The Study On Stability Of Neutral Stochastic Functional Differential Equations

It is well known that the trend of neutral functional differential equations depends not only on the current and past time states,but also on the rate of change in the past time states.Such systems can be characterized by neutral stochastic functional differential equations when stochastic disturbance is considered.Because its exact solution is difficult to give,it is generally approximate by numerical methods.Many results discuss the stability of numerical solutions of this equation using Rzaumikhin theorem.For neutral stochastic functional differential equation with Markov switching and proportional delay,neutral term and Markov switching not only coexist,but also related to the state of the past period and the rate of change in the state.There are very few stability studies of such equations.This paper focuses on the stability of numerical solutions of neutral stochastic functional differential equations and the stability of hybrid pantograph neutral stochastic functional differential equations with Markov switching.The specific research content is as follows:In chapter 1,we mainly introduce the research background and significance of the topic selection,briefly expounds the main innovation points of this paper,and some preparatory knowledge.In chapter 2,when the drift term and dissipation term satisfy the global Lipschitz condition and the compressibility condition,the discrete random version of Razumikhin type theorem is established to analyze the stability of Euler-Maruyuma numerical solutions of neutral stochastic functional differential equations;In addition,the almost sure exponential stability of such equations is discussed by using Borel-Cantelli lemma and stochastic analysis theoryIn chapter 3,by using multiple Lyapunov functions,extending the ?Ito formula and the nonnegative semi-martingale convergence theorem,the boundedness,exponential stability and almost sure exponential stability of hybrid pantograph neutral stochastic functional differential equations with Markov switching are established...