	26	17.085661386138	17.085661386138	NUM
cana-6007	143	27	0.034351101380	0.034351101380	NUM
cana-6007	143	28	0.004800760970	0.004800760970	NUM
cana-6007	143	29	0.9020	0.9020	NUM
cana-6007	143	30	14.892091213402	14.892091213402	NUM
cana-6007	143	31	0.032302845402	0.032302845402	NUM
cana-6007	143	32	0.003242818054	0.003242818054	NUM
cana-6007	143	33	communications	communication	NOUN
cana-6007	143	34	on	on	ADP
cana-6007	143	35	applied	apply	VERB
cana-6007	143	36	nonlinear	nonlinear	ADJ
cana-6007	143	37	analysis	analysis	NOUN
cana-6007	143	38	issn	issn	NOUN
cana-6007	143	39	:	:	PUNCT
cana-6007	143	40	1074	1074	NUM
cana-6007	143	41	-	-	PUNCT
cana-6007	143	42	133x	133x	NUM
cana-6007	143	43	vol	vol	VERB
cana-6007	143	44	32	32	NUM
cana-6007	143	45	no	no	NOUN
cana-6007	143	46	.	.	PUNCT
cana-6007	144	1	10s	10	NOUN
cana-6007	144	2	(	(	PUNCT
cana-6007	144	3	2025	2025	NUM
cana-6007	144	4	)	)	PUNCT
cana-6007	144	5	3236	3236	NUM
cana-6007	145	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	145	2	4._conclusion	4._conclusion	NOUN
cana-6007	145	3	in	in	ADP
cana-6007	145	4	this	this	DET
cana-6007	145	5	study	study	NOUN
cana-6007	145	6	,	,	PUNCT
cana-6007	145	7	we	we	PRON
cana-6007	145	8	compare	compare	VERB
cana-6007	145	9	the	the	DET
cana-6007	145	10	euler	euler	NOUN
cana-6007	145	11	–	–	PUNCT
cana-6007	145	12	maruyama	maruyama	NOUN
cana-6007	145	13	and	and	CCONJ
cana-6007	145	14	milstein	milstein	ADJ
cana-6007	145	15	methods	method	NOUN
cana-6007	145	16	using	use	VERB
cana-6007	145	17	two	two	NUM
cana-6007	145	18	nonlinear	nonlinear	ADJ
cana-6007	145	19	stochastic	stochastic	ADJ
cana-6007	145	20	differential	differential	ADJ
cana-6007	145	21	equations	equation	NOUN
cana-6007	145	22	(	(	PUNCT
cana-6007	145	23	sdes	sde	NOUN
cana-6007	145	24	)	)	PUNCT
cana-6007	145	25	with	with	ADP
cana-6007	145	26	known	know	VERB
cana-6007	145	27	exact	exact	ADJ
cana-6007	145	28	solutions	solution	NOUN
cana-6007	145	29	.	.	PUNCT
cana-6007	146	1	overall	overall	ADV
cana-6007	146	2	,	,	PUNCT
cana-6007	146	3	the	the	DET
cana-6007	146	4	results	result	NOUN
cana-6007	146	5	show	show	VERB
cana-6007	146	6	that	that	SCONJ
cana-6007	146	7	the	the	DET
cana-6007	146	8	milstein	milstein	ADJ
cana-6007	146	9	method	method	NOUN
cana-6007	146	10	is	be	AUX
cana-6007	146	11	usually	usually	ADV
cana-6007	146	12	more	more	ADV
cana-6007	146	13	accurate	accurate	ADJ
cana-6007	146	14	,	,	PUNCT
cana-6007	146	15	but	but	CCONJ
cana-6007	146	16	its	its	PRON
cana-6007	146	17	performance	performance	NOUN
cana-6007	146	18	depends	depend	VERB
cana-6007	146	19	largely	largely	ADV
cana-6007	146	20	on	on	ADP
cana-6007	146	21	the	the	DET
cana-6007	146	22	sde	sde	NOUN
cana-6007	146	23	's	's	PART
cana-6007	146	24	structural	structural	ADJ
cana-6007	146	25	properties	property	NOUN
cana-6007	146	26	,	,	PUNCT
cana-6007	146	27	especially	especially	ADV
cana-6007	146	28	the	the	DET
cana-6007	146	29	diffusion	diffusion	NOUN
cana-6007	146	30	term	term	NOUN
cana-6007	146	31	's	's	PART
cana-6007	146	32	nonlinearity	nonlinearity	NOUN
cana-6007	146	33	and	and	CCONJ
cana-6007	146	34	differentiability	differentiability	NOUN
cana-6007	147	1	.	.	PUNCT
cana-6007	147	2	milstein	milstein	PROPN
cana-6007	147	3	clearly	clearly	ADV
cana-6007	147	4	gives	give	VERB
cana-6007	147	5	better	well	ADJ
cana-6007	147	6	results	result	NOUN
cana-6007	147	7	than	than	ADP
cana-6007	147	8	euler	euler	NOUN
cana-6007	147	9	–	–	PUNCT
cana-6007	147	10	maruyama	maruyama	NOUN
cana-6007	147	11	when	when	SCONJ
cana-6007	147	12	the	the	DET
cana-6007	147	13	diffusion	diffusion	NOUN
cana-6007	147	14	term	term	NOUN
cana-6007	147	15	is	be	AUX
cana-6007	147	16	regular	regular	ADJ
cana-6007	147	17	and	and	CCONJ
cana-6007	147	18	highly	highly	ADV
cana-6007	147	19	nonlinear	nonlinear	ADJ
cana-6007	147	20	.	.	PUNCT
cana-6007	148	1	the	the	DET
cana-6007	148	2	numerical	numerical	ADJ
cana-6007	148	3	experiments	experiment	NOUN
cana-6007	148	4	also	also	ADV
cana-6007	148	5	demonstrate	demonstrate	VERB
cana-6007	148	6	that	that	SCONJ
cana-6007	148	7	milstein	milstein	NOUN
cana-6007	148	8	is	be	AUX
cana-6007	148	9	more	more	ADV
cana-6007	148	10	accurate	accurate	ADJ
cana-6007	148	11	in	in	ADP
cana-6007	148	12	both	both	DET
cana-6007	148	13	cases	case	NOUN
cana-6007	148	14	,	,	PUNCT
cana-6007	148	15	but	but	CCONJ
cana-6007	148	16	the	the	DET
cana-6007	148	17	amount	amount	NOUN
cana-6007	148	18	of	of	ADP
cana-6007	148	19	improvement	improvement	NOUN
cana-6007	148	20	is	be	AUX
cana-6007	148	21	different	different	ADJ
cana-6007	148	22	.	.	PUNCT
cana-6007	149	1	thus	thus	ADV
cana-6007	149	2	,	,	PUNCT
cana-6007	149	3	the	the	DET
cana-6007	149	4	structural	structural	ADJ
cana-6007	149	5	properties	property	NOUN
cana-6007	149	6	of	of	ADP
cana-6007	149	7	the	the	DET
cana-6007	149	8	sde	sde	PROPN
cana-6007	149	9	specifically	specifically	ADV
cana-6007	149	10	the	the	DET
cana-6007	149	11	forms	form	NOUN
cana-6007	149	12	of	of	ADP
cana-6007	149	13	the	the	DET
cana-6007	149	14	drift	drift	NOUN
cana-6007	149	15	and	and	CCONJ
cana-6007	149	16	diffusion	diffusion	NOUN
cana-6007	149	17	coefficients	coefficient	NOUN
cana-6007	149	18	,	,	PUNCT
cana-6007	149	19	should	should	AUX
cana-6007	149	20	be	be	AUX
cana-6007	149	21	considered	consider	VERB
cana-6007	149	22	when	when	SCONJ
cana-6007	149	23	selecting	select	VERB
cana-6007	149	24	a	a	DET
cana-6007	149	25	suitable	suitable	ADJ
cana-6007	149	26	numerical	numerical	ADJ
cana-6007	149	27	method	method	NOUN
cana-6007	149	28	.	.	PUNCT
cana-6007	150	1	acknowledgement	acknowledgement	NOUN
cana-6007	150	2	:	:	PUNCT
cana-6007	150	3	iu	iu	ADP
cana-6007	150	4	/	/	SYM
cana-6007	150	5	r&d/2025	r&d/2025	NOUN
cana-6007	150	6	-	-	PUNCT
cana-6007	150	7	mcn0003831	mcn0003831	ADJ
cana-6007	150	8	office	office	NOUN
cana-6007	150	9	of	of	ADP
cana-6007	150	10	research	research	NOUN
cana-6007	150	11	and	and	CCONJ
cana-6007	150	12	development	development	NOUN
cana-6007	150	13	integral	integral	ADJ
cana-6007	150	14	university	university	NOUN
cana-6007	150	15	,	,	PUNCT
cana-6007	150	16	lucknow	lucknow	PROPN
cana-6007	150	17	.	.	PUNCT
cana-6007	151	1	references	reference	NOUN
cana-6007	151	2	[	[	X
cana-6007	151	3	1	1	NUM
cana-6007	151	4	]	]	PUNCT
cana-6007	151	5	b.	b.	NOUN
cana-6007	151	6	øksendal	øksendal	NOUN
cana-6007	151	7	,	,	PUNCT
cana-6007	151	8	stochastic	stochastic	ADJ
cana-6007	151	9	differential	differential	ADJ
cana-6007	151	10	equations	equation	NOUN
cana-6007	151	11	:	:	PUNCT
cana-6007	151	12	an	an	DET
cana-6007	151	13	introduction	introduction	NOUN
cana-6007	151	14	with	with	ADP
cana-6007	151	15	applications	application	NOUN
cana-6007	151	16	,	,	PUNCT
cana-6007	151	17	6th	6th	ADJ
cana-6007	151	18	ed	ed	NOUN
cana-6007	151	19	.	.	PUNCT
cana-6007	152	1	berlin	berlin	PROPN
cana-6007	152	2	,	,	PUNCT
cana-6007	152	3	germany	germany	PROPN
cana-6007	152	4	:	:	PUNCT
cana-6007	152	5	springer	springer	NOUN
cana-6007	152	6	,	,	PUNCT
cana-6007	152	7	2003	2003	NUM
cana-6007	152	8	.	.	PUNCT
cana-6007	153	1	[	[	X
cana-6007	153	2	2	2	NUM
cana-6007	153	3	]	]	X
cana-6007	153	4	b.	b.	PROPN
cana-6007	153	5	j.	j.	PROPN
cana-6007	153	6	akinbo	akinbo	PROPN
cana-6007	153	7	,	,	PUNCT
cana-6007	153	8	t.	t.	PROPN
cana-6007	153	9	faniran	faniran	PROPN
cana-6007	153	10	,	,	PUNCT
cana-6007	153	11	and	and	CCONJ
cana-6007	153	12	e.	e.	PROPN
cana-6007	153	13	o.	o.	PROPN
cana-6007	153	14	ayoola	ayoola	PROPN
cana-6007	153	15	,	,	PUNCT
cana-6007	153	16	“	"	PUNCT
cana-6007	153	17	numerical	numerical	ADJ
cana-6007	153	18	solution	solution	NOUN
cana-6007	153	19	of	of	ADP
cana-6007	153	20	stochastic	stochastic	ADJ
cana-6007	153	21	differential	differential	ADJ
cana-6007	153	22	equations	equation	NOUN
cana-6007	153	23	,	,	PUNCT
cana-6007	153	24	”	"	PUNCT
cana-6007	153	25	int	int	NOUN
cana-6007	153	26	.	.	PUNCT
cana-6007	154	1	j.	j.	PROPN
cana-6007	154	2	adv	adv	PROPN
cana-6007	154	3	.	.	PUNCT
cana-6007	155	1	res	res	PROPN
cana-6007	155	2	.	.	PUNCT
cana-6007	156	1	sci	sci	PROPN
cana-6007	156	2	.	.	PUNCT
cana-6007	157	1	eng	eng	PROPN
cana-6007	157	2	.	.	PROPN
cana-6007	158	1	technol	technol	PROPN
cana-6007	158	2	.	.	PROPN
cana-6007	158	3	,	,	PUNCT
cana-6007	158	4	vol	vol	NOUN
cana-6007	158	5	.	.	PROPN
cana-6007	159	1	2	2	NUM
cana-6007	159	2	,	,	PUNCT
cana-6007	159	3	no	no	INTJ
cana-6007	159	4	.	.	NOUN
cana-6007	159	5	5	5	NUM
cana-6007	159	6	,	,	PUNCT
cana-6007	159	7	pp	pp	ADJ
cana-6007	159	8	.	.	PUNCT
cana-6007	160	1	608–616	608–616	NUM
cana-6007	160	2	,	,	PUNCT
cana-6007	160	3	2015	2015	NUM
cana-6007	160	4	.	.	PUNCT
cana-6007	161	1	[	[	X
cana-6007	161	2	3	3	X
cana-6007	161	3	]	]	X
cana-6007	161	4	d.	d.	PROPN
cana-6007	161	5	j.	j.	PROPN
cana-6007	161	6	higham	higham	PROPN
cana-6007	161	7	,	,	PUNCT
cana-6007	161	8	“	"	PUNCT
cana-6007	161	9	an	an	DET
cana-6007	161	10	algorithmic	algorithmic	ADJ
cana-6007	161	11	introduction	introduction	NOUN
cana-6007	161	12	to	to	ADP
cana-6007	161	13	numerical	numerical	ADJ
cana-6007	161	14	simulation	simulation	NOUN
cana-6007	161	15	of	of	ADP
cana-6007	161	16	stochastic	stochastic	ADJ
cana-6007	161	17	differential	differential	ADJ
cana-6007	161	18	equations	equation	NOUN
cana-6007	161	19	,	,	PUNCT
cana-6007	161	20	”	"	PUNCT
cana-6007	161	21	siam	siam	PROPN
cana-6007	161	22	rev	rev	PROPN
cana-6007	161	23	.	.	PROPN
cana-6007	161	24	,	,	PUNCT
cana-6007	161	25	vol	vol	NOUN
cana-6007	161	26	.	.	PROPN
cana-6007	161	27	43	43	NUM
cana-6007	161	28	,	,	PUNCT
cana-6007	161	29	no	no	INTJ
cana-6007	161	30	.	.	NOUN
cana-6007	161	31	3	3	NUM
cana-6007	161	32	,	,	PUNCT
cana-6007	161	33	pp	pp	ADJ
cana-6007	161	34	.	.	PUNCT
cana-6007	162	1	525–546	525–546	NUM
cana-6007	162	2	,	,	PUNCT
cana-6007	162	3	2001	2001	NUM
cana-6007	162	4	.	.	PUNCT
cana-6007	163	1	[	[	X
cana-6007	163	2	4	4	X
cana-6007	163	3	]	]	X
cana-6007	163	4	e.	e.	PROPN
cana-6007	163	5	buckwar	buckwar	PROPN
cana-6007	163	6	and	and	CCONJ
cana-6007	163	7	t.	t.	NOUN
cana-6007	163	8	sickenberger	sickenberger	NOUN
cana-6007	163	9	,	,	PUNCT
cana-6007	163	10	“	"	PUNCT
cana-6007	163	11	a	a	DET
cana-6007	163	12	comparative	comparative	ADJ
cana-6007	163	13	linear	linear	NOUN
cana-6007	163	14	mean	mean	ADJ
cana-6007	163	15	-	-	PUNCT
cana-6007	163	16	square	square	ADJ
cana-6007	163	17	stability	stability	NOUN
cana-6007	163	18	analysis	analysis	NOUN
cana-6007	163	19	of	of	ADP
cana-6007	163	20	maruyamaand	maruyamaand	PROPN
cana-6007	163	21	milstein	milstein	NOUN
cana-6007	163	22	-	-	PUNCT
cana-6007	163	23	type	type	NOUN
cana-6007	163	24	methods	method	NOUN
cana-6007	163	25	,	,	PUNCT
cana-6007	163	26	”	"	PUNCT
cana-6007	163	27	math	math	NOUN
cana-6007	163	28	.	.	PUNCT
cana-6007	164	1	comput	comput	NOUN
cana-6007	164	2	.	.	PUNCT
cana-6007	165	1	simul	simul	PROPN
cana-6007	165	2	.	.	PROPN
cana-6007	165	3	,	,	PUNCT
cana-6007	165	4	vol	vol	NOUN
cana-6007	165	5	.	.	PROPN
cana-6007	165	6	81	81	NUM
cana-6007	165	7	,	,	PUNCT
cana-6007	165	8	no	no	INTJ
cana-6007	165	9	.	.	NOUN
cana-6007	165	10	6	6	NUM
cana-6007	165	11	,	,	PUNCT
cana-6007	165	12	pp	pp	ADJ
cana-6007	165	13	.	.	PUNCT
cana-6007	166	1	1110–1127	1110–1127	NUM
cana-6007	166	2	,	,	PUNCT
cana-6007	166	3	2011	2011	NUM
cana-6007	166	4	.	.	PUNCT
cana-6007	167	1	[	[	X
cana-6007	167	2	5	5	X
cana-6007	167	3	]	]	PUNCT
cana-6007	167	4	e.	e.	PROPN
cana-6007	167	5	s.	s.	PROPN
cana-6007	167	6	rahman	rahman	PROPN
cana-6007	167	7	,	,	PUNCT
cana-6007	167	8	“	"	PUNCT
cana-6007	167	9	euler	euler	NOUN
cana-6007	167	10	-	-	PUNCT
cana-6007	167	11	maruyama	maruyama	NOUN
cana-6007	167	12	’s	’s	PART
cana-6007	167	13	method	method	NOUN
cana-6007	167	14	for	for	ADP
cana-6007	167	15	numerical	numerical	ADJ
cana-6007	167	16	solution	solution	NOUN
cana-6007	167	17	of	of	ADP
cana-6007	167	18	ornstein	ornstein	PROPN
cana-6007	167	19	–	–	PUNCT
cana-6007	167	20	uhlenbeck	uhlenbeck	PROPN
cana-6007	167	21	’s	’s	PART
cana-6007	167	22	equation	equation	NOUN
cana-6007	167	23	,	,	PUNCT
cana-6007	167	24	”	"	PUNCT
cana-6007	167	25	dept	dept	NOUN
cana-6007	167	26	.	.	PROPN
cana-6007	167	27	math	math	PROPN
cana-6007	167	28	.	.	PUNCT
cana-6007	167	29	,	,	PUNCT
cana-6007	167	30	fac	fac	PROPN
cana-6007	167	31	.	.	PROPN
cana-6007	167	32	math	math	PROPN
cana-6007	167	33	.	.	PUNCT
cana-6007	168	1	nat	nat	PROPN
cana-6007	168	2	.	.	PUNCT
cana-6007	169	1	sci	sci	PROPN
cana-6007	169	2	.	.	PROPN
cana-6007	169	3	,	,	PUNCT
cana-6007	169	4	padang	padang	PROPN
cana-6007	169	5	state	state	PROPN
cana-6007	169	6	univ	univ	PROPN
cana-6007	169	7	.	.	PROPN
cana-6007	169	8	,	,	PUNCT
cana-6007	169	9	2020	2020	NUM
cana-6007	169	10	.	.	PUNCT
cana-6007	170	1	[	[	X
cana-6007	170	2	6	6	NUM
cana-6007	170	3	]	]	PUNCT
cana-6007	170	4	g.	g.	PROPN
cana-6007	170	5	n.	n.	PROPN
cana-6007	170	6	mil’shtein	mil’shtein	PROPN
cana-6007	170	7	,	,	PUNCT
cana-6007	170	8	“	"	PUNCT
cana-6007	170	9	approximate	approximate	ADJ
cana-6007	170	10	integration	integration	NOUN
cana-6007	170	11	of	of	ADP
cana-6007	170	12	stochastic	stochastic	ADJ
cana-6007	170	13	differential	differential	ADJ
cana-6007	170	14	equations	equation	NOUN
cana-6007	170	15	,	,	PUNCT
cana-6007	170	16	”	"	PUNCT
cana-6007	170	17	theory	theory	NOUN
cana-6007	170	18	probab	probab	PROPN
cana-6007	170	19	.	.	PUNCT
cana-6007	171	1	appl	appl	PROPN
cana-6007	171	2	.	.	PROPN
cana-6007	171	3	,	,	PUNCT
cana-6007	171	4	vol	vol	NOUN
cana-6007	171	5	.	.	PROPN
cana-6007	171	6	19	19	NUM
cana-6007	171	7	,	,	PUNCT
cana-6007	171	8	no	no	INTJ
cana-6007	171	9	.	.	NOUN
cana-6007	171	10	3	3	NUM
cana-6007	171	11	,	,	PUNCT
cana-6007	171	12	pp	pp	ADJ
cana-6007	171	13	.	.	PUNCT
cana-6007	172	1	557–562	557–562	NUM
cana-6007	172	2	,	,	PUNCT
cana-6007	172	3	1974	1974	NUM
cana-6007	172	4	.	.	PUNCT
cana-6007	173	1	[	[	X
cana-6007	173	2	7	7	X
cana-6007	173	3	]	]	PUNCT
cana-6007	173	4	k.	k.	PROPN
cana-6007	173	5	burrage	burrage	PROPN
cana-6007	173	6	,	,	PUNCT
cana-6007	173	7	p.	p.	PROPN
cana-6007	173	8	burrage	burrage	PROPN
cana-6007	173	9	,	,	PUNCT
cana-6007	173	10	and	and	CCONJ
cana-6007	173	11	t.	t.	PROPN
cana-6007	173	12	mitsui	mitsui	PROPN
cana-6007	173	13	,	,	PUNCT
cana-6007	173	14	“	"	PUNCT
cana-6007	173	15	numerical	numerical	ADJ
cana-6007	173	16	solutions	solution	NOUN
cana-6007	173	17	of	of	ADP
cana-6007	173	18	stochastic	stochastic	ADJ
cana-6007	173	19	differential	differential	ADJ
cana-6007	173	20	equations	equation	NOUN
cana-6007	173	21	—	—	PUNCT
cana-6007	173	22	implementation	implementation	NOUN
cana-6007	173	23	and	and	CCONJ
cana-6007	173	24	stability	stability	NOUN
cana-6007	173	25	issues	issue	NOUN
cana-6007	173	26	,	,	PUNCT
cana-6007	173	27	”	"	PUNCT
cana-6007	173	28	j.	j.	PROPN
cana-6007	173	29	comput	comput	PROPN
cana-6007	173	30	.	.	PUNCT
cana-6007	174	1	appl	appl	PROPN
cana-6007	174	2	.	.	PROPN
cana-6007	174	3	math	math	PROPN
cana-6007	174	4	.	.	PUNCT
cana-6007	175	1	,	,	PUNCT
cana-6007	175	2	vol	vol	NOUN
cana-6007	175	3	.	.	PROPN
cana-6007	175	4	125	125	NUM
cana-6007	175	5	,	,	PUNCT
cana-6007	176	1	pp	pp	ADJ
cana-6007	176	2	.	.	PUNCT
cana-6007	177	1	171	171	NUM
cana-6007	177	2	–	–	PUNCT
cana-6007	177	3	182	182	NUM
cana-6007	177	4	,	,	PUNCT
cana-6007	177	5	2000	2000	NUM
cana-6007	177	6	.	.	PUNCT
cana-6007	178	1	[	[	X
cana-6007	178	2	8	8	NUM
cana-6007	178	3	]	]	X
cana-6007	178	4	m.	m.	NOUN
cana-6007	178	5	bayram	bayram	PROPN
cana-6007	178	6	,	,	PUNCT
cana-6007	178	7	t.	t.	PROPN
cana-6007	178	8	partal	partal	PROPN
cana-6007	178	9	,	,	PUNCT
cana-6007	178	10	and	and	CCONJ
cana-6007	178	11	g.	g.	PROPN
cana-6007	178	12	o.	o.	PROPN
cana-6007	178	13	buyukoz	buyukoz	PROPN
cana-6007	178	14	,	,	PUNCT
cana-6007	178	15	“	"	PUNCT
cana-6007	178	16	numerical	numerical	ADJ
cana-6007	178	17	methods	method	NOUN
cana-6007	178	18	for	for	ADP
cana-6007	178	19	simulation	simulation	NOUN
cana-6007	178	20	of	of	ADP
cana-6007	178	21	stochastic	stochastic	ADJ
cana-6007	178	22	differential	differential	ADJ
cana-6007	178	23	equations	equation	NOUN
cana-6007	178	24	,	,	PUNCT
cana-6007	178	25	”	"	PUNCT
cana-6007	178	26	math	math	NOUN
cana-6007	178	27	.	.	PUNCT
cana-6007	179	1	comput	comput	NOUN
cana-6007	179	2	.	.	PUNCT
cana-6007	180	1	simul	simul	PROPN
cana-6007	180	2	.	.	PROPN
cana-6007	180	3	,	,	PUNCT
cana-6007	180	4	2018	2018	NUM
cana-6007	180	5	.	.	PUNCT
cana-6007	181	1	[	[	X
cana-6007	181	2	9	9	NUM
cana-6007	181	3	]	]	PUNCT
cana-6007	181	4	m.	m.	NOUN
cana-6007	181	5	t.	t.	PROPN
cana-6007	181	6	griggs	griggs	PROPN
cana-6007	181	7	,	,	PUNCT
cana-6007	181	8	k.	k.	PROPN
cana-6007	181	9	burrage	burrage	PROPN
cana-6007	181	10	,	,	PUNCT
cana-6007	181	11	and	and	CCONJ
cana-6007	181	12	p.	p.	PROPN
cana-6007	181	13	m.	m.	PROPN
cana-6007	181	14	burrage	burrage	PROPN
cana-6007	181	15	,	,	PUNCT
cana-6007	181	16	“	"	PUNCT
cana-6007	181	17	magnus	magnus	NOUN
cana-6007	181	18	methods	method	NOUN
cana-6007	181	19	for	for	ADP
cana-6007	181	20	stochastic	stochastic	ADJ
cana-6007	181	21	delaydifferential	delaydifferential	ADJ
cana-6007	181	22	equations	equation	NOUN
cana-6007	181	23	,	,	PUNCT
cana-6007	181	24	”	"	PUNCT
cana-6007	181	25	arxiv	arxiv	PROPN
cana-6007	181	26	preprint	preprint	NOUN
cana-6007	181	27	arxiv:2506.16908	arxiv:2506.16908	PROPN
cana-6007	181	28	,	,	PUNCT
cana-6007	181	29	jun	jun	PROPN
cana-6007	181	30	.	.	PROPN
cana-6007	181	31	2025	2025	NUM
cana-6007	181	32	.	.	PUNCT
cana-6007	182	1	[	[	X
cana-6007	182	2	10	10	NUM
cana-6007	182	3	]	]	X
cana-6007	182	4	b.	b.	PROPN
cana-6007	182	5	m.	m.	PROPN
cana-6007	182	6	singh	singh	PROPN
cana-6007	182	7	and	and	CCONJ
cana-6007	182	8	n.	n.	PROPN
cana-6007	182	9	ahmad	ahmad	PROPN
cana-6007	182	10	,	,	PUNCT
cana-6007	182	11	“	"	PUNCT
cana-6007	182	12	numerical	numerical	ADJ
cana-6007	182	13	solution	solution	NOUN
cana-6007	182	14	of	of	ADP
cana-6007	182	15	volterra	volterra	PROPN
cana-6007	182	16	nonlinear	nonlinear	ADJ
cana-6007	182	17	integral	integral	ADJ
cana-6007	182	18	equation	equation	NOUN
cana-6007	182	19	by	by	ADP
cana-6007	182	20	using	use	VERB
cana-6007	182	21	laplace	laplace	NOUN
cana-6007	182	22	adomian	adomian	NOUN
cana-6007	182	23	decomposition	decomposition	NOUN
cana-6007	182	24	method	method	NOUN
cana-6007	182	25	,	,	PUNCT
cana-6007	182	26	”	"	PUNCT
cana-6007	182	27	int	int	NOUN
cana-6007	182	28	.	.	PUNCT
cana-6007	183	1	j.	j.	PROPN
cana-6007	183	2	appl	appl	PROPN
cana-6007	183	3	.	.	PROPN
cana-6007	183	4	math	math	PROPN
cana-6007	183	5	.	.	PUNCT
cana-6007	184	1	,	,	PUNCT
cana-6007	184	2	vol	vol	NOUN
cana-6007	184	3	.	.	PROPN
cana-6007	185	1	35	35	NUM
cana-6007	185	2	,	,	PUNCT
cana-6007	185	3	no	no	INTJ
cana-6007	185	4	.	.	NOUN
cana-6007	185	5	1	1	NUM
cana-6007	185	6	,	,	PUNCT
cana-6007	185	7	pp	pp	ADJ
cana-6007	185	8	.	.	PUNCT
cana-6007	186	1	39–48	39–48	NUM
cana-6007	186	2	,	,	PUNCT
cana-6007	186	3	mar	mar	PROPN
cana-6007	186	4	.	.	PROPN
cana-6007	186	5	2022	2022	NUM
cana-6007	186	6	.	.	PUNCT
cana-6007	187	1	[	[	X
cana-6007	187	2	11	11	NUM
cana-6007	187	3	]	]	PUNCT
cana-6007	187	4	s.	s.	PROPN
cana-6007	187	5	charan	charan	PROPN
cana-6007	187	6	and	and	CCONJ
cana-6007	187	7	n.	n.	PROPN
cana-6007	187	8	ahmad	ahmad	PROPN
cana-6007	187	9	,	,	PUNCT
cana-6007	187	10	“	"	PUNCT
cana-6007	187	11	a	a	DET
cana-6007	187	12	comparative	comparative	ADJ
cana-6007	187	13	study	study	NOUN
cana-6007	187	14	on	on	ADP
cana-6007	187	15	numerical	numerical	ADJ
cana-6007	187	16	solution	solution	NOUN
cana-6007	187	17	of	of	ADP
cana-6007	187	18	ordinary	ordinary	ADJ
cana-6007	187	19	differential	differential	ADJ
cana-6007	187	20	equation	equation	NOUN
cana-6007	187	21	by	by	ADP
cana-6007	187	22	different	different	ADJ
cana-6007	187	23	method	method	NOUN
cana-6007	187	24	with	with	ADP
cana-6007	187	25	initial	initial	ADJ
cana-6007	187	26	value	value	NOUN
cana-6007	187	27	problem	problem	NOUN
cana-6007	187	28	,	,	PUNCT
cana-6007	187	29	”	"	PUNCT
cana-6007	187	30	int	int	NOUN
cana-6007	187	31	.	.	PUNCT
cana-6007	188	1	j.	j.	PROPN
cana-6007	188	2	recent	recent	PROPN
cana-6007	188	3	sci	sci	PROPN
cana-6007	188	4	.	.	PUNCT
cana-6007	189	1	res	res	PROPN
cana-6007	189	2	.	.	PROPN
cana-6007	189	3	,	,	PUNCT
cana-6007	189	4	vol	vol	NOUN
cana-6007	189	5	.	.	PROPN
cana-6007	189	6	8	8	NUM
cana-6007	189	7	,	,	PUNCT
cana-6007	189	8	no	no	INTJ
cana-6007	189	9	.	.	NOUN
cana-6007	189	10	10	10	NUM
cana-6007	189	11	,	,	PUNCT
cana-6007	189	12	pp	pp	ADJ
cana-6007	189	13	.	.	PUNCT
cana-6007	190	1	21134–21139	21134–21139	NUM
cana-6007	190	2	,	,	PUNCT
cana-6007	190	3	oct	oct	PROPN
cana-6007	190	4	.	.	PROPN
cana-6007	190	5	2017	2017	NUM
cana-6007	190	6	.	.	PUNCT
cana-6007	191	1	[	[	X
cana-6007	191	2	12	12	NUM
cana-6007	191	3	]	]	X
cana-6007	191	4	n.	n.	NOUN
cana-6007	191	5	ahamad	ahamad	PROPN
cana-6007	191	6	and	and	CCONJ
cana-6007	191	7	s.	s.	PROPN
cana-6007	191	8	charan	charan	PROPN
cana-6007	191	9	,	,	PUNCT
cana-6007	191	10	“	"	PUNCT
cana-6007	191	11	study	study	NOUN
cana-6007	191	12	of	of	ADP
cana-6007	191	13	numerical	numerical	ADJ
cana-6007	191	14	solution	solution	NOUN
cana-6007	191	15	of	of	ADP
cana-6007	191	16	fourth	fourth	ADJ
cana-6007	191	17	order	order	NOUN
cana-6007	191	18	ordinary	ordinary	ADJ
cana-6007	191	19	differential	differential	ADJ
cana-6007	191	20	equations	equation	NOUN
cana-6007	191	21	by	by	ADP
cana-6007	191	22	fifth	fifth	ADJ
cana-6007	191	23	order	order	NOUN
cana-6007	191	24	runge	runge	NOUN
cana-6007	191	25	-	-	PUNCT
cana-6007	191	26	kutta	kutta	NOUN
cana-6007	191	27	method	method	NOUN
cana-6007	191	28	,	,	PUNCT
cana-6007	191	29	”	"	PUNCT
cana-6007	191	30	int	int	NOUN
cana-6007	191	31	.	.	PUNCT
cana-6007	192	1	j.	j.	PROPN
cana-6007	192	2	sci	sci	PROPN
cana-6007	192	3	.	.	PUNCT
cana-6007	193	1	res	res	PROPN
cana-6007	193	2	.	.	PUNCT
cana-6007	194	1	sci	sci	PROPN
cana-6007	194	2	.	.	PUNCT
cana-6007	195	1	eng	eng	PROPN
cana-6007	195	2	.	.	PROPN
cana-6007	196	1	technol	technol	PROPN
cana-6007	196	2	.	.	PUNCT
cana-6007	197	1	(	(	PUNCT
cana-6007	197	2	ijsrset	ijsrset	NOUN
cana-6007	197	3	)	)	PUNCT
cana-6007	197	4	,	,	PUNCT
cana-6007	197	5	vol	vol	NOUN
cana-6007	197	6	.	.	PROPN
cana-6007	198	1	6	6	NUM
cana-6007	198	2	,	,	PUNCT
cana-6007	198	3	no	no	INTJ
cana-6007	198	4	.	.	NOUN
cana-6007	198	5	1	1	NUM
cana-6007	198	6	,	,	PUNCT
cana-6007	198	7	pp	pp	ADJ
cana-6007	198	8	.	.	PUNCT
cana-6007	199	1	230–238	230–238	NUM
cana-6007	199	2	,	,	PUNCT
cana-6007	199	3	jan.–feb	jan.–feb	NOUN
cana-6007	199	4	.	.	NOUN
cana-6007	199	5	2019	2019	NUM
cana-6007	199	6	.	.	PUNCT
cana-6007	200	1	[	[	X
cana-6007	200	2	13	13	NUM
cana-6007	200	3	]	]	PUNCT
cana-6007	200	4	p.	p.	PROPN
cana-6007	200	5	e.	e.	PROPN
cana-6007	200	6	kloeden	kloeden	PROPN
cana-6007	200	7	and	and	CCONJ
cana-6007	200	8	e.	e.	PROPN
cana-6007	200	9	platen	platen	PROPN
cana-6007	200	10	,	,	PUNCT
cana-6007	200	11	numerical	numerical	ADJ
cana-6007	200	12	solution	solution	NOUN
cana-6007	200	13	of	of	ADP
cana-6007	200	14	stochastic	stochastic	ADJ
cana-6007	200	15	differential	differential	ADJ
cana-6007	200	16	equations	equation	NOUN
cana-6007	200	17	.	.	PUNCT
cana-6007	201	1	berlin	berlin	PROPN
cana-6007	201	2	,	,	PUNCT
cana-6007	201	3	germany	germany	PROPN
cana-6007	201	4	:	:	PUNCT
cana-6007	201	5	springer	springer	NOUN
cana-6007	201	6	,	,	PUNCT
cana-6007	201	7	1992	1992	NUM
cana-6007	201	8	.	.	PUNCT
cana-6007	202	1	communications	communication	NOUN
cana-6007	202	2	on	on	ADP
cana-6007	202	3	applied	apply	VERB
cana-6007	202	4	nonlinear	nonlinear	ADJ
cana-6007	202	5	analysis	analysis	NOUN
cana-6007	202	6	issn	issn	NOUN
cana-6007	202	7	:	:	PUNCT
cana-6007	202	8	1074	1074	NUM
cana-6007	202	9	-	-	PUNCT
cana-6007	202	10	133x	133x	NUM
cana-6007	202	11	vol	vol	VERB
cana-6007	202	12	32	32	NUM
cana-6007	202	13	no	no	NOUN
cana-6007	202	14	.	.	PUNCT
cana-6007	203	1	10s	10	NOUN
cana-6007	203	2	(	(	PUNCT
cana-6007	203	3	2025	2025	NUM
cana-6007	203	4	)	)	PUNCT
cana-6007	203	5	3237	3237	NUM
cana-6007	203	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-6007	204	1	[	[	X
cana-6007	204	2	14	14	NUM
cana-6007	204	3	]	]	X
cana-6007	204	4	s.	s.	PROPN
cana-6007	204	5	deng	deng	PROPN
cana-6007	204	6	,	,	PUNCT
cana-6007	204	7	c.	c.	PROPN
cana-6007	204	8	fei	fei	PROPN
cana-6007	204	9	,	,	PUNCT
cana-6007	204	10	w.	w.	PROPN
cana-6007	204	11	fei	fei	PROPN
cana-6007	204	12	,	,	PUNCT
cana-6007	204	13	and	and	CCONJ
cana-6007	204	14	x.	x.	PROPN
cana-6007	204	15	mao	mao	PROPN
cana-6007	204	16	,	,	PUNCT
cana-6007	204	17	“	"	PUNCT
cana-6007	204	18	positivity	positivity	NOUN
cana-6007	204	19	-	-	PUNCT
cana-6007	204	20	preserving	preserve	VERB
cana-6007	204	21	truncated	truncated	ADJ
cana-6007	204	22	euler	euler	NOUN
cana-6007	204	23	and	and	CCONJ
cana-6007	204	24	milstein	milstein	ADJ
cana-6007	204	25	methods	method	NOUN
cana-6007	204	26	for	for	ADP
cana-6007	204	27	financial	financial	ADJ
cana-6007	204	28	sdes	sde	NOUN
cana-6007	204	29	with	with	ADP
cana-6007	204	30	super	super	ADJ
cana-6007	204	31	-	-	ADJ
cana-6007	204	32	linear	linear	ADJ
cana-6007	204	33	coefficients	coefficient	NOUN
cana-6007	204	34	,	,	PUNCT
cana-6007	204	35	”	"	PUNCT
cana-6007	204	36	arxiv:2410.05614	arxiv:2410.05614	X
cana-6007	204	37	[	[	X
cana-6007	204	38	math.na	math.na	X
cana-6007	204	39	]	]	PUNCT
cana-6007	204	40	,	,	PUNCT
cana-6007	204	41	oct	oct	PROPN
cana-6007	204	42	.	.	PROPN
cana-6007	204	43	8	8	NUM
cana-6007	204	44	,	,	PUNCT
cana-6007	204	45	2024	2024	NUM
cana-6007	204	46	.	.	PUNCT
cana-6007	205	1	[	[	X
cana-6007	205	2	15	15	NUM
cana-6007	205	3	]	]	X
cana-6007	205	4	s.	s.	PROPN
cana-6007	205	5	e.	e.	PROPN
cana-6007	205	6	fadugba	fadugba	PROPN
cana-6007	205	7	,	,	PUNCT
cana-6007	205	8	b.	b.	PROPN
cana-6007	205	9	j.	j.	PROPN
cana-6007	205	10	adegboyegun	adegboyegun	PROPN
cana-6007	205	11	,	,	PUNCT
cana-6007	205	12	and	and	CCONJ
cana-6007	205	13	o.	o.	PROPN
cana-6007	205	14	t.	t.	PROPN
cana-6007	205	15	ogunbiyi	ogunbiyi	PROPN
cana-6007	205	16	,	,	PUNCT
cana-6007	205	17	“	"	PUNCT
cana-6007	205	18	on	on	ADP
cana-6007	205	19	convergence	convergence	NOUN
cana-6007	205	20	of	of	ADP
cana-6007	205	21	eulermaruyama	eulermaruyama	NOUN
cana-6007	205	22	and	and	CCONJ
cana-6007	205	23	milstein	milstein	ADJ
cana-6007	205	24	scheme	scheme	NOUN
cana-6007	205	25	for	for	ADP
cana-6007	205	26	solution	solution	NOUN
cana-6007	205	27	of	of	ADP
cana-6007	205	28	stochastic	stochastic	ADJ
cana-6007	205	29	differential	differential	ADJ
cana-6007	205	30	equations	equation	NOUN
cana-6007	205	31	,	,	PUNCT
cana-6007	205	32	”	"	PUNCT
cana-6007	205	33	int	int	NOUN
cana-6007	205	34	.	.	PUNCT
cana-6007	206	1	j.	j.	PROPN
cana-6007	206	2	appl	appl	PROPN
cana-6007	206	3	.	.	PROPN
cana-6007	206	4	math	math	PROPN
cana-6007	206	5	.	.	PUNCT
cana-6007	207	1	model	model	PROPN
cana-6007	207	2	.	.	PUNCT
cana-6007	207	3	,	,	PUNCT
cana-6007	207	4	vol	vol	NOUN
cana-6007	207	5	.	.	PROPN
cana-6007	207	6	1	1	NUM
cana-6007	207	7	,	,	PUNCT
cana-6007	207	8	no	no	INTJ
cana-6007	207	9	.	.	NOUN
cana-6007	207	10	1	1	NUM
cana-6007	207	11	,	,	PUNCT
cana-6007	207	12	pp	pp	ADJ
cana-6007	207	13	.	.	PUNCT
cana-6007	208	1	9–15	9–15	PROPN
cana-6007	208	2	,	,	PUNCT
cana-6007	208	3	2013	2013	NUM
cana-6007	208	4	.	.	PUNCT
cana-6007	209	1	[	[	X
cana-6007	209	2	16	16	NUM
cana-6007	209	3	]	]	PUNCT
cana-6007	209	4	s.	s.	PROPN
cana-6007	209	5	j.	j.	PROPN
cana-6007	209	6	kayode	kayode	PROPN
cana-6007	209	7	and	and	CCONJ
cana-6007	209	8	a.	a.	NOUN
cana-6007	209	9	a.	a.	NOUN
cana-6007	209	10	ganiyu	ganiyu	NOUN
cana-6007	209	11	,	,	PUNCT
cana-6007	209	12	“	"	PUNCT
cana-6007	209	13	effect	effect	NOUN
cana-6007	209	14	of	of	ADP
cana-6007	209	15	varying	vary	VERB
cana-6007	209	16	step	step	NOUN
cana-6007	209	17	sizes	size	NOUN
cana-6007	209	18	in	in	ADP
cana-6007	209	19	numerical	numerical	ADJ
cana-6007	209	20	approximation	approximation	NOUN
cana-6007	209	21	of	of	ADP
cana-6007	209	22	stochastic	stochastic	ADJ
cana-6007	209	23	differential	differential	ADJ
cana-6007	209	24	equations	equation	NOUN
cana-6007	209	25	using	use	VERB
cana-6007	209	26	one	one	NUM
cana-6007	209	27	step	step	NOUN
cana-6007	209	28	milstein	milstein	ADP
cana-6007	209	29	method	method	NOUN
cana-6007	209	30	,	,	PUNCT
cana-6007	209	31	”	"	PUNCT
cana-6007	209	32	appl	appl	NOUN
cana-6007	209	33	.	.	PUNCT
cana-6007	210	1	comput	comput	PROPN
cana-6007	210	2	.	.	PUNCT
cana-6007	211	1	math	math	NOUN
cana-6007	211	2	.	.	PUNCT
cana-6007	212	1	,	,	PUNCT
cana-6007	212	2	vol	vol	NOUN
cana-6007	212	3	.	.	PROPN
cana-6007	213	1	4	4	NUM
cana-6007	213	2	,	,	PUNCT
cana-6007	213	3	no	no	INTJ
cana-6007	213	4	.	.	NOUN
cana-6007	213	5	5	5	NUM
cana-6007	213	6	,	,	PUNCT
cana-6007	213	7	pp	pp	ADJ
cana-6007	213	8	.	.	PUNCT
cana-6007	214	1	351–362	351–362	NUM
cana-6007	214	2	,	,	PUNCT
cana-6007	214	3	2015	2015	NUM
cana-6007	214	4	.	.	PUNCT
cana-6007	215	1	[	[	X
cana-6007	215	2	17	17	NUM
cana-6007	215	3	]	]	PUNCT
cana-6007	215	4	x.	x.	NOUN
cana-6007	215	5	mao	mao	PROPN
cana-6007	215	6	and	and	CCONJ
cana-6007	215	7	c.	c.	PROPN
cana-6007	215	8	yuan	yuan	PROPN
cana-6007	215	9	,	,	PUNCT
cana-6007	215	10	stochastic	stochastic	ADJ
cana-6007	215	11	differential	differential	ADJ
cana-6007	215	12	equations	equation	NOUN
cana-6007	215	13	with	with	ADP
cana-6007	215	14	markovian	markovian	ADJ
cana-6007	215	15	switching	switching	NOUN
cana-6007	215	16	.	.	PUNCT
cana-6007	216	1	london	london	PROPN
cana-6007	216	2	,	,	PUNCT
cana-6007	216	3	u.k	u.k	PROPN
cana-6007	216	4	.	.	PROPN
cana-6007	216	5	:	:	PUNCT
cana-6007	216	6	imperial	imperial	ADJ
cana-6007	216	7	college	college	NOUN
cana-6007	216	8	press	press	NOUN
cana-6007	216	9	,	,	PUNCT
cana-6007	216	10	2006	2006	NUM
cana-6007	216	11	.	.	PUNCT