| 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 α-stable processes,α∈(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. |
