Covariance structure of parabolic stochastic partial differential equations

Artikel i vetenskaplig tidskrift, 2013

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.