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

Author

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  • Lelièvre, Tony
  • Ramil, Mouad
  • Reygner, Julien

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.

Suggested Citation

  • Lelièvre, Tony & Ramil, Mouad & Reygner, Julien, 2022. "Quasi-stationary distribution for the Langevin process in cylindrical domains, Part I: Existence, uniqueness and long-time convergence," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 173-201.
    • Handle: RePEc:eee:spapps:v:144:y:2022:i:c:p:173-201
    DOI: 10.1016/j.spa.2021.11.005
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    References listed on IDEAS

    as
    1. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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