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Doubly probabilistic representation for the stochastic porous media type equation. (English. French summary) Zbl 1387.35635

Summary: 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 \(\mathbb{R}^{1}\) 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.

MSC:

35R60 PDEs with randomness, stochastic partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G46 Martingales and classical analysis
35C99 Representations of solutions to partial differential equations
58J65 Diffusion processes and stochastic analysis on manifolds
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
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