THE FOKKER-PLANCK EQUATION WITH SUBCRITICAL CONFINEMENT FORCE

O Kavian (1) , Stéphane Mischler (2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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: Fokker-Planck equation; semigroup; weak Poincaré inequality; weak dissipativity; Krein-Rutman theorem; spectral mapping theorem Contents

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]; Théorie spectrale [math.SP]

O Kavian, Stéphane Mischler. THE FOKKER-PLANCK EQUATION WITH SUBCRITICAL CONFINEMENT FORCE. 2015. ⟨hal-01241680v1⟩