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.

参考文献

[1] Blythe S, Mao X, Shah A. Razumikhin-type theorems on stability of stochastic neural networks with delays. Stoch Anal Appl, 2001, 19(1): 85–101

[2] Hale J K, Lunel S M V. Introduction to Functional Differential Equations. Springer-Verlag, 1993

[3] He X. The Lyapunov functionals for delay Lotka–Volterra-type models. SIAM J Appl Math, 1998, 58: 1222–1236.

[4] Hu Y, Wu F, Huang C. Robustness of exponential stability of a class of stochastic functional differential equations with infinite delay. Automatica, 2009, 45: 2577–2584

[5] Iserles A, Liu Y. On neutral functional-differential equations with proportional delays. J Math Anal Appl, 1997, 207: 73–95

[6] Kolmanovskii V B, Nosov V R. Stability of Functional Differential Equations. Academic Press, 1986

[7] Kolmanovskii V B, Myshkis A. Applied Theory of Functional Differential Equations. Kluwer Academic Publishers

[8] Mao X. Exponential stability in mean square of neutral stochastic differential functional equations. Systems & Control Letters, 1995, 26: 245–251

[9] Mao X. Razumikhin-type theorems on exponential stability of stochastic functional differential equations. Stoch Proc Appl, 1996, 65: 233–250

[10] Mao X. Stochatic Differential Equations and Applications. Horwood: Chichester, 1997

[11] Mao X. Razumikhin-type theorems on exponential stability of neutral stochastic functional differential. SIAM J Math Anal, 1997, 28: 389–401

[12] Mao X. Comments on “an improved Razumikhin-type theorem and its applications”. IEEE Trans Aut Contr, 1997, 43(3): 429–430

[13] Mao X, Rodkina A, Koroleva N. Razumikhin-type theorems for neutral stochastic functional differential equations. Funct Differ Equ, 1998, 5(1/2): 195–211

[14] Mao X, Lam J, Xu S, Gao H. Razumikhin method and exponential stability of hybrid stochastic delay interval systems. J Math Anal Appl, 2006, 314: 45–66

[15] Randielovic J, Jankovic S. On the pth moment exponential stability criteria of neutral stochastic functional differential equations. J Math Anal Appl, 2007, 326: 266–280

[16] Razumikhin B S. On the stability of systems with a delay. Rossiiskaya Akademiya Nauk: Prikladnaya Matematika i Mekhanika, 1956, 20: 500–512

[17] Razumikhin B S. Application of Lyapunov’s method to problems in the stability of systems with a delay. Rossiiskaya Akademiya Nauk: Avtomatika i Telemekhanika, 1960, 21: 740–749

[18] Wu F, Xu Y. Stochastic Lotka-Volterra population dynamics with infinite delay. SIAM J Appl Math, 2009, 70: 641–657

[19] Wu F, Hu S, Huang C. Robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay. System & Control Letter, 2010, 59: 95–202

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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