The Research On Stochastic Differential Equations Driven By Fractional Brownian Motions With Markov Switching

With the continuous development and progress of science and technology,stochastic differential equations with Markov switching have been widely used in many fields such as biology,ecology,economics and mathematical finance.In recent years,the theory of stochastic differential equations driven by non-L?evy processes is progressing rapidly and has attracted plenty of attention.Based on the above works,we study the stability of stochastic differential equations driven by fractional Brownian motions with Markov switching under perturbation of transition rate matrices.This paper consists of three parts.In Chapter 1,we introduce the background and preliminaries on fractional calculus,fractional Brownian motion and Markov chain.In Chapter 2,we mainly study stochastic differential equations driven by fractional Brownian motion B~H(Hurst parameter H?(1/2,1))with Markov switching.When the coefficients satisfy regular conditions,we obtain the stability of the solutions of this type of equations under perturbation of transition rate matrices via the Wasserstein distance.In Chapter 3,we mainly discuss stochastic differential equations driven by fractional Brownian motion B~H(Hurst parameter H?(0,1/2))with Markov switching.When the coefficients satisfy locally unbounded conditions,we derive the stability of the solutions of this kind of equations under perturbation of transition rate matrices via the Fortet-Mourier distance.