Dr Chunrong Feng chunrong.feng@durham.ac.uk
Associate Professor
Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations
Feng, Chunrong; Qu, Baoyou; Zhao, Huaizhong
Authors
Baoyou Qu
Professor Huaizhong Zhao huaizhong.zhao@durham.ac.uk
Professor
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 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 286 |
Pages | 119-163 |
DOI | https://doi.org/10.1016/j.jde.2021.03.022 |
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http://creativecommons.org/licenses/by-nc/4.0/
Copyright 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/
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