Convergence to equilibrium for the kinetic Fokker-Planck equation on the torus
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2015
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| _version_ | 1866912287213748224 |
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| author | Dietert, Helge Evans, Josephine Holding, Thomas |
| author_facet | Dietert, Helge Evans, Josephine Holding, Thomas |
| contents | We study convergence to equilibrium for the kinetic Fokker-Planck equation on the torus. Solving the stochastic differential equation, we show exponential convergence in the Monge-Kantorovich-Wasserstein $\mathcal{W}_2$ distance. Finally, we investigate if such a coupling can be obtained by a co-adapted coupling, and show that then the bound must depend on the square root of the initial distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1506_06173 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Convergence to equilibrium for the kinetic Fokker-Planck equation on the torus Dietert, Helge Evans, Josephine Holding, Thomas Probability Analysis of PDEs 60J60, 35Q84, 60H30, 82C31 We study convergence to equilibrium for the kinetic Fokker-Planck equation on the torus. Solving the stochastic differential equation, we show exponential convergence in the Monge-Kantorovich-Wasserstein $\mathcal{W}_2$ distance. Finally, we investigate if such a coupling can be obtained by a co-adapted coupling, and show that then the bound must depend on the square root of the initial distance. |
| title | Convergence to equilibrium for the kinetic Fokker-Planck equation on the torus |
| topic | Probability Analysis of PDEs 60J60, 35Q84, 60H30, 82C31 |
| url | https://arxiv.org/abs/1506.06173 |