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

Feng, Chunrong; Qu, Baoyou; Zhao, Huaizhong

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


Authors

Baoyou Qu



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

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