Almost sure and moment exponential stability of predictor-corrector methods for stochastic differential equations

被引：4

作者：

Niu, Yuanling ^{[1
,2
]}

Zhang, Chengjian ^{[1
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Cent S Univ, Sch Math & Stat, Changsha 410075, Hunan, Peoples R China

来源：

JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY | 2012年 / 25卷 / 04期

关键词：

Almost sure stability; moment exponential stability; numerical experiment; stochastic differential equations; NUMERICAL-SIMULATION; ASYMPTOTIC STABILITY; THETA METHOD; SYSTEMS;

D O I：

10.1007/s11424-012-0183-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper deals with almost sure and moment exponential stability of a class of predictor-corrector methods applied to the stochastic differential equations of It-type. Stability criteria for this type of methods are derived. The methods are shown to maintain almost sure and moment exponential stability for all sufficiently small timesteps under appropriate conditions. A numerical experiment further testifies these theoretical results.

引用

页码：736 / 743

页数：8

共 50 条

[1] ALMOST SURE AND MOMENT EXPONENTIAL STABILITY OF PREDICTOR-CORRECTOR METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS
Yuanling NIU
Chengjian ZHANG
Journal of Systems Science & Complexity, 2012, 25 (04) : 736 - 743
[2] Almost sure and moment exponential stability of predictor-corrector methods for stochastic differential equations
Yuanling Niu
Chengjian Zhang
Journal of Systems Science and Complexity, 2012, 25 : 736 - 743
[3] Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations
Higham, Desmond J.
Mao, Xuerong
Yuan, Chenggui
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2007, 45 (02) : 592 - 609
[4] Strong predictor-corrector Euler methods for stochastic differential equations
Bruti-Liberati, Nicola
Platen, Eckhard
STOCHASTICS AND DYNAMICS, 2008, 8 (03) : 561 - 581
[5] Almost sure exponential stability of the θ-method for stochastic differential equations
Chen, Lin
Wu, Fuke
STATISTICS & PROBABILITY LETTERS, 2012, 82 (09) : 1669 - 1676
[6] Almost Sure Exponential Stability of Stochastic Differential Delay Equations
Zhang, Wei
Song, M. H.
Liu, M. Z.
FILOMAT, 2019, 33 (03) : 789 - 814
[7] ALMOST SURE EXPONENTIAL STABILITY OF STOCHASTIC DIFFERENTIAL DELAY EQUATIONS
Guo, Qian
Mao, Xuerong
Yue, Rongxian
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2016, 54 (04) : 1919 - 1933
[8] STABILITY PROPERTIES OF PREDICTOR-CORRECTOR METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS
CHASE, PE
JOURNAL OF THE ACM, 1962, 9 (04) : 457 - &
[9] On the MS-stability of predictor-corrector schemes for stochastic differential equations
Tocino, A.
Zeghdane, R.
Senosiain, M. J.
MATHEMATICS AND COMPUTERS IN SIMULATION, 2021, 180 (180) : 289 - 305
[10] Almost sure exponential stability of neutral stochastic differential difference equations
Huazhong Univ of Science and, Technology, Wuhan, China
J Math Anal Appl, 2 (554-570):

← 1 2 3 4 5 →