Some parabolic PDEs whose drift is an irregular random noise in space

Francesco Russo; Gerald Trutnau

doi:10.1214/009117906000001178

Some parabolic PDEs whose drift is an irregular random noise in space

Francesco Russo
, Gerald Trutnau

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

Abstract

A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a probabilistic interpretation is investigated.

Original language	English
Pages (from-to)	2213-2262
Number of pages	50
Journal	Annals of Probability
Volume	35
Issue number	6
DOIs	https://doi.org/10.1214/009117906000001178
Publication status	Published - 1 Dec 2007
Externally published	Yes

Keywords

Dirichlet processes
Distributional drift
Martingale problem
Singular drifted PDEs
Stochastic partial differential equations

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10.1214/009117906000001178

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title = "Some parabolic PDEs whose drift is an irregular random noise in space",

abstract = "A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a probabilistic interpretation is investigated.",

keywords = "Dirichlet processes, Distributional drift, Martingale problem, Singular drifted PDEs, Stochastic partial differential equations",

author = "Francesco Russo and Gerald Trutnau",

year = "2007",

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AU - Russo, Francesco

AU - Trutnau, Gerald

PY - 2007/12/1

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N2 - A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a probabilistic interpretation is investigated.

AB - A new class of random partial differential equations of parabolic type is considered, where the stochastic term consists of an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a probabilistic interpretation is investigated.

KW - Dirichlet processes

KW - Distributional drift

KW - Martingale problem

KW - Singular drifted PDEs

KW - Stochastic partial differential equations

U2 - 10.1214/009117906000001178

DO - 10.1214/009117906000001178

M3 - Article

AN - SCOPUS:51949103211

SN - 0091-1798

VL - 35

SP - 2213

EP - 2262

JO - Annals of Probability

JF - Annals of Probability

IS - 6

ER -

Some parabolic PDEs whose drift is an irregular random noise in space

Abstract

Keywords

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