Consider the Langevin process, described by a vector (positions and momenta) in . Let be a open bounded and connected set of . Recent works showed the existence of a unique quasi-stationary distribution (QSD) of the Langevin process on the domain . 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 .
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.
"Quasi-stationary distribution for the Langevin process in cylindrical domains, part II: overdamped limit." Electron. J. Probab. 27 1 - 18, 2022. https://doi.org/10.1214/22-EJP789