id	sid	eid	entity	type
ma-117	1	1	2023	CARDINAL
ma-117	2	1	j. math	PERSON
ma-117	4	1	3 (	CARDINAL
ma-117	4	2	2023	CARDINAL
ma-117	5	1	10.28924	CARDINAL
ma-117	5	2	o. c. badibi1,∗	PERSON
ma-117	5	3	i. ramadhani2	PERSON
ma-117	5	4	m. a. ndondo1	PERSON
ma-117	6	1	s. d. kumwimba1	PERSON
ma-117	7	1	1université de	DATE
ma-117	7	2	faculté des sciences	ORG
ma-117	7	3	département de mathématiques et informatique	ORG
ma-117	7	4	democratic republic	GPE
ma-117	7	5	2université de kinshasa	PERSON
ma-117	7	6	faculté des sciences et technologies	ORG
ma-117	7	7	département de mathématiques	ORG
ma-117	7	8	informatique et statistiques	ORG
ma-117	7	9	democratic republic	GPE
ma-117	14	1	geometricbrownian	NORP
ma-117	15	1	1	CARDINAL
ma-117	16	1	second	ORDINAL
ma-117	16	2	6	CARDINAL
ma-117	17	1	8	CARDINAL
ma-117	19	1	20	CARDINAL
ma-117	19	2	2022	CARDINAL
ma-117	21	1	schemes;vasicek	NORP
ma-117	22	1	1	CARDINAL
ma-117	23	1	j. math	PERSON
ma-117	25	1	10.28924	CARDINAL
ma-117	26	1	2	CARDINAL
ma-117	26	2	gikhman	PERSON
ma-117	26	3	a.v.	PERSON
ma-117	27	1	3	CARDINAL
ma-117	27	2	a. friedman	PERSON
ma-117	27	3	4	CARDINAL
ma-117	30	1	5	CARDINAL
ma-117	30	2	euler-maruyama	PERSON
ma-117	30	3	euler	PERSON
ma-117	32	1	2	CARDINAL
ma-117	32	2	2.1	CARDINAL
ma-117	35	1	2.1	CARDINAL
ma-117	36	1	sde	ORG
ma-117	37	1	13	CARDINAL
ma-117	37	2	ω	ORDINAL
ma-117	38	1	sde	ORG
ma-117	39	1	0	CARDINAL
ma-117	40	1	0	CARDINAL
ma-117	41	1	2.1	CARDINAL
ma-117	42	1	2.1	CARDINAL
ma-117	43	1	14	CARDINAL
ma-117	46	1	j. math	PERSON
ma-117	48	1	10.28924	CARDINAL
ma-117	48	2	3(2	CARDINAL
ma-117	49	1	2.1	CARDINAL
ma-117	50	1	xt)t∈[0,t	ORG
ma-117	50	2	0≤t≤t |x2	QUANTITY
ma-117	51	1	2.2	CARDINAL
ma-117	52	1	1	CARDINAL
ma-117	52	2	24	CARDINAL
ma-117	52	3	∈	ORG
ma-117	52	4	lim	PERSON
ma-117	53	1	1	CARDINAL
ma-117	53	2	2.3	CARDINAL
ma-117	55	1	23	CARDINAL
ma-117	55	2	2	CARDINAL
ma-117	55	3	2.1	CARDINAL
ma-117	56	1	0	CARDINAL
ma-117	57	1	2	CARDINAL
ma-117	57	2	2	CARDINAL
ma-117	57	3	2.1	CARDINAL
ma-117	57	4	∈	ORG
ma-117	57	5	lim	PERSON
ma-117	57	6	0 2.2	CARDINAL
ma-117	59	1	three	CARDINAL
ma-117	59	2	euler-maruyama	PERSON
ma-117	59	3	euler-maruyama	PERSON
ma-117	60	1	2.4	CARDINAL
ma-117	61	1	euler-maruyama	PERSON
ma-117	61	2	10	CARDINAL
ma-117	62	1	11	CARDINAL
ma-117	63	1	0	CARDINAL
ma-117	64	1	euler	PERSON
ma-117	64	2	2.1	CARDINAL
ma-117	65	1	− tk	PERSON
ma-117	65	2	+ σ(tk	DATE
ma-117	67	1	x(0	PERSON
ma-117	69	1	2.2	CARDINAL
ma-117	70	1	j. math	PERSON
ma-117	72	1	10.28924	CARDINAL
ma-117	72	2	4	CARDINAL
ma-117	72	3	2.5	CARDINAL
ma-117	73	1	euler-maruyama	PERSON
ma-117	73	2	10	CARDINAL
ma-117	73	3	euler-maruyama	PERSON
ma-117	73	4	euler	PERSON
ma-117	75	1	euler	PERSON
ma-117	75	2	b(xk+1)∆tk	ORG
ma-117	76	1	euler-maruyama	PERSON
ma-117	76	2	2.1	CARDINAL
ma-117	76	3	2.3	CARDINAL
ma-117	76	4	2.6	CARDINAL
ma-117	77	1	2.1	CARDINAL
ma-117	77	2	0	CARDINAL
ma-117	80	1	0	CARDINAL
ma-117	82	1	x(0	PERSON
ma-117	82	2	2.4	CARDINAL
ma-117	82	3	2.1	CARDINAL
ma-117	83	1	euler	PERSON
ma-117	83	2	1 2	CARDINAL
ma-117	83	3	1	CARDINAL
ma-117	83	4	3	CARDINAL
ma-117	83	5	3.1	CARDINAL
ma-117	84	1	1977	DATE
ma-117	84	2	one	CARDINAL
ma-117	84	3	first	ORDINAL
ma-117	84	4	ornstein	PERSON
ma-117	84	5	15	CARDINAL
ma-117	86	1	x0 ∀θ1	DATE
ma-117	86	2	0	CARDINAL
ma-117	87	1	3.1	CARDINAL
ma-117	87	2	3.1	CARDINAL
ma-117	87	3	θ2 +	PERSON
ma-117	87	4	x0	CARDINAL
ma-117	88	1	3.2	CARDINAL
ma-117	88	2	3.1	CARDINAL
ma-117	89	1	3.3	CARDINAL
ma-117	90	1	j. math	PERSON
ma-117	92	1	10.28924	CARDINAL
ma-117	92	2	5the	CARDINAL
ma-117	92	3	3.3	CARDINAL
ma-117	92	4	θ ∫	ORG
ma-117	94	1	3.4	CARDINAL
ma-117	94	2	3.2	CARDINAL
ma-117	94	3	θ2 ∀	PERSON
ma-117	95	1	3 2θ2	CARDINAL
ma-117	95	2	0	CARDINAL
ma-117	95	3	3 2θ2	CARDINAL
ma-117	95	4	3.2	CARDINAL
ma-117	95	5	θ2 + θ3e	PERSON
ma-117	95	6	3.5	CARDINAL
ma-117	95	7	3.1	CARDINAL
ma-117	95	8	euler-maruyama	PERSON
ma-117	95	9	euler-maruyama	PERSON
ma-117	95	10	5	CARDINAL
ma-117	96	1	3.2	CARDINAL
ma-117	96	2	euler-maruyama	PERSON
ma-117	97	1	euler	PERSON
ma-117	97	2	− θ2xk	ORG
ma-117	98	1	1− θ2∆t)xk + θ3 √ ∆tzk	DATE
ma-117	98	2	3.6	CARDINAL
ma-117	98	3	3.2.1	CARDINAL
ma-117	99	1	euler-maruyama	PERSON
ma-117	100	1	3.1	CARDINAL
ma-117	101	1	euler-maruyama	PERSON
ma-117	101	2	euler	PERSON
ma-117	101	3	3.6	CARDINAL
ma-117	101	4	3.1	CARDINAL
ma-117	102	1	1− θ2∆t)k+1e[x0	TIME
ma-117	102	2	1−	ORDINAL
ma-117	102	3	3.7	CARDINAL
ma-117	102	4	1	CARDINAL
ma-117	102	5	lim ∆t→0	PERSON
ma-117	102	6	lim k→+∞ e	PERSON
ma-117	103	1	j. math	PERSON
ma-117	105	1	10.28924	CARDINAL
ma-117	105	2	6	CARDINAL
ma-117	106	1	3.1	CARDINAL
ma-117	106	2	5	CARDINAL
ma-117	107	1	1−	ORDINAL
ma-117	109	1	1−	TIME
ma-117	112	1	1− θ2∆t)e	LAW
ma-117	113	1	0	CARDINAL
ma-117	113	2	1	CARDINAL
ma-117	113	3	1−	ORDINAL
ma-117	114	1	1−	TIME
ma-117	114	2	1−	TIME
ma-117	116	1	1− θ2∆t)2e[xk−1	PRODUCT
ma-117	116	2	1−	TIME
ma-117	117	1	1− θ2∆t)2e[xk−1	PRODUCT
ma-117	117	2	1−	TIME
ma-117	118	1	1− θ2∆t)2	PRODUCT
ma-117	118	2	1−	TIME
ma-117	118	3	1−	TIME
ma-117	121	1	1− θ2∆t)2	PRODUCT
ma-117	124	1	1− θ2∆t))k+1 + (	PERCENT
ma-117	124	2	1− θ2∆t)k+1e[x0	TIME
ma-117	124	3	1−	ORDINAL
ma-117	124	4	1− θ2∆t)k+1e[x0	TIME
ma-117	125	1	1−	TIME
ma-117	125	2	1−	TIME
ma-117	125	3	1−	TIME
ma-117	125	4	1−	TIME
ma-117	126	1	3.8	CARDINAL
ma-117	126	2	3.8	CARDINAL
ma-117	126	3	1	CARDINAL
ma-117	126	4	3.8	CARDINAL
ma-117	126	5	k → +∞	ORG
ma-117	126	6	lim	PERSON
ma-117	126	7	lim k→+∞ e	PERSON
ma-117	127	1	euler-maruyama	PERSON
ma-117	128	1	3.2	CARDINAL
ma-117	129	1	euler-maruyama	PERSON
ma-117	129	2	euler	PERSON
ma-117	129	3	3.1	CARDINAL
ma-117	130	1	1−	WORK_OF_ART
ma-117	131	1	∆t k+1∑ i=0	ORG
ma-117	131	2	1−	ORDINAL
ma-117	132	1	j. math	PERSON
ma-117	134	1	10.28924	CARDINAL
ma-117	134	2	7	CARDINAL
ma-117	134	3	two	CARDINAL
ma-117	134	4	1	CARDINAL
ma-117	135	1	1	CARDINAL
ma-117	135	2	2	CARDINAL
ma-117	135	3	lim k→+∞ e	PERSON
ma-117	135	4	2	CARDINAL
ma-117	135	5	3 2θ2	CARDINAL
ma-117	137	1	3.1	CARDINAL
ma-117	139	1	+ e	PERSON
ma-117	139	2	1	CARDINAL
ma-117	139	3	1−	ORDINAL
ma-117	139	4	1−	ORDINAL
ma-117	139	5	1− θ2∆t)2	MONEY
ma-117	141	1	1− θ2∆t)4e	TIME
ma-117	142	1	1− θ2∆t)2	MONEY
ma-117	144	1	1− θ2∆t)2	MONEY
ma-117	145	1	1− θ2∆t)8e	MONEY
ma-117	146	1	1−	ORDINAL
ma-117	146	2	1− θ2∆t)4 +	DATE
ma-117	146	3	1− θ2∆t)2	MONEY
ma-117	147	1	1− θ2∆t)2k+1e	PRODUCT
ma-117	147	2	1− θ2∆t)2k +	DATE
ma-117	148	1	1− θ2∆t)4 +	DATE
ma-117	148	2	1− θ2∆t)0	PRODUCT
ma-117	149	1	1−	WORK_OF_ART
ma-117	150	1	∆t k+1∑	ORG
ma-117	151	1	1−	ORDINAL
ma-117	151	2	1− θ2∆t)2k+2	LAW
ma-117	153	1	1− |1−	TIME
ma-117	154	1	1− θ2∆t)2k+2	LAW
ma-117	156	1	1	CARDINAL
ma-117	156	2	3.9	CARDINAL
ma-117	156	3	3.9	CARDINAL
ma-117	156	4	1	CARDINAL
ma-117	156	5	3.9	CARDINAL
ma-117	156	6	k → +∞	ORG
ma-117	156	7	lim	PERSON
ma-117	156	8	lim k→+∞ e	PERSON
ma-117	157	1	3 2θ2	TIME
ma-117	158	1	j. math	PERSON
ma-117	160	1	10.28924	CARDINAL
ma-117	160	2	83.3	CARDINAL
ma-117	162	1	3.1	CARDINAL
ma-117	163	1	1− θ2∆t)xk + θ3 √ ∆tzk	DATE
ma-117	163	2	3.10	CARDINAL
ma-117	163	3	euler	PERSON
ma-117	163	4	3.3	CARDINAL
ma-117	164	1	3.10	CARDINAL
ma-117	164	2	vasicek model(3.1	ORG
ma-117	165	1	k+1∑ i=0	ORG
ma-117	165	2	1−	ORDINAL
ma-117	166	1	two	CARDINAL
ma-117	166	2	1	CARDINAL
ma-117	167	1	1	CARDINAL
ma-117	167	2	2	CARDINAL
ma-117	167	3	lim k→+∞ e	PERSON
ma-117	167	4	3.4	CARDINAL
ma-117	168	1	3.10	CARDINAL
ma-117	168	2	3.1	CARDINAL
ma-117	170	1	1−	ORDINAL
ma-117	170	2	1−	ORDINAL
ma-117	170	3	two	CARDINAL
ma-117	170	4	1	CARDINAL
ma-117	171	1	1	CARDINAL
ma-117	171	2	2	CARDINAL
ma-117	171	3	lim k→+∞ e	PERSON
ma-117	171	4	2	CARDINAL
ma-117	171	5	3 2θ2	CARDINAL
ma-117	173	1	3.4	CARDINAL
ma-117	174	1	euler-maruyama	PERSON
ma-117	175	1	euler-maruyama	PERSON
ma-117	175	2	3.1	CARDINAL
ma-117	178	1	1 + θ2∆t + 1 1 +	QUANTITY
ma-117	180	1	j. math	PERSON
ma-117	182	1	10.28924	CARDINAL
ma-117	182	2	1	CARDINAL
ma-117	184	1	3.11	CARDINAL
ma-117	184	2	3.4.1	CARDINAL
ma-117	185	1	euler-maruyama	PERSON
ma-117	186	1	3.5	CARDINAL
ma-117	187	1	euler-maruyama	PERSON
ma-117	187	2	euler-maruyama	PERSON
ma-117	187	3	3.11	CARDINAL
ma-117	187	4	3.1	CARDINAL
ma-117	189	1	1 1 +	CARDINAL
ma-117	189	2	x0	ORG
ma-117	190	1	k+1∑ i=0	ORG
ma-117	191	1	two	CARDINAL
ma-117	191	2	1	CARDINAL
ma-117	193	1	1	CARDINAL
ma-117	193	2	2	CARDINAL
ma-117	193	3	lim k→∞	PERSON
ma-117	193	4	θ2 proof	PERSON
ma-117	194	1	euler-maruyama	PERSON
ma-117	194	2	3.11	CARDINAL
ma-117	198	1	1	CARDINAL
ma-117	200	1	1	CARDINAL
ma-117	203	1	1 + θ2∆t +	QUANTITY
ma-117	205	1	1 1 +	CARDINAL
ma-117	205	2	2	CARDINAL
ma-117	206	1	1	CARDINAL
ma-117	208	1	1 1 +	CARDINAL
ma-117	208	2	3	CARDINAL
ma-117	209	1	3	CARDINAL
ma-117	210	1	2	CARDINAL
ma-117	212	1	1 1 +	CARDINAL
ma-117	212	2	4	CARDINAL
ma-117	213	1	4	CARDINAL
ma-117	214	1	3	CARDINAL
ma-117	214	2	+ 1	DATE
ma-117	215	1	1 1 +	CARDINAL
ma-117	215	2	x0	ORG
ma-117	216	1	k+1∑ i=0	ORG
ma-117	217	1	3.12	CARDINAL
ma-117	217	2	3.12	CARDINAL
ma-117	217	3	1 1 +	QUANTITY
ma-117	218	1	1	CARDINAL
ma-117	219	1	j. math	PERSON
ma-117	221	1	10.28924	CARDINAL
ma-117	221	2	10or	CARDINAL
ma-117	222	1	1by	ORDINAL
ma-117	222	2	3.12	CARDINAL
ma-117	222	3	k → +∞	ORG
ma-117	222	4	lim	PERSON
ma-117	222	5	lim k→+∞ e	PERSON
ma-117	224	1	euler-maruyama	PERSON
ma-117	225	1	3.6	CARDINAL
ma-117	226	1	euler-maruyama	PERSON
ma-117	226	2	3.1	CARDINAL
ma-117	227	1	2(k+1	DATE
ma-117	228	1	∆t k+1∑ i=0	ORG
ma-117	228	2	2i	CARDINAL
ma-117	228	3	1	CARDINAL
ma-117	228	4	lim ∆t→0	PERSON
ma-117	228	5	lim k→∞	PERSON
ma-117	229	1	3 2θ2	CARDINAL
ma-117	230	1	euler-maruyama	PERSON
ma-117	230	2	3.11	CARDINAL
ma-117	231	1	3∆t	CARDINAL
ma-117	231	2	1(∆t)2	CARDINAL
ma-117	231	3	1 + θ2∆t)2	QUANTITY
ma-117	233	1	3∆t	CARDINAL
ma-117	233	2	1 + θ2∆t)2	QUANTITY
ma-117	234	1	1(∆t)2	ORG
ma-117	234	2	3∆t	CARDINAL
ma-117	237	1	2	CARDINAL
ma-117	237	2	2	CARDINAL
ma-117	237	3	1 + θ2∆t)2	QUANTITY
ma-117	237	4	1 1 +	CARDINAL
ma-117	237	5	4	CARDINAL
ma-117	238	1	4	CARDINAL
ma-117	239	1	2	CARDINAL
ma-117	240	1	2(k+1	DATE
ma-117	242	1	2i	CARDINAL
ma-117	243	1	2(k+1	DATE
ma-117	246	1	2i	CARDINAL
ma-117	247	1	1	CARDINAL
ma-117	247	2	k → +∞	ORG
ma-117	247	3	lim	PERSON
ma-117	247	4	lim k→+∞ e	PERSON
ma-117	248	1	3 2θ2	DATE
ma-117	249	1	j. math	PERSON
ma-117	251	1	10.28924	CARDINAL
ma-117	251	2	11	CARDINAL
ma-117	251	3	4	CARDINAL
ma-117	252	1	4.1	CARDINAL
ma-117	255	1	26	CARDINAL
ma-117	257	1	13	CARDINAL
ma-117	259	1	x0 ∀θ1	DATE
ma-117	259	2	∈	ORG
ma-117	259	3	4.1	CARDINAL
ma-117	260	1	1 2	CARDINAL
ma-117	260	2	4.2	CARDINAL
ma-117	260	3	1 2 θ2 2)t+θ2(bt−bs	CARDINAL
ma-117	260	4	4.3	CARDINAL
ma-117	260	5	xse	ORG
ma-117	260	6	4.3	CARDINAL
ma-117	260	7	two	CARDINAL
ma-117	262	1	0e	CARDINAL
ma-117	262	2	2θ1+θ2	CARDINAL
ma-117	262	3	4.5	CARDINAL
ma-117	262	4	4.1	CARDINAL
ma-117	263	1	lim t→∞	PERSON
ma-117	264	1	lim k→∞	PERSON
ma-117	265	1	0	CARDINAL
ma-117	265	2	2	CARDINAL
ma-117	265	3	2θ1 +	DATE
ma-117	265	4	t →∞	ORG
ma-117	266	1	lim t→∞	FAC
ma-117	267	1	0	CARDINAL
ma-117	267	2	2θ1 +	DATE
ma-117	267	3	euler-maruyama	PERSON
ma-117	267	4	andimplicit euler-maruyama	PERSON
ma-117	269	1	j. math	PERSON
ma-117	271	1	10.28924	CARDINAL
ma-117	271	2	124.2	CARDINAL
ma-117	271	3	euler-maruyama	PERSON
ma-117	272	1	euler	PERSON
ma-117	272	2	4.1	CARDINAL
ma-117	273	1	1 +	DATE
ma-117	274	1	4.6	CARDINAL
ma-117	275	1	euler-maruyama	PERSON
ma-117	276	1	4.1	CARDINAL
ma-117	277	1	euler-maruyama	PERSON
ma-117	277	2	euler	PERSON
ma-117	277	3	4.6	CARDINAL
ma-117	277	4	4.1	CARDINAL
ma-117	277	5	1 + θ2∆t)k+1e	QUANTITY
ma-117	277	6	x0	ORG
ma-117	278	1	lim ∆t→0	PERSON
ma-117	278	2	lim k→+∞ e	PERSON
ma-117	280	1	θ2 √	ORG
ma-117	281	1	1 +	CARDINAL
ma-117	284	1	0	CARDINAL
ma-117	284	2	1	CARDINAL
ma-117	285	1	1 +	CARDINAL
ma-117	285	2	1 + θ2∆t)e	DATE
ma-117	286	1	1 +	CARDINAL
ma-117	287	1	1 + θ1∆t)2	DATE
ma-117	287	2	1 + θ2∆t)e	DATE
ma-117	287	3	xk−2	ORG
ma-117	288	1	1 + θ2∆t)k+1e	QUANTITY
ma-117	288	2	x0	ORG
ma-117	288	3	1 + θ2∆t)k+1e	QUANTITY
ma-117	288	4	x0	ORG
ma-117	289	1	1	CARDINAL
ma-117	289	2	k → +∞	ORG
ma-117	289	3	lim	PERSON
ma-117	289	4	lim k→+∞ e	PERSON
ma-117	290	1	j. math	PERSON
ma-117	292	1	10.28924	CARDINAL
ma-117	292	2	134.2.2	CARDINAL
ma-117	293	1	euler-maruyama	PERSON
ma-117	294	1	4.2	CARDINAL
ma-117	295	1	euler-maruyama	PERSON
ma-117	295	2	euler	PERSON
ma-117	295	3	4.1	CARDINAL
ma-117	296	1	lim ∆t→0	PERSON
ma-117	296	2	lim k→∞	PERSON
ma-117	298	1	4.6	CARDINAL
ma-117	300	1	2	CARDINAL
ma-117	302	1	∣∣∣θ2 √	LAW
ma-117	302	2	2e	CARDINAL
ma-117	302	3	|xk(1 +	DATE
ma-117	303	1	|xt	NORP
ma-117	305	1	1	CARDINAL
ma-117	305	2	k → +∞, lim ∆t→0	ORG
ma-117	305	3	lim k→∞	PERSON
ma-117	307	1	j. math	PERSON
ma-117	309	1	10.28924	CARDINAL
ma-117	309	2	144.3	CARDINAL
ma-117	313	1	+ 1 2 θ2xtθ2	DATE
ma-117	314	1	+ 1 2 θ2 2xk	DATE
ma-117	316	1	2xk∆tz2	CARDINAL
ma-117	316	2	1 +	CARDINAL
ma-117	317	1	θ2 2xk∆tz2 kwe	PERSON
ma-117	317	2	1 +	CARDINAL
ma-117	318	1	4.7	CARDINAL
ma-117	321	1	4.3	CARDINAL
ma-117	322	1	4.7	CARDINAL
ma-117	324	1	1 +	CARDINAL
ma-117	324	2	x0	ORG
ma-117	324	3	lim ∆t→0	PERSON
ma-117	324	4	lim k→∞	PERSON
ma-117	328	1	1 +	CARDINAL
ma-117	330	1	1 +	CARDINAL
ma-117	332	1	1 2	CARDINAL
ma-117	333	1	1 +	CARDINAL
ma-117	335	1	1 + θ1∆t)e	DATE
ma-117	336	1	1 +	CARDINAL
ma-117	336	2	x0	ORG
ma-117	337	1	j. math	PERSON
ma-117	339	1	10.28924	CARDINAL
ma-117	341	1	1 +	CARDINAL
ma-117	342	1	lim	PERSON
ma-117	342	2	lim k→∞	PERSON
ma-117	345	1	4.4	CARDINAL
ma-117	346	1	4.7	CARDINAL
ma-117	346	2	4.1	CARDINAL
ma-117	347	1	2∆t	CARDINAL
ma-117	347	2	1	CARDINAL
ma-117	347	3	2θ	CARDINAL
ma-117	347	4	lim ∆t→0	PERSON
ma-117	347	5	lim k→∞	PERSON
ma-117	350	1	2xk∆tz2	CARDINAL
ma-117	352	1	∣∣∣θ2xk √ ∆tzk	DATE
ma-117	352	2	2xk∆tz2	CARDINAL
ma-117	353	1	|2)+ ∣∣∣θ2 √ ∆t ∣∣∣2 e	WORK_OF_ART
ma-117	353	2	|2)+	GPE
ma-117	353	3	2∆t	CARDINAL
ma-117	354	1	2∆t	CARDINAL
ma-117	356	1	2∆t	CARDINAL
ma-117	357	1	2∆t	CARDINAL
ma-117	357	2	k → +∞	ORG
ma-117	357	3	lim	PERSON
ma-117	357	4	lim k→∞	PERSON
ma-117	359	1	j. math	PERSON
ma-117	361	1	10.28924	CARDINAL
ma-117	361	2	164.4	CARDINAL
ma-117	362	1	euler-maruyama	PERSON
ma-117	363	1	euler-maruyama	PERSON
ma-117	363	2	iem)gives	ORG
ma-117	367	1	xk+1	TIME
ma-117	367	2	1−	TIME
ma-117	368	1	1 1−	TIME
ma-117	369	1	1	CARDINAL
ma-117	369	2	4.8	CARDINAL
ma-117	369	3	4.4.1	CARDINAL
ma-117	370	1	euler-maruyama	PERSON
ma-117	371	1	4.5	CARDINAL
ma-117	372	1	euler-maruyama	PERSON
ma-117	372	2	euler-maruyama	PERSON
ma-117	372	3	4.8	CARDINAL
ma-117	372	4	4.1	CARDINAL
ma-117	373	1	1 1− θ1∆t	TIME
ma-117	373	2	x0	ORG
ma-117	373	3	4.9	CARDINAL
ma-117	373	4	1	CARDINAL
ma-117	373	5	lim ∆t→0	PERSON
ma-117	373	6	lim k→∞	PERSON
ma-117	375	1	euler-maruyama	PERSON
ma-117	376	1	1 1−	TIME
ma-117	377	1	1−	TIME
ma-117	377	2	xk √ ∆tzk	PERSON
ma-117	378	1	1 1−	TIME
ma-117	379	1	1− θ1∆t √ ∆t	TIME
ma-117	379	2	1 1−	TIME
ma-117	380	1	1 1−	TIME
ma-117	381	1	1 1−	TIME
ma-117	381	2	2	CARDINAL
ma-117	381	3	xk−1	ORDINAL
ma-117	382	1	1 1− θ1∆t	TIME
ma-117	382	2	3	CARDINAL
ma-117	382	3	xk−2	ORG
ma-117	383	1	1 1− θ1∆t	TIME
ma-117	384	1	x0	ORG
ma-117	384	2	1 1− θ1∆t	TIME
ma-117	384	3	x0	ORG
ma-117	385	1	j. math	PERSON
ma-117	387	1	10.28924	CARDINAL
ma-117	388	1	k → +∞	ORG
ma-117	388	2	lim ∆t→0	PERSON
ma-117	388	3	lim k→∞	PERSON
ma-117	389	1	4.4.2	CARDINAL
ma-117	390	1	euler-maruyama	PERSON
ma-117	391	1	4.6	CARDINAL
ma-117	392	1	euler-maruyama	PERSON
ma-117	392	2	4.1	CARDINAL
ma-117	393	1	1 + ∣∣θ2 √	QUANTITY
ma-117	393	2	1−	TIME
ma-117	393	3	lim ∆t→0	PERSON
ma-117	393	4	lim k→∞	PERSON
ma-117	396	1	1 1−	TIME
ma-117	398	1	2 	DATE
ma-117	398	2	1 1−	TIME
ma-117	398	3	2	CARDINAL
ma-117	398	4	1 1− θ1∆t	TIME
ma-117	398	5	2	CARDINAL
ma-117	399	1	∣∣∣+θ2 √ ∆txkzk ∣∣∣2	DATE
ma-117	400	1	1 1−	TIME
ma-117	401	1	|2)+	GPE
ma-117	401	2	∣∣∣+θ2 √	DATE
ma-117	402	1	1 + ∣∣θ2 √	QUANTITY
ma-117	402	2	1− θ1∆t)2 e ( |xk |2	LAW
ma-117	402	3	1 + ∣∣θ2 √	QUANTITY
ma-117	402	4	1− θ1∆t)2	LAW
ma-117	402	5	1 + ∣∣θ2 √	QUANTITY
ma-117	402	6	1− θ1∆t)2 e (	LAW
ma-117	403	1	1 + ∣∣θ2 √	QUANTITY
ma-117	403	2	1−	TIME
ma-117	403	3	k → +∞	ORG
ma-117	403	4	lim	PERSON
ma-117	403	5	lim k→∞	PERSON
ma-117	405	1	j. math	PERSON
ma-117	407	1	10.28924	CARDINAL
ma-117	407	2	185	CARDINAL
ma-117	408	1	euler-maruyama	PERSON
ma-117	408	2	euler-maruyama	PERSON
ma-117	409	1	5.1	CARDINAL
ma-117	411	1	brownian	NORP
ma-117	412	1	1	CARDINAL
ma-117	413	1	j. math	PERSON
ma-117	415	1	10.28924	CARDINAL
ma-117	415	2	19	CARDINAL
ma-117	415	3	2	CARDINAL
ma-117	415	4	3	CARDINAL
ma-117	416	1	j. math	PERSON
ma-117	418	1	10.28924	CARDINAL
ma-117	418	2	20	CARDINAL
ma-117	418	3	4	CARDINAL
ma-117	418	4	5.2	CARDINAL
ma-117	420	1	5.2.1	CARDINAL
ma-117	420	2	vasicek	ORG
ma-117	421	1	1	CARDINAL
ma-117	421	2	2	CARDINAL
ma-117	421	3	euler	PERSON
ma-117	422	1	first	ORDINAL
ma-117	422	2	two	CARDINAL
ma-117	422	3	1	CARDINAL
ma-117	423	1	0.2280	CARDINAL
ma-117	423	2	0.2258	CARDINAL
ma-117	423	3	1	CARDINAL
ma-117	423	4	0.3007	CARDINAL
ma-117	423	5	0.2851	MONEY
ma-117	423	6	2	CARDINAL
ma-117	423	7	0.2268	MONEY
ma-117	423	8	0.2268	CARDINAL
ma-117	423	9	0.2237	CARDINAL
ma-117	424	1	5.2.2	DATE
ma-117	425	1	3	CARDINAL
ma-117	425	2	4	CARDINAL
ma-117	426	1	first	ORDINAL
ma-117	426	2	three	CARDINAL
ma-117	426	3	3	CARDINAL
ma-117	426	4	3	CARDINAL
ma-117	426	5	two	CARDINAL
ma-117	426	6	4	CARDINAL
ma-117	427	1	first	ORDINAL
ma-117	427	2	3	CARDINAL
ma-117	427	3	0.0027	CARDINAL
ma-117	427	4	0.0011	CARDINAL
ma-117	427	5	third	ORDINAL
ma-117	427	6	3	CARDINAL
ma-117	427	7	0.0111	ORG
ma-117	427	8	0.0128	CARDINAL
ma-117	428	1	4	CARDINAL
ma-117	428	2	0.0054	CARDINAL
ma-117	428	3	0.0022	CARDINAL
ma-117	428	4	0.0026	CARDINAL
ma-117	428	5	5.1	CARDINAL
ma-117	430	1	6	CARDINAL
ma-117	431	1	euler-maruyama	PERSON
ma-117	431	2	euler-maruyama	PERSON
ma-117	431	3	schemes.these	NORP
ma-117	433	1	j. math	PERSON
ma-117	435	1	10.28924	CARDINAL
ma-117	435	2	21additive	CARDINAL
ma-117	435	3	multiplicative	ORG
ma-117	436	1	second	ORDINAL
ma-117	437	1	two	CARDINAL
ma-117	438	1	1] a.m.	TIME
ma-117	439	1	lyapunov	PERSON
ma-117	440	1	j. control	PERSON
ma-117	441	1	55	CARDINAL
ma-117	441	2	1992	DATE
ma-117	441	3	531?534	CARDINAL
ma-117	443	1	i. kats	PERSON
ma-117	443	2	first	ORDINAL
ma-117	443	3	j. appl	PERSON
ma-117	445	1	1967	DATE
ma-117	445	2	478?482	DATE
ma-117	446	1	https://doi.org/10.1016/0021-8928(67)90030-5.[3	GPE
ma-117	446	2	gihman	PERSON
ma-117	446	3	a.v.	PERSON
ma-117	446	4	springer berlin heidelberg	ORG
ma-117	446	5	1972	DATE
ma-117	447	1	10.1007/978	CARDINAL
ma-117	447	2	a. friedman	PERSON
ma-117	450	1	y. saito	PERSON
ma-117	451	1	119	CARDINAL
ma-117	451	2	richard	PERSON
ma-117	451	3	mathematiques pour les systemes dynamiques	ORG
ma-117	451	4	2009).[7	CARDINAL
ma-117	451	5	second	ORDINAL
ma-117	451	6	moscow 3	FAC
ma-117	451	7	m. dekker	PERSON
ma-117	451	8	new york	GPE
ma-117	451	9	1988	DATE
ma-117	452	1	e. planten	PERSON
ma-117	452	2	n. ikeda	PERSON
ma-117	452	3	s. watanabe	PERSON
ma-117	452	4	second	ORDINAL
ma-117	453	1	north-holland mathcmnticnl	NORP
ma-117	453	2	amsterdam	GPE
ma-117	453	3	1989).[10	CARDINAL
ma-117	453	4	p.e	NORP
ma-117	453	5	kloden	GPE
ma-117	453	6	e. platen	PERSON
ma-117	453	7	springer-verlag	ORG
ma-117	453	8	p.e	NORP
ma-117	453	9	kloeden	GPE
ma-117	453	10	e. platen	PERSON
ma-117	453	11	springer berlin heidelberg	ORG
ma-117	453	12	2011).[12	CARDINAL
ma-117	453	13	x. mao	PERSON
ma-117	453	14	chichester	GPE
ma-117	453	15	1997).[13	CARDINAL
ma-117	453	16	sixth	ORDINAL
ma-117	453	17	berlin	GPE
ma-117	453	18	heidelberg	GPE
ma-117	453	19	2003).[14	CARDINAL
ma-117	453	20	s. agnes	PERSON
ma-117	453	21	springer berlin heidelberg	GPE
ma-117	453	22	2007	DATE
ma-117	454	1	https	PERSON
ma-117	454	2	//doi.org/10.1007/978-3-540-69826-5.[15	CARDINAL
ma-117	454	3	iacus	GPE
ma-117	454	4	new york	GPE
ma-117	454	5	2008	DATE
ma-117	455	1	https	PERSON
ma-117	455	2	//doi.org/10.1007/978	CARDINAL
ma-117	455	3	springer berlin heidelberg	GPE
ma-117	455	4	2006	DATE
ma-117	457	1	monte carlo	PERSON
ma-117	458	1	279-300	CARDINAL
ma-117	459	1	y. saito	PERSON
ma-117	459	2	t. mitsui	ORG
ma-117	461	1	28	CARDINAL
ma-117	461	2	269?278	CARDINAL
ma-117	463	1	https://doi.org/10.1007/978-3-540-69826-5 https://doi.org/10.1007/978-3-540-69826-5	PERSON
ma-117	464	1	j. math	PERSON
ma-117	466	1	10.28924	CARDINAL
ma-117	466	2	22	CARDINAL
ma-117	467	1	19	CARDINAL
ma-117	467	2	y. saito	PERSON
ma-117	467	3	t. mitsui	ORG
ma-117	467	4	j. numer.anal.	PERSON
ma-117	468	1	33 (1996	DATE
ma-117	468	2	2254-2267	DATE
ma-117	469	1	k. burrage	PERSON
ma-117	469	2	t. mitsui	ORG
ma-117	470	1	j. comput	PERSON
ma-117	472	1	125	CARDINAL
ma-117	472	2	171?182	TIME
ma-117	473	1	t. mitsui	GPE
ma-117	476	1	333?344	DATE
ma-117	477	1	y. saito	PERSON
ma-117	477	2	t. mitsui	PERSON
ma-117	477	3	vietnam	GPE
ma-117	477	4	j. math.30	PERSON
ma-117	477	5	2002	DATE
ma-117	477	6	551	CARDINAL
ma-117	477	7	r. sakthivel	PERSON
ma-117	477	8	p. revathi	PERSON
ma-117	477	9	n.i. mahmudov	ORG
ma-117	479	1	2013	DATE
ma-117	479	2	2013) 769257	DATE
ma-117	480	1	x. mao	PERSON
ma-117	480	2	syst	ORG
ma-117	481	1	control lett.	PERSON
ma-117	482	1	19 (1992	DATE
ma-117	483	1	71?81	PERSON
ma-117	484	1	r. khasminskii	PERSON
ma-117	484	2	springer berlin heidelberg	ORG
ma-117	484	3	2012	DATE
ma-117	485	1	org/10.1007/978-3-642-23280	CARDINAL
ma-117	485	2	aux modeles de probabilite	PERSON
ma-117	485	3	11e	ORDINAL
ma-117	485	4	amsterdam	GPE
ma-117	485	5	2014	DATE
ma-117	486	1	1	CARDINAL
ma-117	487	1	2	CARDINAL
ma-117	487	2	2.1	CARDINAL
ma-117	488	1	2.2	CARDINAL
ma-117	489	1	3	CARDINAL
ma-117	489	2	3.1	CARDINAL
ma-117	489	3	3.2	CARDINAL
ma-117	489	4	euler-maruyama	PERSON
ma-117	489	5	3.3	CARDINAL
ma-117	490	1	3.4	CARDINAL
ma-117	490	2	euler-maruyama	PERSON
ma-117	490	3	4	CARDINAL
ma-117	490	4	4.1	CARDINAL
ma-117	490	5	4.2	CARDINAL
ma-117	490	6	euler-maruyama	PERSON
ma-117	490	7	4.3	CARDINAL
ma-117	491	1	4.4	CARDINAL
ma-117	492	1	euler-maruyama	PERSON
ma-117	492	2	5	CARDINAL
ma-117	492	3	5.1	CARDINAL
ma-117	493	1	5.2	CARDINAL
ma-117	494	1	6	CARDINAL