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2022 Quasi-stationary distribution for the Langevin process in cylindrical domains, part II: overdamped limit
Mouad Ramil
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Electron. J. Probab. 27: 1-18 (2022). DOI: 10.1214/22-EJP789


Consider the Langevin process, described by a vector (positions and momenta) in Rd×Rd. Let O be a C2 open bounded and connected set of Rd. Recent works showed the existence of a unique quasi-stationary distribution (QSD) of the Langevin process on the domain D:=O×Rd. In this article, we study the overdamped limit of this QSD, i.e. when the friction coefficient goes to infinity. In particular, we show that the marginal law in position of the overdamped limit is the QSD of the overdamped Langevin process on the domain O.

Funding Statement

Supported by the Région Ile-de- France through a PhD fellowship of the Domaine d’Intérêt Majeur (DIM) Math Innov.


This work also benefited from the support of the project ANR QuAMProcs (ANR-19-CE40-0010) from the French National Research Agency. The author would also like to thank Tony Lelièvre and Julien Reygner for fruitfull discussions throughout this work.


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Mouad Ramil. "Quasi-stationary distribution for the Langevin process in cylindrical domains, part II: overdamped limit." Electron. J. Probab. 27 1 - 18, 2022.


Received: 5 July 2021; Accepted: 29 April 2022; Published: 2022
First available in Project Euclid: 6 May 2022

arXiv: 2103.00338
Digital Object Identifier: 10.1214/22-EJP789

Primary: 35B25 , 47B07 , 60H10 , 82C31

Keywords: Langevin process , overdamped Langevin process , overdamped limit , quasi-stationary distribution


Vol.27 • 2022
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