Exponential Ergodicity for SDEs Driven by α-Stable Processes with Markovian Switching in Wasserstein Distances

In this paper, we consider the ergodicity for stochastic differential equations driven by symmetric α-stable processes with Markovian switching in Wasserstein distances. Some sufficient conditions for the exponential ergodicity are presented by using the theory of M-matrix, coupling method and Lyapunov function method. As applications, the Ornstein-Uhlenbeck type process and some other processes driven by symmetric α-stable processes with Markovian switching are presented to illustrate our results. In addition, under some conditions, an explicit expression of the invariant measure for Ornstein-Uhlenbeck process is given.