Stability Of Solutions For A Class Of Impulsive And Delay Stochastic Differential Equations

Functional differential equation theory in real life has important theory and application value,and the stability of impulsive stochastic differential equations and delay stochastic differential equations is of great interest to many researchers.This paper uses the fixed point theory,Lyapunov stability theorem and linear matrix inequality to study the stability of solutions of a class of impulsive stochastic differential equations and a class of time delay stochastic differential equations,and we have obtained the criterion for the stability of the solution of these two types of equations.The content structure of the full text is divided into three chapters.The first chapter concisely narrates the significance of the research and development of the impulsive stochastic differential system and time delay stochastic differential system,as well as the relevant research results of the stability of solutions of the impulsive and time-delay stochastic differential system.Finally,the main work of this article is introduced simply.In the second chapter,the stability of solutions of a class of impulsive stochastic differential equations (?) is discussed by using Banach fixed point theory and Lyapunov functional method.Finally,the judgment basis of the stability of the equations are got.When using the fixed point theory to study the stability of the solution,this chapter first gives the mild solution of the study object and then use the fixed point theorem to obtain conclusion that the mean square exponential stability of the mild solution of the equation.When using the Lyapunov functional method to study the stability of the solution of the equation,this chapter construct the related Lyapunov functional,as well as use theI to?calculus formula and stochastic analysis techniques to prove the stability of the solution.In Chapter 3,we discuss the stability of solutions of a class of time delay stochastic differential equations (?) by using the fixed point theorem and constructing the Lyapunov-Krasovskii functional as well as with the help of the technique of linear matrix inequality.Give the mild solution of the equation firstly,and then use the fixed point theorem to prove the stability of the solution.At the same time,by constructing a new Lyapunov-Krasovskii functional and combining linear matrix inequality,the stability criterion of the solution of time delay stochastic differential equation are obtained.