On the application of ergodic condition to averaging principle for multiscale stochastic systems

Jinghai Shao

Published 2022-12-04Version 1

This work concerns the asymptotic behavior for fully coupled multiscale stochastic systems. We focus on studying the impact of the ergodicity of the fast process on the limit process and the averaging principle. The key point is to investigate the continuity of the invariant probability measures relative to parameters in various distances over the Wasserstein space. An illustrative example is constructed to show the complexity of the fully coupled multiscale system compared with the uncoupled multiscale system, which shows that the averaged coefficients may become discontinuous even they are originally Lipschitz continuous and the fast process is exponentially ergodic.