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

TL;DR

This paper proves the existence of unique solutions for stochastic evolution equations driven by cylindrical Le9vy noise, extending variational methods to handle non-finite moment noise processes.

Contribution

It establishes the existence and uniqueness of solutions for SPDEs with cylindrical Le9vy noise under monotonicity and coercivity conditions, including non-finite moment noise.

Findings

Proves existence and uniqueness of solutions.

Handles cylindrical Le9vy noise without finite moments.

Extends variational approach to broader noise classes.

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.