Open Access
2022 Moments of the superdiffusive elephant random walk with general step distribution
József Kiss, Bálint Vető
Author Affiliations +
Electron. Commun. Probab. 27: 1-12 (2022). DOI: 10.1214/22-ECP485


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 nα in the superdiffusive regime where α is the memory parameter. This extends the results obtained by Bercu in [Ber17].

Funding Statement

The work of the authors was supported by the NKFI (National Research, Development and Innovation Office) grant FK123962. B. Vető was supported by the Bolyai Research Scholarship of the Hungarian Academy of Sciences and by the ÚNKP–21–5 New National Excellence Program of the Ministry for Innovation and Technology from the source of the National Research, Development and Innovation Fund.


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József Kiss. Bálint Vető. "Moments of the superdiffusive elephant random walk with general step distribution." Electron. Commun. Probab. 27 1 - 12, 2022.


Received: 22 April 2022; Accepted: 28 August 2022; Published: 2022
First available in Project Euclid: 23 September 2022

arXiv: 2112.00066
MathSciNet: MR4368695
Digital Object Identifier: 10.1214/22-ECP485

Primary: 60G50

Keywords: elephant random walk , limiting moments

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