Doubly probabilistic representation for the stochastic porous media type equation

Barbu V, Röckner M, Russo F. Doubly probabilistic representation for the stochastic porous media type equation. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. 2017;53(4):2043-2073.The purpose of the present paper consists in proposing and discussing a doubly probabilistic representation for a stochastic porous media equation in the whole space R-1 perturbed by a multiplicative colored noise. For almost all random realizations omega, one associates a stochastic differential equation in law with random coefficients, driven by an independent Brownian motion