An averaging principle for stochastic switched systems with Lé vy noise

Abstract

In this paper, we present an averaging method for stochastic switched systems with L é vy noise under non‐Lipschitz condition. With the help of successive approximation method and Bihari's inequality, the existence and uniqueness of the solutions of original and averaged systems are proved. Then, under suitable assumptions, we show that the solution of stochastic switched system with L é vy noise strongly converges to the solution of the corresponding averaged equation.