Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

Guillin, Arnaud; Gentil, Ivan; Bolley, François

Guillin, Arnaud; Gentil, Ivan; Bolley, François (2012), Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations, Journal of Functional Analysis, 263, 8, p. 2430-2457. http://dx.doi.org/10.1016/j.jfa.2012.07.007

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00632941/fr/

Date

2012

Journal name

Journal of Functional Analysis

Volume

263

Number

Publisher

Elsevier

Pages

2430-2457

Abstract (EN)

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, which to our knowledge is a novelty.

Subjects / Keywords

spectral gap; functional inequalities; Wasserstein distance; Diffusion equations