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

@article{Kirchner2017CovarianceSO, title={Covariance structure of parabolic stochastic partial differential equations with multiplicative L{\'e}vy noise}, author={K. Kirchner and A. Lang and S. Larsson}, journal={Journal of Differential Equations}, year={2017}, volume={262}, pages={5896-5927} }

The characterization of the covariance function of the solution process to a stochastic partial differential equation is considered in the parabolic case with multiplicative Levy noise of affine type. For the second moment of the mild solution, a well-posed deterministic space–time variational problem posed on projective and injective tensor product spaces is derived, which subsequently leads to a deterministic equation for the covariance function.

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Numerical methods for the deterministic second moment equation of parabolic stochastic PDEs

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