Feng, Chunrong and Qu, Baoyou and Zhao, Huaizhong (2021) 'Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations.', Journal of Differential Equations, 286 . pp. 119-163.
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.
| Item Type: | Article |
|---|---|
| Full text: | (AM) Accepted Manuscript Available under License - Creative Commons Attribution Non-commercial 4.0. Download PDF (422Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | https://doi.org/10.1016/j.jde.2021.03.022 |
| Publisher statement: | © 2021 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ |
| Date accepted: | 06 March 2021 |
| Date deposited: | 04 May 2021 |
| Date of first online publication: | 18 March 2021 |
| Date first made open access: | 18 March 2022 |
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