Ergodicity of Random Periodic Processes and Random Quasi-periodic Processes

In this talk, I will first present main ideas of recent results of the ergodicity of random periodic processes. They include random periodic paths, periodic measures, their “equivalence”, their lifts, construction of invariant measures, ergodicity and spectral characteristics. Then I will present random quasi-periodic processes, quasi-periodic measures and lifted invariant measure and ergodicity. Application to concrete SDEs such as stochastic resonance model of Benzi, Parisi, Stera and Vulpiani will also be given. This talk is based on a series of joint work with Chunrong Feng, Yu Liu, Yujia Liu, Baoyou Qu and Johnny Zhong.