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Convergence to equilibrium in Wasserstein distance for Fokker-Planck equations

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Date
2012
Link to item file
http://hal.archives-ouvertes.fr/hal-00632941/fr/
Dewey
Probabilités et mathématiques appliquées
Sujet
spectral gap; functional inequalities; Wasserstein distance; Diffusion equations
Journal issue
Journal of Functional Analysis
Volume
263
Number
8
Publication date
2012
Article pages
2430-2457
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.jfa.2012.07.007
URI
https://basepub.dauphine.fr/handle/123456789/7260
Collections
  • CEREMADE : Publications
Metadata
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Author
Guillin, Arnaud
Gentil, Ivan
Bolley, François
Type
Article accepté pour publication ou publié
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.

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