The Lévy-Fokker-Planck equation: Phi-entropies and convergence to equilibrium

Abstract : In this paper, we study a Fokker-Planck equation of the form u_t = I [u ] + div (x u) where the operator I [u], which is usually the Laplacian, is replaced with a general Lévy operator. We prove by the entropy production method the exponential decay in time of the solution to the only steady state of the associated equation.
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Ivan Gentil, Cyril Imbert. The Lévy-Fokker-Planck equation: Phi-entropies and convergence to equilibrium. Asymptotic Analysis, IOS Press, 2008, 59 (3-4), pp.125-138. ⟨hal-00113806v2⟩

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