arXiv subjects

Go Tokumitsu

Publications and source records attributed to Go Tokumitsu.

4 recordsLinked to original sources

arXiv2026

Elephant Random Walk Conditioned to Avoid Zero

We investigate the long-time limit of an elephant random walk conditioned to avoid zero and show that the resulting process admits a Skorokhod-type embedding into a three-dimensional Bessel process. Using this embedding, we further establish several limit theorems for the conditioned elephant random walk, including a scaling limit to a deterministically rescaled and time-changed three-dimensional Bessel process, and a law of the iterated logarithm.

math.PR↗

arXiv2026

Stable functional CLTs for scaled elephant random walks

We establish stable functional central limit theorems for scaled elephant random walks in the diffusive, critical, and superdiffusive cases using the martingale approach.

math.PR↗

arXiv2025

Functional central limit theorems for the dynamic elephant random walk

We prove functional central limit theorems for the dynamic elephant random walk in the $\sqrt{n}$ and $\sqrt{n\log n}$ orders, by applying the martingale convergence theorem and Karamata's theory of regular variation.

math.PR↗

arXiv2025

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

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.

math.PR↗