Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Doubly probabilistic representation for the stochastic porous media type equation

Viorel Barbu, Michael Röckner, and Francesco Russo

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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.


Cet article propose et discute une représentation doublement probabiliste pour une équation des milieux poreux stochatique dans l’espace tout entier $\mathbb{R}^{1}$, perturbée par un bruit multiplicatif coloré. Pour presque toute réalisation $\omega$ de l’aléa, on associe une équation différentielle stochastique en loi avec coefficients aléatoires, dirigée par un mouvement brownien indépendant.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 53, Number 4 (2017), 2043-2073.

Received: 15 May 2014
Revised: 4 August 2016
Accepted: 5 August 2016
First available in Project Euclid: 27 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60H15: Stochastic partial differential equations [See also 35R60] 60H30: Applications of stochastic analysis (to PDE, etc.) 60H10: Stochastic ordinary differential equations [See also 34F05] 60G46: Martingales and classical analysis 35C99: None of the above, but in this section 58J65: Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60] 82C31: Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]

Stochastic partial differential equations Infinite volume Singular porous media type equation Doubly probabilistic representation Multiplicative noise Singular random Fokker–Planck type equation Filtering


Barbu, Viorel; Röckner, Michael; Russo, Francesco. Doubly probabilistic representation for the stochastic porous media type equation. Ann. Inst. H. Poincaré Probab. Statist. 53 (2017), no. 4, 2043--2073. doi:10.1214/16-AIHP783.

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