Weak Random Periodic Solutions of Random Dynamical Systems

In this paper, we first introduce the definition of weak random periodic solutions of random dynamical systems. Then, we discuss the existence of such periodic solutions. We use concrete examples to illustrate the results. Further, we introduce the definition of weak random periodic measures and study their relationship with weak random periodic solutions. In particular, we establish the existence of invariant measures of random dynamical systems by virtue of their weak random periodic solutions.