Functional central limit theorem for superdiffusive SDEs with stable noise

TL;DR

This paper proves a functional stable central limit theorem for superdiffusive solutions of SDEs driven by alpha-stable noise, advancing understanding of their long-term behavior.

Contribution

It introduces a new functional limit theorem specifically for superdiffusive SDEs with stable noise, extending classical results to non-Gaussian settings.

Findings

Establishes a stable central limit theorem for superdiffusive SDE solutions

Provides a framework for analyzing long-term behavior of stable noise-driven systems

Extends classical CLT results to alpha-stable processes

Abstract

This paper establishes a functional stable central limit theorem for a class of superdiffusive solutions to stochastic differential equations driven by an $\alpha$-stable process.