The central limit theorem for slow-fast systems with L\'evy noise

TL;DR

This paper proves a central limit theorem for slow-fast stochastic systems driven by Lévy noise, showing that deviations can be approximated by a Gaussian process using the perturbed test function method.

Contribution

It introduces a novel application of the perturbed test function method to establish a CLT for systems with Lévy noise, expanding understanding of their probabilistic behavior.

Findings

Deviation approximated by Gaussian process

Central limit theorem established for Lévy-driven systems

Method applicable to complex stochastic systems

Abstract

We consider a slow-fast stochastic differential system with L\'evy noise. We will employ the perturbed test function method to study the normal deviation of the slow-fast system. Our main result states that the deviation can be approximated by a Gaussian process and the central limit theorem is obtained for the system.