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Semi Log-Concave Markov Diffusions

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Séminaire de Probabilités XLVI

Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2123))

Abstract

In this paper we intend to give a comprehensive approach of functional inequalities for diffusion processes under various “curvature” assumptions. One of them coincides with the usual Γ 2 curvature of Bakry and Emery in the case of a (reversible) drifted Brownian motion, but differs for more general diffusion processes. Our approach using simple coupling arguments together with classical stochastic tools, allows us to obtain new results, to recover and to extend already known results, giving in many situations explicit (though non optimal) bounds. In particular, we show new results for gradient/semigroup commutation in the log concave case. Some new convergence to equilibrium in the granular media equation is also exhibited.

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Author information

Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Université de Toulouse, CNRS UMR 5219, 118 route de Narbonne, 31062, Toulouse cedex 09, France

    P. Cattiaux

  2. Laboratoire de Mathématiques, CNRS UMR 6620, Université Blaise Pascal, avenue des Landais, 63177, Aubière, France

    A. Guillin

Authors
  1. P. Cattiaux
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  2. A. Guillin
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Correspondence to P. Cattiaux .

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Editors and Affiliations

  1. Université de Versailles-St-Quentin Laboratoire de Mathématiques, Versailles, France

    Catherine Donati-Martin

  2. INRIA, Nancy-Université, Vandoeuvre-lès-Nancy, France

    Antoine Lejay

  3. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, Versailles, France

    Alain Rouault

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Cattiaux, P., Guillin, A. (2014). Semi Log-Concave Markov Diffusions. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLVI. Lecture Notes in Mathematics(), vol 2123. Springer, Cham. https://doi.org/10.1007/978-3-319-11970-0_9

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