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

Viorel Barbu 1 Michael Roeckner 2 Francesco Russo 3, 4, 5, *
* Corresponding author
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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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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