Study On Stability Of Solutions Of Some Kinds Of Stochastic Functional Differential Equations

For stochastic functional differential equations,the stability study of the solution has always been a central topic.The methodology used in existing literature to study the stability of stochastic functional differential equations is basically based on the Lyapunov function met,hod and the Razumikhin-type theorem,but it is not easy to find a Lyapunov function for random multification equations.In the study of stochastic partial functional different,ial equat,ions,the compression theory offers a concise approach that,under sometimes easily examinable assumptions,systems can be demonstrated to have trajectory convergent multiplier stability properties.This paper is mainly studying the proposed compression and index compression of the stochastic partial functional differential equations,while giving a stability judgment of the stability of the solution of neutral stochastic functional differential equations driven by the time-changed Brownian motion.The main contents of this paper are as follows:In chapter 1,the core work of this paper as well as the objective,significance,and present research status of the study on the stability of stochastic functional differential equations are briefly introduced.In chapter 2,we introduce some preliminary knowledge and some important inequalities needed to study the problem.In chapter 3,the Ito formula is applied to obtain the determination conditions for the quasi contraction of the solution of the stochastic partial functional differential equation,and the determination conditions for the exponentially contraction of the equation are further derived.In chapter 4,the determination condition for exponential stability of the solution of neutral stochastic functional differential equations driven by the time-changed Brownian motion is proved using the Ito formula,which is enhanced for comparison with the determination condition of the previously published article.