Weak Random Periodic Solutions of Random Dynamical Systems

Abstract

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.

References in corpus (6)

• Random Periodic Solutions of Random Dynamical Systems
• Pathwise Random Periodic Solutions of Stochastic Differential Equations
• Stationary Solutions of SPDEs and Infinite Horizon BDSDEs
• Random Periodic Solutions of SPDEs via Integral Equations and Wiener-Sobolev Compact Embedding
• Random Periodic Processes, Periodic Measures and Ergodicity
• Numerical Approximation of Random Periodic Solutions of Stochastic Differential Equations

Cited by in corpus (1)

• Random Almost Periodic Solutions of Random Dynamical Systems