Variational solutions of stochastic partial differential equations with cylindrical L\'evy noise

Tomasz Kosmala; Markus Riedle

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arXiv · 1807.11418

Variational solutions of stochastic partial differential equations with cylindrical L\'evy noise

Tomasz Kosmala·Markus Riedle

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Abstract

In this article, the existence of a unique solution in the variational approach of the stochastic evolution equation $$\dX(t) = F(X(t)) \dt + G(X(t)) \dL(t)$$ driven by a cylindrical L\'evy process $L$ is established. The coefficients $F$ and $G$ are assumed to satisfy the usual monotonicity and coercivity conditions. The noise is modelled by a cylindrical L\'evy processes which is assumed to belong to a certain subclass of cylindrical L\'evy processes and may not have finite moments.

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Tomasz Kosmala, Markus Riedle. 2018-07-30. Variational solutions of stochastic partial differential equations with cylindrical L\'evy noise. https://arxiv.org/abs/1807.11418

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