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

Gentil, Ivan; Imbert, Cyril (2009), Logarithmic Sobolev inequalities: regularizing effect of Lévy operators and asymptotic convergence in the Lévy-Fokker-Planck equation, Stochastics, 81, 3-4, p. 401-414. http://dx.doi.org/10.1080/17442500903080306

Type
Article accepté pour publication ou publié
Date
2009
Journal name
Stochastics
Volume
81
Number
3-4
Publisher
Taylor & Francis
Pages
401-414
Publication identifier
Metadata
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Author(s)
Gentil, Ivan
Imbert, Cyril cc
Abstract (EN)
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.
Subjects / Keywords
Lévy operator; logarithmic Sobolev inequalities; entropy production method; Ornstein-Uhlenbeck equation; Φ-entropy inequalities; fractional Laplacian; ultracontractivity; Fokker-Planck equation