The Annals of Probability

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

Francesco Russo and Gerald Trutnau

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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.

Article information

Source
Ann. Probab., Volume 35, Number 6 (2007), 2213-2262.

Dates
First available in Project Euclid: 8 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1191860420

Digital Object Identifier
doi:10.1214/009117906000001178

Mathematical Reviews number (MathSciNet)
MR2353387

Zentralblatt MATH identifier
1147.60042

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60] 60H05: Stochastic integrals 60G48: Generalizations of martingales 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
Singular drifted PDEs Dirichlet processes martingale problem stochastic partial differential equations distributional drift

Citation

Russo, Francesco; Trutnau, Gerald. Some parabolic PDEs whose drift is an irregular random noise in space. Ann. Probab. 35 (2007), no. 6, 2213--2262. doi:10.1214/009117906000001178. https://projecteuclid.org/euclid.aop/1191860420


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