Elephant Random Walk Conditioned to Avoid Zero

Kohki Iba; Go Tokumitsu

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arXiv · 2607.28728

Elephant Random Walk Conditioned to Avoid Zero

Kohki Iba·Go Tokumitsu

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Abstract

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.

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Kohki Iba, Go Tokumitsu. 2026-07-30. Elephant Random Walk Conditioned to Avoid Zero. https://arxiv.org/abs/2607.28728

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