We extended recently in various works the classical ergodic theory that was known for stationary processes to random periodic processes, random quasi-periodic processes, and sublinear Markovian semigroups. I will discuss their fundamental distinctions from the classical case and mention briefly their intradisciplinary connections with other areas. This talk is based on joint works with Chunrong Feng, Yu Liu, Yujia Liu, Baoyou Qu, Johnny Zhong.

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