Variational solutions of stochastic partial differential equations with cylindrical Lévy noise

Tomasz Kosmala, Markus Riedle

Published 2018-07-30Version 1

In this paper, the existence of a unique solution in the variational approach to 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. In the case of a cylindrical L\'evy process with finite second moments, we derive the result without further assumptions. For the case of cylindrical L\'evy processes without finite moments, we consider a subclass containing numerous examples from the literature. Deriving the existence result in the latter case requires a careful analysis of the jumps of cylindrical L\'evy processes.