Moments of the superdiffusive elephant random walk with general step distribution

TL;DR

This paper analyzes the superdiffusive elephant random walk with general step distribution, deriving the first four moments of its limiting distribution when scaled by n^α, extending previous results.

Contribution

It provides explicit calculations of the first four moments for the limiting distribution of the elephant random walk with general steps in the superdiffusive regime, generalizing prior work.

Findings

Calculated the first four moments of the limiting distribution.

Extended previous results to general step distributions.

Analyzed the superdiffusive regime with memory parameter α.

Abstract

We consider the elephant random walk with general step distribution. We calculate the first four moments of the limiting distribution of the position rescaled by $n^\alpha$ in the superdiffusive regime where $\alpha$ is the memory parameter. This extends the results obtained by Bercu.