Exponential stability of the exact and numerical solutions for neutral stochastic delay differential equations

doi:10.1016/j.apm.2015.05.001

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	Exponential stability of the exact and numerical solutions for neutral stochastic delay differential equations
	Zong, Xiaofeng 1; Wu, Fuke 2
	2016
发表期刊	APPLIED MATHEMATICAL MODELLING
ISSN	0307-904X
卷号	40 期号:1 页码:19-30
摘要	This paper is concerned with pth moment and almost sure exponential stability of the exact and numerical solutions of neutral stochastic delay differential equations (NSDDEs). Moment exponential stability criteria of the continuous and discrete solutions are established by virtue of the Lyapunov method. Then the almost sure exponential stability criterion is derived by the Chebyshev inequality and the Borel-Cantelli lemma. We also examine conditions under which the numerical solution can reproduce the exponential stability of exact solution. It is shown that the linear growth condition is necessary for Euler-Maruyama (EM) method to maintain the moment exponential stability of the exact solution. If the drift coefficient of NSDDE satisfies the one-sided Lipschitz condition, EM method may break down, but we show that the backward EM (BEM) method can share the mean square exponential stability of the exact solution. (C) 2015 Elsevier Inc. All rights reserved.
关键词	Neutral stochastic delay differential equations Moment exponential stability Euler Maruyama method Backward Euler Maruyama method
DOI	10.1016/j.apm.2015.05.001
语种	英语
资助项目	National Natural Science Foundations of China[11422110] ; National Natural Science Foundations of China[61473125]
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000367020900002
出版者	ELSEVIER SCIENCE INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/21596
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, Inst 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. Exponential stability of the exact and numerical solutions for neutral stochastic delay differential equations[J]. APPLIED MATHEMATICAL MODELLING,2016,40(1):19-30.
APA	Zong, Xiaofeng,&Wu, Fuke.(2016).Exponential stability of the exact and numerical solutions for neutral stochastic delay differential equations.APPLIED MATHEMATICAL MODELLING,40(1),19-30.
MLA	Zong, Xiaofeng,et al."Exponential stability of the exact and numerical solutions for neutral stochastic delay differential equations".APPLIED MATHEMATICAL MODELLING 40.1(2016):19-30.