Stability And Numerical Solutions Of SDEs Driven By Stable Processes With Markov Switching

In finance,economics,biology and many other disciplines,hybrid systems are often used to describe the coexistence of internal stochastic dynamic systems and external stochastic environments.In order to study the non-Gaussian fluctuation,we con-sider the stability and numerical solutions of stochastic differential equations driven by ?-stable processes,??(1,2),with Markov switching.Firstly,the existence and uniqueness of solutions for non-Gaussian hybrid systems are given by using the tech-nique of Lyapunov function.Then the long time behaviour of a class of asymmetric non-Gaussian hybrid systems is discussed and a series of criteria for the stability of the systems are obtained.The results of the asymptotic behaviour of the system include a class of nonlinear systems,which meets the needs of many practical applications.At the same time,we consider the numerical solutions of a class of symmetric non-Gaussian hybrid systems.The Euler-Maruyama method is constructed,and the convergence rate between numerical solutions and explicit,solutions is given by Burkholder-Davis-Gundy inequality.