Strong averaging principle for a class of slow-fast singular SPDEs driven by $\alpha$-stable process

TL;DR

This paper establishes a strong averaging principle for a class of slow-fast stochastic partial differential equations driven by alpha-stable processes, using Zvonkin's transformation and Khasminskii's discretization.

Contribution

It introduces a novel approach combining Zvonkin's transformation with Khasminskii's method for SPDEs driven by alpha-stable noise, expanding the theoretical understanding of such systems.

Findings

Proves the strong averaging principle for the specified class of SPDEs.

Provides an example illustrating the application of the theoretical results.

Enhances the analytical tools for studying slow-fast SPDEs with jump noise.

Abstract

In this paper, the strong averaging principle is researched for a class of H\"{o}lder continuous drift slow-fast SPDEs with $\alpha$-stable process by the Zvonkin's transformation and the classical Khasminkii's time discretization method. As applications, an example is also provided to explain our result.