RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

doi:10.1016/S0252-9602(11)60312-3

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (4): 1245-1258.doi: 10.1016/S0252-9602(11)60312-3

RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

吴付科¹, 胡适耕¹, 毛学荣²

1.School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China； 2.Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK

收稿日期:2008-10-07 修回日期:2010-08-18 出版日期:2011-07-20 发布日期:2011-07-20
基金资助:
Supported by NSFC (11001091) and Chinese University Research Foundation (2010MS129).

RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

WU Fu-Ke¹, HU Shi-Geng¹, MAO Xue-Rong²

1.School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China； 2.Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK

Received:2008-10-07 Revised:2010-08-18 Online:2011-07-20 Published:2011-07-20
Supported by:
Supported by NSFC (11001091) and Chinese University Research Foundation (2010MS129).

摘要/Abstract

摘要：

This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with un-bounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.

关键词: neutral stochastic functional differential equations, Razumikhin-type theo-rem, stability, exponential stability, polynomial stability

Abstract:

Key words: neutral stochastic functional differential equations, Razumikhin-type theo-rem, stability, exponential stability, polynomial stability

中图分类号:

34K40

吴付科, 胡适耕, 毛学荣. RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY[J]. 数学物理学报(英文版), 2011, 31(4): 1245-1258.

WU Fu-Ke, HU Shi-Geng, MAO Xue-Rong. RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY[J]. Acta mathematica scientia,Series B, 2011, 31(4): 1245-1258.

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RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

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