Some Parabolic Pdes Whose Drift is an Irregular Random Noise in Space

2006/02/28 by Russo, Francesco, Trutnau, Gerald
#60G48 #60H05 #60H10 #60H15 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.math/0602669

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.

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