Logarithmic Sobolev inequalities: regularizing effect of Lévy operators and asymptotic convergence in the Lévy-Fokker-Planck equation - Archive ouverte HAL Access content directly
Journal Articles Stochastics: An International Journal of Probability and Stochastic Processes Year : 2009

Logarithmic Sobolev inequalities: regularizing effect of Lévy operators and asymptotic convergence in the Lévy-Fokker-Planck equation

Abstract

In this paper we study some applications of the Lévy logarithmic Sobolev inequality to the study of the regularity of the solution of the fractal heat equation, i. e. the heat equation where the Laplacian is replaced with the fractional Laplacian. It is also used to the study of the asymptotic behaviour of the Lévy-Ornstein-Uhlenbeck process.
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Dates and versions

hal-00321828 , version 1 (15-09-2008)

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Ivan Gentil, Cyril Imbert. Logarithmic Sobolev inequalities: regularizing effect of Lévy operators and asymptotic convergence in the Lévy-Fokker-Planck equation. Stochastics: An International Journal of Probability and Stochastic Processes, 2009, 81 (3-4), pp.401-414. ⟨hal-00321828⟩
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