Stable functional CLTs for scaled elephant random walks

TL;DR

This paper proves stable functional central limit theorems for scaled elephant random walks across different diffusive regimes, using martingale techniques to unify the understanding of their asymptotic behavior.

Contribution

It introduces a unified martingale-based approach to establish stable functional CLTs for elephant random walks in various diffusive regimes.

Findings

Proves stable functional CLTs in diffusive, critical, and superdiffusive cases.

Uses martingale methods to analyze asymptotic behavior.

Provides a comprehensive framework for understanding elephant random walks.

Abstract

We establish stable functional central limit theorems for scaled elephant random walks in the diffusive, critical, and superdiffusive cases using the martingale approach.