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3 results

  • Weak random periodic solutions of random dynamical systems

  • Part of
  • Wei Sun, Zuo-Huan Zheng
  • Journal:
    Canadian Mathematical Bulletin / Volume 67 / Issue 1 / March 2024
    Published online by Cambridge University Press:
    12 July 2023, pp. 137-151
    Print publication:
    March 2024
    • Article
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  • 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. We use concrete examples to illustrate the weak random periodic phenomena of dynamical systems induced by random and stochastic differential equations.