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 in the superdiffusive regime where α is the memory parameter. This extends the results obtained by Bercu in [Ber17].
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.
"Moments of the superdiffusive elephant random walk with general step distribution." Electron. Commun. Probab. 27 1 - 12, 2022. https://doi.org/10.1214/22-ECP485