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We consider a linear parabolic problem with random elliptic operator in theusual Gelfand triple setting. We do not assume uniform bounds on the coercivityand boundedness constants, but allow them to be random variables. The parabolicproblem is studied in a weak space-time formulation, where we can deriveexplicit formulas for the inf-sup constants. Under suitable assumptions weprove existence of moments of the solution. We also prove quasi-optimal errorestimates for piecewise polynomial Petrov-Galerkin discretizations.

Quasi-optimality of Petrov-Galerkin discretizations of parabolic problems with random coefficients