Diffusion approximation type theorem for a system with weakly ergodic Markov perturbations

We develop a method of proving limit theorems (CLT, and more generally diffusion approximation type theorems) for systems with random entries given by Markov processes which intrinsic memory. The method mainly exploits weak ergodic rates for the underlying Markov processes and is, to a great extent, insensitive w.r.t. to the structure of the process. The talk is based on a joint research with A.Veretennikov (Leeds, UK).