Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case

* Auteur correspondant
4 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : We consider a possibly degenerate porous media type equation over all of $\R^d$ with $d = 1$, with monotone discontinuous coefficients with linear growth and prove a probabilistic representation of its solution in terms of an associated microscopic diffusion. This equation is motivated by some singular behaviour arising in complex self-organized critical systems. The main idea consists in approximating the equation by equations with monotone non-degenerate coefficients and deriving some new analytical properties of the solution.
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Article dans une revue
Probability Theory and Related Fields, Springer Verlag, 2011, 〈10.1007/s00440-010-0291-x〉
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https://hal.inria.fr/inria-00410248
Contributeur : Francesco Russo <>
Soumis le : mardi 18 août 2009 - 22:22:14
Dernière modification le : jeudi 5 janvier 2017 - 01:52:17
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Viorel Barbu, Michael Roeckner, Francesco Russo. Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case. Probability Theory and Related Fields, Springer Verlag, 2011, 〈10.1007/s00440-010-0291-x〉. 〈inria-00410248〉

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