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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| Accès en ligne: | https://arxiv.org/abs/2001.08265 |
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| _version_ | 1866908340954595328 |
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| author | Lima, Davi Lucena, Rafael |
| author_facet | Lima, Davi Lucena, Rafael |
| contents | In this article we derive a regularity result for the disintegration of the invariant measure associated to a class of Random Dynamical Systems - RDS. The results of this work are obtained by constructing a suitable anisotropic normed space defined by the Wasserstein-Kantorovich-like metric and understanding the dynamics of the associated transfer operator in a neighborhood of its fixed point. Precisely, we employ functional analytic techniques to demonstrate a spectral gap for its action on suitable spaces of signed measures. We apply this analysis to prove an exponential decay of correlation statement for Lipschitz observables and statistical properties of the RDS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_08265 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Lipschitz regularity of the invariant measure of random dynamical systems Lima, Davi Lucena, Rafael Dynamical Systems Functional Analysis 37A25, 37A10, 37C30, 37D50 In this article we derive a regularity result for the disintegration of the invariant measure associated to a class of Random Dynamical Systems - RDS. The results of this work are obtained by constructing a suitable anisotropic normed space defined by the Wasserstein-Kantorovich-like metric and understanding the dynamics of the associated transfer operator in a neighborhood of its fixed point. Precisely, we employ functional analytic techniques to demonstrate a spectral gap for its action on suitable spaces of signed measures. We apply this analysis to prove an exponential decay of correlation statement for Lipschitz observables and statistical properties of the RDS. |
| title | Lipschitz regularity of the invariant measure of random dynamical systems |
| topic | Dynamical Systems Functional Analysis 37A25, 37A10, 37C30, 37D50 |
| url | https://arxiv.org/abs/2001.08265 |