The P-moment Stability Of Stochastic Functional Differential Equation With Poisson Jump

Since the theory established for stochastic differential equation,it has been widely used in various fields.Many practical systems may have delay phenomenon or sudden changes due to external impact,yet by traditional stochastic differen-tial equations can not describe the systems very well.Considering these possible situations,in recent years,people have introduced stochastic functional differen-tial equations with Poisson jump.Since stability is the core issue in the study of stochastic differential dynamic systems,so the stability of stochastic functional d-ifferential equations with Poisson jumps has been a concern of many scholars for many years.However,the study of this kind of problem mainly focuses on the ex-ponential stability of the equation at present.In fact,many of these equations are not exponentially stable,but are stable in other ways.For example,the p-moment stability,the p-moment uniform stability,the p-moment asymptotic stability and the p-moment uniform asympt.otic stability also have important theoretical signifi-cance and practical value.Therefore,This paper studies these p-moment stability problems of stochastic functional differential equations with Poisson jumps.The main research results of this paper are as follows:(1)In this paper,the definitions of p-moment stability of stochastic functional differential equations with Poisson jumps are given.Under the assumptions that the solution of this equation is existence and unique,based on stochastic analysis theory,Lyapunov function method,Ito formula and some inequalities,sufficient conditi'ons of p-moment stability,p-moment uniform stability,p-moment asymptotic stability,p-moment uniform asymptotic stability and p-moment instability of this equation are given respectively.(2)Based on the conclusions in(1),the p-moment stability of stochastic dif-ferential equations with time-varying delays and Poisson jumps is further discussed,and sufficient conditions of some kinds of p-moment stability of this equation are obt ained.(3)The validity and practicability of the obtained conditions are verified by numerical examples.