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

## TL;DR

This paper proves pathwise uniqueness for a class of stochastic partial differential equations driven by cylindrical alpha-stable processes with Hölder continuous drift, extending finite-dimensional results to infinite dimensions using a non-local Kolmogorov equation.

## Contribution

It generalizes the pathwise uniqueness result for SPDEs driven by cylindrical alpha-stable processes to infinite dimensions, employing a non-local Kolmogorov equation approach.

## Key findings

- Established pathwise uniqueness for the class of SPDEs considered.
- Extended finite-dimensional results to infinite-dimensional settings.
- Utilized a non-local Kolmogorov equation in the proof.

## Abstract

We show the pathwise uniqueness for stochastic partial differential equation driven by a cylindrical $\alpha$-stable process with H\"older 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.