Elephant Random Walk Conditioned to Avoid Zero

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.

37 pages, 1 figure