Quasi-stationary distribution for kinetic SDEs with low regularity coefficients

2024/10/01 by Nicolas Champagnat, Tony Lelièvre, Champagnat, Nicolas +7 · 1 citation
Economics, Econometrics and Finance · Engineering · Physics and Astronomy · #Stochastic processes and financial applications #Radiative Heat Transfer Studies #Advanced Thermodynamics and Statistical Mechanics

paper · pdf · doi:10.48550/arxiv.2410.01042

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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