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Covariance structure of parabolic stochastic partial differential equations

Authors Annika Lang
Stig Larsson
Christoph Schwab
Publication year 2012
Published at Department of Mathematical Sciences, Mathematics
Language en
Keywords Wiener process, covarariance, tensorized, stochastic partial differential equation
Subject categories Probability Theory and Statistics


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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