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

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

2008-09-16

arxiv.org/abs/0809.2654v1

Stochastics: An International Journal of Probability and Stochastics Processes 81, 3-4 (2009) 401?414

Mathematics

Probability

Scientific paper

In this paper we study some applications of the L\'evy 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 L\'evy-Ornstein-Uhlenbeck process.

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