Covariance structure of parabolic stochastic partial differential equations with multiplicative L\'evy noise

Kristin Kirchner; Annika Lang; Stig Larsson

doi:10.1016/j.jde.2017.02.021

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arXiv · 1506.00624

Covariance structure of parabolic stochastic partial differential equations with multiplicative L\'evy noise

Kristin Kirchner·Annika Lang·Stig Larsson

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Abstract

The characterization of the covariance function of the solution process to a stochastic partial differential equation is considered in the parabolic case with multiplicative L\'evy 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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Kristin Kirchner, Annika Lang, Stig Larsson. 2015-06-01. Covariance structure of parabolic stochastic partial differential equations with multiplicative L\'evy noise. https://doi.org/10.1016/j.jde.2017.02.021

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