English

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}
}