Stability of nonlinear stochastic Volterra difference equations with continuous time

CHEN Ling; GUO Lifang; CHEN Min

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Stability of nonlinear stochastic Volterra difference equations with continuous time

CHEN Ling 1 #,GUO Lifang 2,CHEN Min 2 *

1.Department of Mathematics, Ningbo University

2.Department of Mathematics, Ningbo University, Ningbo 315211

*Correspondence author

#Submitted by

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Funding: This paper is supported by the National Natural Science Foundation of China（No.No.10571095）

Opened online:16 May 2011

Accepted by: none

Citation: CHEN Ling,GUO Lifang,CHEN Min.Stability of nonlinear stochastic Volterra difference equations with continuous time[OL]. [16 May 2011] http://en.paper.edu.cn/en_releasepaper/content/4425936

In recent years, many authors investigated the systems of stochastic difference equations with discrete time or the systems of numerical solution for stochastic difference equations with continue time. Lyapunov functionals are used to study the hereditary systems about problems of stability and optimal control. Besides, Lyapunov functionals construction has been widely used to discuss the stability for stochastic differential equations with delay and for stochastic difference equations with discrete time. Based on the general method of Lyapunov functionals construction, the stability of nonlinear stochastic Volterra difference equations is studied here. Particularly, the system considered here have continuous time. Sufficient conditions are obtained not only to ensure the mean square stability to nonlinear stochastic Volterra difference equations with continuous time but also the asymptotical mean square quasi-stability for this system. Furthermore, it is easy to know the considered system is mean square integrable when the system here is asymptotical mean square quasi-stable.

Keywords:Nonlinear stochastic difference equations; Stability; Lyapunov functional construction; Continuous time

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