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November 2007 Some parabolic PDEs whose drift is an irregular random noise in space
Francesco Russo, Gerald Trutnau
Ann. Probab. 35(6): 2213-2262 (November 2007). DOI: 10.1214/009117906000001178


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.


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Francesco Russo. Gerald Trutnau. "Some parabolic PDEs whose drift is an irregular random noise in space." Ann. Probab. 35 (6) 2213 - 2262, November 2007.


Published: November 2007
First available in Project Euclid: 8 October 2007

zbMATH: 1147.60042
MathSciNet: MR2353387
Digital Object Identifier: 10.1214/009117906000001178

Primary: 60G48 , 60H05 , 60H10 , 60H15

Keywords: Dirichlet processes , distributional drift , Martingale problem , Singular drifted PDEs , Stochastic partial differential equations

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 6 • November 2007
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