UNSPECIFIED (2004) A singular parabolic Anderson model. ELECTRONIC JOURNAL OF PROBABILITY, 9 . pp. 98-144. ISSN 1083-6489

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Abstract

We consider the following stochastic partial differential equation: partial derivativeu/partial derivativet = 1/2 delu + kappau(F) over dot, for X is an element of R-d in dimension d greater than or equal to 3, where (F) over dot (t, x) is a mean zero Gaussian noise with the singular covariance E{(F) over dot(t, x)(F) over dot(x, y)] = delta(t-s)/\x-y\(2). Solutions ut(dx) exist as singular measures, under suitable assumptions on the initial conditions and for sufficiently small kappa. We investigate various properties of the solutions using such tools as scaling, self-duality and moment formulae.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ELECTRONIC JOURNAL OF PROBABILITY
Publisher:	UNIV WASHINGTON, DEPT MATHEMATICS
ISSN:	1083-6489
Date:	2004
Volume:	9
Number of Pages:	47
Page Range:	pp. 98-144
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/8158

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