Covariance structure of parabolic stochastic partial differential equations with multiplicative Lévy noise

Preprint, 2015

We consider parabolic stochastic partial differential equations driven by multiplicative L\'evy noise of an affine type. For the second moment of the mild solution, we derive a well-posed deterministic space-time variational problem posed on tensor product spaces, which subsequently leads to a deterministic equation for the covariance function.