Exponential stability of stochastic differential delay equations

Abstract

In this paper we study both pth moment and almost sure exponential stability of the stochastic differential delay equation . Introduce the corresponding stochastic differential equation (without delay) and assume it is exponentially stable which is guaranteed by the existence of the Lyapunov function. We shall show that the original stochastic differential delay equation remains exponentially stable provided the time lag τ is sufficiently small, and a bound for such τ is obtained

Keywords:

• Stochastic differential delay equations
• Lyapunov function
• Lyapunov exponent
• Borel-Cantelli lemma
• AMS 1991 Classifications' 60H10, 34K30

^†Author for Correspondence. Tel. [phone]. ext 3812

^*Supported by the RD fund of Strathclyde University

^†Author for Correspondence. Tel. [phone]. ext 3812

^*Supported by the RD fund of Strathclyde University

Notes

^†Author for Correspondence. Tel. [phone]. ext 3812

^*Supported by the RD fund of Strathclyde University