The moment exponential stability criterion of nonlinear hybrid stochastic differential equations and its discrete approximations

doi:10.1017/S030821051500089X

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	The moment exponential stability criterion of nonlinear hybrid stochastic differential equations and its discrete approximations
	Zong, Xiaofeng 1; Wu, Fuke 2; Huang, Chengming 2
	2016-12-01
发表期刊	PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
ISSN	0308-2105
卷号	146 期号:6 页码:1303-1328
摘要	Based 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.
关键词	hybrid SDEs moment exponential stability Markov chain Euler-Maruyama approximation backward Euler-Maruyama approximation split-step backward Euler-Maruyama approximation
DOI	10.1017/S030821051500089X
语种	英语
资助项目	China 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研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000388874800008
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24244
专题	中国科学院数学与系统科学研究院
通讯作者	Zong, Xiaofeng
作者单位	1.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
推荐引用方式 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.