Doubly probabilistic representation for the stochastic porous media type equation

2016/08/09 by Barbu, Viorel, Röckner, Michael, Russo, Francesco
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1608.02718

Abstract

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 R¹ perturbed by a multiplicative coloured noise. For almost all random realizations ω, one associates a stochastic differential equation in law with random coefficients, driven by an independent Brownian motion.

Related

• A stochastic Fokker-Planck equation and double probabilistic representation for the stochastic porous media type equation
• Weak Solutions to the Stochastic Porous Media Equation via Kolmogorov Equations: The Degenerate Case
• A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise
• Probabilistic representation for solutions of a porous media type equation with Neumann boundary condition: the case of the half-line
• Probabilistic representation for solutions of an irregular porous media type equation