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The moment exponential stability criterion of nonlinear hybrid stochastic differential equations and its discrete approximations
Zong, Xiaofeng1; Wu, Fuke2; Huang, Chengming2
2016-12-01
Source PublicationPROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
ISSN0308-2105
Volume146Issue:6Pages:1303-1328
AbstractBased on the martingale theory and large deviation techniques, we investigate the pth moment exponential stability criterion of the exact and numerical solutions to hybrid stochastic differential equations (SDEs) under the local Lipschitz condition. This new stability criterion shows that Markovian switching can serve as a stochastic stabilizing factor by its logarithmic moment-generating function. We also investigate the pth moment exponential stability of Euler-Maruyama (EM), backward EM (BEM) and split-step backward EM (SSBEM) approximations for hybrid SDEs and show that, under the additional linear growth condition, the EM method can share the mean-square exponential stability of the exact solution for sufficiently small step size. However, the BEM method can work without the linear growth condition. We further investigate the SSBEM method under a coupled condition.
Keywordhybrid SDEs moment exponential stability Markov chain Euler-Maruyama approximation backward Euler-Maruyama approximation split-step backward Euler-Maruyama approximation
DOI10.1017/S030821051500089X
Language英语
Funding ProjectChina Postdoctoral Science Foundation[2015M571146] ; National Science Foundation of China[61473125] ; National Science Foundation of China[11422110] ; National Natural Science Foundation of China[11371157] ; National Natural Science Foundation of China[91130003]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000388874800008
PublisherCAMBRIDGE UNIV PRESS
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/24244
Collection中国科学院数学与系统科学研究院
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China
Recommended Citation
GB/T 7714
Zong, Xiaofeng,Wu, Fuke,Huang, Chengming. The moment exponential stability criterion of nonlinear hybrid stochastic differential equations and its discrete approximations[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,2016,146(6):1303-1328.
APA Zong, Xiaofeng,Wu, Fuke,&Huang, Chengming.(2016).The moment exponential stability criterion of nonlinear hybrid stochastic differential equations and its discrete approximations.PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS,146(6),1303-1328.
MLA Zong, Xiaofeng,et al."The moment exponential stability criterion of nonlinear hybrid stochastic differential equations and its discrete approximations".PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS 146.6(2016):1303-1328.
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