题目：Euler-Maruyama’s approximations of regime-switching jump diffusion processes
摘要：For a kind of regime-switching jump diffusion process (Xt, Zt)t≥0, under some mild conditions, it is exponentially ergodic with invariant measure µ. We aim to approximate µ using the Euler-Maruyama (EM) scheme with constant step γ and decreasing step sequence (γn)n≥1, respectively. We show that the error between µ and the invariant measure associated with the EM scheme is bounded by O(γ1/2) (in the constant-step case) and O(γ1/2 ) (in the decreasing-step case). In particular, we derive a faster convergence rate for the additive model and the continuous model. For the constant step approximation we use the Stein’s method, while for the variable step we mainly rely on the method recently developed in Pagg`es and Panloup (2020). This talk is based on a recent work together with Chen, Jin and Su.