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| Stability of a Neutral Stochastic Functional Differential Equations | |
| 引用本文： | LI Bi-wen. Stability of a Neutral Stochastic Functional Differential Equations[J]. 武汉大学学报:自然科学英文版, 2005, 10(6): 957-960. DOI: 10.1007/BF02832447 |
| 作者姓名： | LI Bi-wen |
| 作者单位： | [1]Department of Mathematics, Hubei Normal University, Huangshi 435002, Hubei, China [2]Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China |
| 基金项目： | Supported by the National Natural Science Foundation of China （19531070） and the Major Project Foundation of Hubei Province Education Department （2004Z001） |
| 摘 要： | 0IntroductionStmoachnyas stiocp dhiifsftiecraetnetdia ld yenqauamtiicoanls s ycsatne mbse i uns epdh ytsoic adle s,cbriibo-elogical , medical andsocial sciences ,they have beenstudiedformore thanfifty years and developed very quicklly,in particu-lar ,Lyapunov’s second method has been developed to dealwith stochastic stability by many authcrs ,e.g.Ref .[1-3] in-troduced a class of neutral stochastic functional differentialequations .But sofar such equations have been discussed alit-tle unlike … |
| 关 键 词： | Lyapunov函数 随机函数 微分方程 稳定性 渐进线 |
| 文章编号： | 1007-1202（2005）06-0957-04 |
| 收稿时间： | 2004-12-20 |
Stability of a neutral stochastic functional differential equations |
|
| Li Bi-wen. Stability of a neutral stochastic functional differential equations[J]. Wuhan University Journal of Natural Sciences, 2005, 10(6): 957-960. DOI: 10.1007/BF02832447 | |
| Authors: | Li Bi-wen |
| Affiliation: | (1) Department of Mathematics, Hubei Normal University, 135002 Huangshi, Hubei, China;(2) Department of Mathematics, Huazhong University of Science and Technology, 430074 Wuhan, Hubei, China |
| Abstract: | Sufficient condition for stochastic unifrom stability of a neutral stochastic functional differential equation is given, especially, new techniques are developed to cope with the neutral delay case, we obtained the sufficient condition for asymptotic stability of neutral stochastic differential delay equations. Due to the new techniques developed in this paper, the results obtained arc very general and useful. The theory developed here gives a unified treatment for various asymptotic estimates e.g. exponential and polynomial bounds. |
| Keywords: | Lyapunov function D operator It?’ s formula stochastic unifrom stabillty asymptotic stability |
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