Limit theorems for the fluctuation of the dynamic elephant random walk in the superdiffusive case

Go Tokumitsu; Kouji Yano

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arXiv · 2503.13810

Limit theorems for the fluctuation of the dynamic elephant random walk in the superdiffusive case

Go Tokumitsu·Kouji Yano

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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.

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Go Tokumitsu, Kouji Yano. 2025-03-18. Limit theorems for the fluctuation of the dynamic elephant random walk in the superdiffusive case. https://arxiv.org/abs/2503.13810

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