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
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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 / KeywordsLévy operator; logarithmic Sobolev inequalities; entropy production method; Ornstein-Uhlenbeck equation; Φ-entropy inequalities; fractional Laplacian; ultracontractivity; Fokker-Planck equation
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