The Numerical Invariant Measure Of Stochastic Differential Equations With Markovian Switching

This paper investigates stochastic differential equations with Markovian switching.First of all, we show the existence and uniqueness of invariant measure for the equation when the drift coefficient and diffusion coefficient satisfy certain conditions. We study the existence and uniqueness of invariant measure for the numerical solutions of the backward Euler method. Thus we improve the conclusions in [25] and remove the condition that the drift coefficient satisfies. We reveal that the numerical invariant measure converges to the underlying one in the Wasserstein metric. In the end, we give two examples to illustrate the conclusions.