The Long Time Behavior Of Stochastic Differential Equations With Markovian Switching And Its Application

Pth moment exponential stability and the weak convergence of stochastic differential equations with Markovian switching and time-varying delays are studied in this paper, and then the weak convergence of stochastic recurrent neural networks with Markovian switching and time-varying delay is discussed.This paper is divided into five chapters.In Chapter 1, we mainly introduce the background, significance of this study,and then introduce the main content and innovation of the research.In Chapter 2, pth moment exponential stability for stochastic differential equations with Markovian switching and time-varying delay are discussed. By using generalized It(?) formula, generalized Halanay inequality and stochastic analysis technique, some novel sufficient conditions on pth moment exponential stability of stochastic differential equations with Markovian switching and time-varying delays are derived. The conditions of time delays bounded, derivable and its derivative is less than 1 are removed,which are required in typically literature. Moreover, some examples and numerical simulations are also provided.In Chapter 3, the weak convergence of stochastic differential equations with Markovian switching and time-varying delay are discussed. By using generalized It(?) formula, Lyapunov function, generalized Halanay inequality and stochastic analysis technique, algebraic expression on weak convergence is given, and the examples and numerical simulation are given.In Chapter 4, the weak convergence of stochastic recurrent neural networks with Markovian switching and time-varying delays are discussed. By using generalized Halanay inequality and stochastic analysis technique, some sufficient conditions on the weak convergence are given. The examples and numerical simulations are provided.In Chapter 5, the conclusions of this paper are summarized.