Due to the existence of uncertain factors or people's limited knowledge of our world, many systems need to consider the influence of random factors. So we need to consider the dynamical behavior of a system evolving over time under the action of random factors, which leads to the generation of random dynamic systems. In this talk, we will focus on the topics of recurrent motions for stochastic differential equations and stability of invariant sets or invariant measures under stochastic perturbations; the former topic is closely related to the limit distribution of inhomogeneous Markov processes and the latter one is closely related to Kolmogorov's problem on the limit behavior of stationary distributions of diffusion processes.

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