Variable-Step Euler-Maruyama Approximations of Regime-Switching Jump Diffusion Processes

Let (X-t, Z(t))(t >= 0) be the regime-switching jump diffusion processwith invariant measure mu. We aim to approximate mu using the Euler-Maruyama (EM) scheme with decreasing step sequence Gamma = (gamma(n))(n is an element of N). Under some appropriate dissipative conditions and uniform ellipticity assumptions on the coefficients of the related stochastic differential equation (SDE), we show that the error between mu and the invariant measure associated with the EM scheme is bounded by O(root gamma n). In particular, we derive a better convergence rate O(gamma n) for the additive case and the continuous case.