  We first introduce the concept of weak random periodic solutions of random
dynamical systems. Then, we discuss the existence of such periodic solutions.
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. Finally, we use concrete
examples to illustrate the weak random periodic phenomena of dynamical systems
induced by random and stochastic differential equations.
