Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations
| Autor: | Feng, Chunrong, Qu, Baoyou, Zhao, Huaizhong |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Journal of Differential Equations, Vol. 286 (2021), 119-163 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jde.2021.03.022 |
| Popis: | 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. Comment: 37 pages |
| Databáze: | arXiv |
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