Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations

Feng, Chunrong; Qu, Baoyou; Zhao, Huaizhong

Abstract

In this paper, we define random quasi-periodic paths for random dynamical systems and quasi-periodic measures for Markovian semigroups. We give a sufficient condition for the existence and uniqueness of random quasi-periodic paths and quasi-periodic measures for stochastic differential equations and a sufficient condition for the density of the quasi-periodic measure to exist and to satisfy the Fokker-Planck equation. We obtain an invariant measure by considering lifted flow and semigroup on cylinder and the tightness of the average of lifted quasi-periodic measures. We further prove that the invariant measure is unique, and thus ergodic.

Citation

Feng, C., Qu, B., & Zhao, H. (2021). Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations. Journal of Differential Equations, 286, 119-163. https://doi.org/10.1016/j.jde.2021.03.022

• Journal Article Type: Article
• Acceptance Date: Mar 6, 2021
• Online Publication Date: Mar 18, 2021
• Publication Date: Jun 15, 2021
• Deposit Date: May 4, 2021
• Publicly Available Date: Mar 18, 2022
• Journal: Journal of Differential Equations
• Print ISSN: 0022-0396
• Electronic ISSN: 1090-2732
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 286
• Pages: 119-163
• DOI: https://doi.org/10.1016/j.jde.2021.03.022
• Public URL: https://durham-repository.worktribe.com/output/1243398