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

Let X t , Z t t ≥ 0 be the regime-switching jump diffusion process with invariant measure μ . We aim to approximate μ using the Euler–Maruyama (EM) scheme with decreasing step sequence Γ = ( γ n ) n ∈ 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 μ and the invariant measure associated with the EM scheme is bounded by O ( γ n ) . In particular, we derive a better convergence rate O ( γ n ) for the additive case and the continuous case.