Limit theorems for the fluctuation of the dynamic elephant random walk in the superdiffusive case
Probability
2025-05-19 v3
Abstract
Motivated by the previous results by Coletti-de Lima-Gava-Luiz (2020) and Shiozawa (2022), we study the fluctuation of the dynamic elephant random walk in the superdiffusive case with a strong elephant component. Applying the martingale convergence theorem, we prove the Central Limit Theorem and the Law of Iterated Logarithm, where a random drift is subtracted from the process considered.
Keywords
Cite
@article{arxiv.2503.13810,
title = {Limit theorems for the fluctuation of the dynamic elephant random walk in the superdiffusive case},
author = {Go Tokumitsu and Kouji Yano},
journal= {arXiv preprint arXiv:2503.13810},
year = {2025}
}