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The Fokker-Planck equation with subcritical confinement force

Kavian, Otared; Mischler, Stéphane; Ndaoud, Mohamed (2021), The Fokker-Planck equation with subcritical confinement force, Journal de mathématiques pures et appliquées, 151, p. 171-211. 10.1016/j.matpur.2021.04.007

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Type
Article accepté pour publication ou publié
Date
2021
Nom de la revue
Journal de mathématiques pures et appliquées
Volume
151
Éditeur
Elsevier
Pages
171-211
Identifiant publication
Métadonnées
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Auteur(s)
Kavian, Otared
Laboratoire de Mathématiques de Versailles [LMV]
Mischler, Stéphane
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Ndaoud, Mohamed
Centre de Recherche en Économie et Statistique [CREST]
Résumé (EN)
We consider the Fokker-Planck equation with subcritical confinement force field which may not derive from a potential function. We prove the existence of an equilibrium (in the case of a general force) and we establish some (polynomial and stretch exponential) rate of convergence to the equilibrium (depending on the space to which belongs the initial datum). Our results improve similar results established by Toscani, Villani [29] and Röchner , Wang [27]: the force field is more general, the spaces are more general, the rates are sharper.
Mots-clés
weak Poincaré inequality; weak dissipativity; Krein-Rutman theorem; spectral mapping theorem Contents; Fokker-Planck equation; semigroup