Weak Random Periodic Solutions of Random Dynamical Systems
Dynamical Systems
2022-08-03 v3
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.
Cite
@article{arxiv.1906.06536,
title = {Weak Random Periodic Solutions of Random Dynamical Systems},
author = {Wei Sun and Zuo-Huan Zheng},
journal= {arXiv preprint arXiv:1906.06536},
year = {2022}
}