KMS Of Academy of mathematics and systems sciences, CAS
| Exponential stability of the exact and numerical solutions for neutral stochastic delay differential equations | |
| Zong, Xiaofeng1; Wu, Fuke2 | |
| 2016 | |
| Source Publication | APPLIED MATHEMATICAL MODELLING
 |
| ISSN | 0307-904X |
| Volume | 40Issue:1Pages:19-30 |
| Abstract | 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. |
| Keyword | Neutral stochastic delay differential equations Moment exponential stability Euler Maruyama method Backward Euler Maruyama method |
| DOI | 10.1016/j.apm.2015.05.001 |
| Language | 英语 |
| Funding Project | National Natural Science Foundations of China[11422110] ; National Natural Science Foundations of China[61473125] |
| WOS Research Area | Engineering ; Mathematics ; Mechanics |
| WOS Subject | Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics |
| WOS ID | WOS:000367020900002 |
| Publisher | ELSEVIER SCIENCE INC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/21596 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Zong, Xiaofeng |
| Affiliation | 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 |
| 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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