The paper is a sequel to the paper [Veretennikov A.Yu., Kulik A.M. Diffusion approximation for systems with weakly ergodic Markov perturbations I. Submitted to Teor. Imov. Mat. Stat.]. Corollaries are given in some particular cases of self-contained interest. An example of the process solution to a Lґevy driven SDE is considered, which illustrates that the assumptions imposed on the process X within the scopes of our approach can be verified in an effective way.
