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Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

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
8
Publisher
Elsevier
Pages
2430-2457
Publication identifier
http://dx.doi.org/10.1016/j.jfa.2012.07.007
Metadata
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Author(s)
Guillin, Arnaud
Gentil, Ivan
Bolley, François
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

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