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Exponential stability of the exact and numerical solutions for neutral stochastic delay differential equations
Zong, Xiaofeng1; Wu, Fuke2
2016
Source PublicationAPPLIED MATHEMATICAL MODELLING
ISSN0307-904X
Volume40Issue:1Pages:19-30
AbstractThis 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.
KeywordNeutral stochastic delay differential equations Moment exponential stability Euler Maruyama method Backward Euler Maruyama method
DOI10.1016/j.apm.2015.05.001
Language英语
Funding ProjectNational Natural Science Foundations of China[11422110] ; National Natural Science Foundations of China[61473125]
WOS Research AreaEngineering ; Mathematics ; Mechanics
WOS SubjectEngineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS IDWOS:000367020900002
PublisherELSEVIER SCIENCE INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21596
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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