Phi-entropy inequalities and Fokker-Planck equations

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Date
2010
Link to item file
https://hal.archives-ouvertes.fr/hal-00459423
Dewey
Probabilités et mathématiques appliquées
Sujet
Logarithmic Sobolev inequality; Poincaré inequality; Fokker-Planck equation; $Phi$-entropies; Bakry-Emery criterion; diffusion semigroups
DOI
http://dx.doi.org/10.1142/9789814313179_0060
Conference country
UNITED KINGDOM
Book title
PROGRESS IN ANALYSIS AND ITS APPLICATIONS. Proceedings of the 7th International ISAAC CongressPROGRESS IN ANALYSIS AND ITS APPLICATIONSProceedings of the 7th International ISAAC Congress
Author
Wirth, Jens
Publisher
World Scientific
Year
2010
ISBN
978-981-4313-16-2
URI
https://basepub.dauphine.fr/handle/123456789/4047
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Author
Bolley, François
Gentil, Ivan
Type
Communication / Conférence
Item number of pages
463-469
Abstract (EN)
We present new $\Phi$-entropy inequalities for diffusion semigroups under the curvature-dimension criterion. They include the isoperimetric function of the Gaussian measure. Applications to the long time behaviour of solutions to Fokker-Planck equations are given.