Exponential stability of the exact and numerical solutions for neutral stochastic delay differential equations
文献类型：期刊论文
| 作者 | Zong, Xiaofeng1; Wu, Fuke2 |
| 刊名 | APPLIED MATHEMATICAL MODELLING
 |
| 出版日期 | 2016 |
| 卷号 | 40期号:1页码:19-30 |
| 关键词 | Neutral stochastic delay differential equations Moment exponential stability Euler Maruyama method Backward Euler Maruyama method |
| ISSN号 | 0307-904X |
| DOI | 10.1016/j.apm.2015.05.001 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000367020900002 |
| 出版者 | ELSEVIER SCIENCE INC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/21595]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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