Covariance structure of parabolic stochastic partial differential equations

Annika Lang, Stig Larsson, Christoph Schwab

Published 2012-10-12, updated 2013-07-13Version 2

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.