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Covariance structure of parabolic stochastic partial differential equations

Journal article
Authors Annika Lang
Stig Larsson
Ch. Schwab
Published in Stochastic Partial Differential Equations: Analysis and Computations
Volume 1
Issue 2
Pages 351-364
ISSN 2194-0401
Publication year 2013
Published at Department of Mathematical Sciences, Mathematics
Pages 351-364
Language en
Links dx.doi.org/10.1007/s40072-013-0012-...
Subject categories Mathematical Analysis, Probability Theory and Statistics

Abstract

In this paper parabolic random partial differential equations and parabolic stochastic partial differential equations driven by a Wiener process are considered. A deterministic, tensorized evolution equation for the second moment and the covariance of the solutions of the parabolic stochastic partial differential equations is derived. Well-posedness of a space–time weak variational formulation of this tensorized equation is established.

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