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

DOI10.1080/17442500903080306zbMath1202.47093arXiv0809.2654OpenAlexW1986275872MaRDI QIDQ3396077

Ivan Gentil, Cyril Imbert

Publication date: 16 September 2009

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.2654

zbMATH Keywords

logarithmic Sobolev inequalitiesFokker-Plank equationfractional LaplacianultracontractivityOrnstein-Uhlenbeck equationLévy operatorentropy production method\(\Phi\)-entropy inequalities

Mathematics Subject Classification ID

Random fields (60G60) Markov semigroups and applications to diffusion processes (47D07) Applications of operator theory to differential and integral equations (47N20) Initial value problems for second-order parabolic equations (35K15) Integro-differential operators (47G20) Applications of functional analysis to differential and integral equations (46N20)

Related Items (5)

Regularity for semigroups of Ornstein-Uhlenbeck processes ⋮ Dimension dependent hypercontractivity for Gaussian kernels ⋮ Existence and regularity of a linear nonlocal Fokker-Planck equation with growing drift ⋮ Lévy-Ornstein-Uhlenbeck transition semigroup as second quantized operator ⋮ Fractional Fokker--Planck Equation with General Confinement Force

Cites Work

• Unnamed Item
• Fractal first-order partial differential equations
• Logarithmic Sobolev Inequalities

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