Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

被引：67

作者：

Bolley, Francois ^{[1
]}

Gentil, Ivan ^{[2
]}

Guillin, Arnaud ^{[3
,4
]}

机构：

[1] Univ Paris 09, CNRS, Umr 7534, CEREMADE, F-75016 Paris 16, France

[2] Univ Lyon 1, CNRS, Umr 5208, Inst Camille Jordan, F-69622 Villeurbanne, France

[3] Univ Blaise Pascal, Inst Univ France, F-63177 Clermont Ferrand, France

[4] Univ Blaise Pascal, Lab Math, CNRS, Umr 6620, F-63177 Clermont Ferrand, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 263卷 / 08期

关键词：

Diffusion equations; Wasserstein distance; Functional inequalities; Spectral gap; LONG-TIME ASYMPTOTICS; INEQUALITIES;

D O I：

10.1016/j.jfa.2012.07.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional inequality, which links the distance with its dissipation and ensures a spectral gap in Wasserstein distance. We give practical criteria for this inequality and compare it to classical ones. The key point is to quantify the contribution of the diffusion term to the rate of convergence, in any dimension, which to our knowledge is a novelty. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：2430 / 2457

页数：28

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