Pathwise uniqueness for a class of SPDEs driven by cylindrical $\alpha$-stable processes

Abstract

We show the pathwise uniqueness for stochastic partial differential equation driven by a cylindrical $\alpha$-stable process with Hölder continuous drift, thus obtaining an infinite dimensional generalization of the result of Priola [Osaka J. Math., 2012] in the case $H={\mathbb{R}}^d$. The proof is based on an infinite dimensional Kolmogorov equation with non-local operator.