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.
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.
|Full text:||(AM) Accepted Manuscript|
Available under License - Creative Commons Attribution Non-commercial 4.0.
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|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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