Quasi-stationary distribution for the Langevin process in cylindrical domains, Part I: Existence, uniqueness and long-time convergence

Tony Lelièvre, Mouad Ramil and Julien Reygner

Stochastic Processes and their Applications, 2022, vol. 144, issue C, 173-201

Abstract: Consider the Langevin process which models the evolution of positions (in Rd) and associated momenta (in Rd) of interacting particles. Let O be a C2 open bounded and connected set of Rd. We prove the compactness of the semigroup of the Langevin process absorbed at the boundary of the bounded-in-position domain D≔O×Rd. We then obtain the existence of a unique quasi-stationary distribution (QSD) for the Langevin process on D. We provide a spectral interpretation of this QSD and obtain an exponential convergence of the Langevin process conditioned on non-absorption towards the QSD. We also give an explicit formula for the first exit point distribution from D, starting from the QSD.

Keywords: Langevin process; Quasi-stationary distribution; Compactness; Spectral decomposition (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:144:y:2022:i:c:p:173-201

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DOI: 10.1016/j.spa.2021.11.005

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