Doubly probabilistic representation for the stochastic porous media type equation

Viorel Barbu; Michael Röckner; Francesco Russo

doi:10.1214/16-AIHP783

Doubly probabilistic representation for the stochastic porous media type equation

Viorel Barbu
, Michael Röckner
, Francesco Russo

Research output: Contribution to journal › Article › peer-review

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

Original language	English
Pages (from-to)	2043-2073
Number of pages	31
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	53
Issue number	4
DOIs	https://doi.org/10.1214/16-AIHP783
Publication status	Published - 1 Nov 2017
Externally published	Yes

Keywords

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

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10.1214/16-AIHP783

Cite this

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title = "Doubly probabilistic representation for the stochastic porous media type equation",

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

keywords = "Doubly probabilistic representation, Filtering, Infinite volume, Multiplicative noise, Singular porous media type equation, Singular random Fokker-Planck type equation, Stochastic partial differential equations",

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AU - Röckner, Michael

AU - Russo, Francesco

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PY - 2017/11/1

Y1 - 2017/11/1

N2 - 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 colored noise. For almost all random realizations ω, one associates a stochastic differential equation in law with random coefficients, driven by an independent Brownian motion.

AB - 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 colored noise. For almost all random realizations ω, one associates a stochastic differential equation in law with random coefficients, driven by an independent Brownian motion.

KW - Doubly probabilistic representation

KW - Filtering

KW - Infinite volume

KW - Multiplicative noise

KW - Singular porous media type equation

KW - Singular random Fokker-Planck type equation

KW - Stochastic partial differential equations

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SN - 0246-0203

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JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 4

ER -

Doubly probabilistic representation for the stochastic porous media type equation

Abstract

Keywords

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