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- W3151796744 abstract "We consider the Fokker-Planck equation with subcritical confinement force field which may not derive from a potential function. We prove the existence of a unique positive equilibrium of mass one and we establish some subgeometric, or geometric, rate of convergence to a multiple of this equilibrium (depending on the space to which belongs the initial datum) in many spaces. Our results generalize similar results introduced by Toscani, Villani [33] and Röckner, Wang [31] for some forces associated to a potential and extended by Douc, Fort, Guillin [12] and Bakry, Cattiaux, Guillin [4] for some general forces: however in our approach the spaces are more general, and the rates of convergence to equilibrium are sharper. Nous considérons une équation de Fokker-Planck avec une force de confinement sous-critique, qui peut ne pas être le gradient d'un potentiel. Nous prouvons l'existence d'un unique état d'équilibre positif de masse unité, et nous établissons la convergence des solutions positives de l'équation d'évolution vers un multiple de cet état d'équilibre, avec des vitesses de convergence sous-géométriques, ou géométriques, dépendant de l'espcace dans lequel la convergence est étudiée. Nos résultats généralisent au cas de forces générales des résultats analogues introduits par Toscani, Villani [33] et Röckner, Wang [31] pour le cas où la force de confinement est associée à un potentiel, résultats qui ont été étendus par la suite par Douc, Fort, Guillin [12] and Bakry, Cattiaux, Guillin [4] pour quelques forces plus générales. Cependant dans notre approche les espaces sont plus généraux et les vitesses de convergence vers l'équilibre sont plus précis." @default.
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- W3151796744 date "2021-07-01" @default.
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- W3151796744 title "The Fokker-Planck equation with subcritical confinement force" @default.
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- W3151796744 doi "https://doi.org/10.1016/j.matpur.2021.04.007" @default.
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