Probabilistic representation for solutions to nonlinear Fokker-Planck equations

Abstract

One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in ${\mathbb{R}}^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear stochastic differential equation. The case of a nonlinear Fokker-Planck equation with linear space dependent drift is also studied.

21 pages