Quasi-stationary distribution for kinetic SDEs with low regularity coefficients

Nicolas Champagnat; Tony Lelièvre; Mouad Ramil; Julien Reygner; Denis Villemonais

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arXiv · 2410.01042

Quasi-stationary distribution for kinetic SDEs with low regularity coefficients

Nicolas Champagnat·Tony Lelièvre·Mouad Ramil·Julien Reygner·Denis Villemonais

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Abstract

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.

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BibTeX RIS

Nicolas Champagnat, Tony Lelièvre, Mouad Ramil, Julien Reygner, Denis Villemonais. 2024-10-01. Quasi-stationary distribution for kinetic SDEs with low regularity coefficients. https://arxiv.org/abs/2410.01042

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