Quasi-stationary distribution for the Langevin process in cylindrical domains, part I: existence, uniqueness and long-time convergence - Archive ouverte HAL Access content directly
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Quasi-stationary distribution for the Langevin process in cylindrical domains, part I: existence, uniqueness and long-time convergence

Abstract

Consider the Langevin process, described by a vector (position,momentum) in Rd×Rd. 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 domain D:=O×Rd. We then obtain the existence of a unique quasi-stationary distribution (QSD) for the Langevin process on D. We also provide a spectral interpretation of this QSD and obtain an exponential convergence of the Langevin process conditioned on non-absorption towards the QSD.
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Dates and versions

hal-03123442 , version 1 (27-01-2021)
hal-03123442 , version 2 (26-08-2021)
hal-03123442 , version 3 (27-09-2021)

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Tony Lelièvre, Mouad Ramil, Julien Reygner. Quasi-stationary distribution for the Langevin process in cylindrical domains, part I: existence, uniqueness and long-time convergence. 2021. ⟨hal-03123442v2⟩
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