A stochastic Fokker-Planck equation and double probabilistic representation for the stochastic porous media 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.
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Submitted on : Sunday, April 20, 2014 - 10:09:35 PM
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  • HAL Id : hal-00981113, version 1
  • ARXIV : 1404.5120

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Viorel Barbu, Michael Röckner, Francesco Russo. A stochastic Fokker-Planck equation and double probabilistic representation for the stochastic porous media type equation.. 2014. ⟨hal-00981113⟩

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