Strong Convergence Rate for Two-Time-Scale Jump-Diffusion Stochastic Differential Systems

We study a two-time-scale system of jump-diffusion stochastic differential equations. The main goal is to study the convergence rate of the slow components to the effective dynamics. The convergence established here is in the strong sense, i. e., uniformly in time. For the ergodicity assumptions, we use the existence of a Lyapunov function to control the return times. This assumption is weaker than the one- sided Lipschitz condition, frequently used for deriving rates.