Quasi-stationary distribution for kinetic SDEs with low regularity coefficients
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908068405575680 |
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| author | Champagnat, Nicolas Lelièvre, Tony Ramil, Mouad Reygner, Julien Villemonais, Denis |
| author_facet | Champagnat, Nicolas Lelièvre, Tony Ramil, Mouad Reygner, Julien Villemonais, Denis |
| contents | We consider kinetic SDEs with low regularity coefficients in the setting recently introduced in [6]. For the solutions to such equations, we first prove a Harnack inequality. Using the abstract approach of [5], this inequality then allows us to prove, under a Lyapunov condition, the existence and uniqueness (in a suitable class of measures) of a quasi-stationary distribution in cylindrical domains of the phase space. We finally exhibit two settings in which the Lyapunov condition holds: general kinetic SDEs in domains which are bounded in position, and Langevin processes with a non-conservative force and a suitable growth condition on the force. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_01042 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-stationary distribution for kinetic SDEs with low regularity coefficients Champagnat, Nicolas Lelièvre, Tony Ramil, Mouad Reygner, Julien Villemonais, Denis Probability Analysis of PDEs We consider kinetic SDEs with low regularity coefficients in the setting recently introduced in [6]. For the solutions to such equations, we first prove a Harnack inequality. Using the abstract approach of [5], this inequality then allows us to prove, under a Lyapunov condition, the existence and uniqueness (in a suitable class of measures) of a quasi-stationary distribution in cylindrical domains of the phase space. We finally exhibit two settings in which the Lyapunov condition holds: general kinetic SDEs in domains which are bounded in position, and Langevin processes with a non-conservative force and a suitable growth condition on the force. |
| title | Quasi-stationary distribution for kinetic SDEs with low regularity coefficients |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2410.01042 |