Using Stein's Method to Analyze Euler-Maruyama Approximations of Regime-Switching Jump Diffusion Processes

For a kind of regime-switching jump diffusion process (X-t, Z(t))(t >= 0), under some conditions, it is exponentially ergodic under the weighted total variation distance with ergodic measure mu. We use the Euler-Maruyama scheme of the process (X-t, Z(t))(t >= 0) which has an ergodic measure mu(eta) (eta is the step size of the Euler-Maruyama scheme) to approximate the ergodic measure mu. Furthermore, we use Stein's method to prove that the convergence rate of mu(eta) to mu is eta(1/2) in terms of some function-class distance dG(mu, mu(eta)).