Stability Of Stochastic Nonlinear Integro-differential Equations With Delay

In this paper,the stability of a class of stochastic nonlinear integro-differential equations with delay is studied.A new method to study the stability of stochastic differential equations with time delay has always been one of the subjects for scholars.In this paper,the constant variant formula of the equation is first established,and the expression form of the solution is given.Secondly,the inequality analysis technique is used to construct the appro-priate integral inequality with delay and exponential integral inequality with delay.Finally,using the stochastic analysis theory and the inequality analysis technique,the sufficient condi-tions of the pth moment stability?pth moment asymptotic stability?pth moment uniformly asymptotic stability?pth moment globally uniformly asymptotic stability?pth moment ex-ponential stability and pth moment globally exponential stability of the stochastic nonlinear integro-differential equations with delay are established by means of the constructed time-delay integral inequality(p>2).The examples are given to illustrate the effectiveness of the method of delay integral inequality.