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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2000-7
February 2000

Some regularity results for the stochastic pressure equation of Wick-type


Fred Espen Benth, Thomas Gorm Theting


We prove that the solution of the stochastic pressure equation of Wick-type belongs to a space of generalized random fields having square integrable homogeneous chaos kernels. We find the chaos expansion, and calculate its stochastic regularity in distributional sense. Furthermore, we show that the solution is stable under perturbations of the permeability field and the source term.

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This paper has now been published in Stochastic Anal. Appl. 20, 1191--1223 (2002)