A stochastic Fokker-Planck equation and double probabilistic representation for the stochastic porous media type equation.

Viorel Barbu, Michael Röckner and Francesco Russo
2014
Publication type:
Lecture note
Journal:
HAL-INRIA 00981113
arXiv:
images/icons/icon_arxiv.png 1404.5120
Keywords :
stochastic partial differential equations; infinite volume; singular porous media type equation; double probabilistic representation; multiplicative noise; singular random Fokker-Planck type equation.
Abstract:
The purpose of the present paper consists in proposing and discussing a double probabilistic representation for a porous media equation in the whole space 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. The key ingredient is a uniqueness lemma for a linear SPDE of Fokker-Planck type with measurable bounded (possibly degenerated) random coefficients.
BibTeX:
@misc{Bar-Roc-Rus-2014,
    title={A stochastic Fokker-Planck equation and double probabilistic 
           representation for the stochastic porous media type equation. },
    journal={HAL-INRIA 00981113 },
    year={2014 },
    comment={{umatype:'cours'}},
}