Moments of the superdiffusive elephant random walk with general step distribution

József Kiss, Bálint Vető

Published 2021-11-30, updated 2022-09-30Version 2

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.