On multidimensional elephant random walk with stops and random step sizes
Probability
2026-03-10 v2
Abstract
In this paper, we study the number of moves in a multidimensional elephant random walk with stops. We establish several convergence results for the number of moves, including the law of large numbers and the law of iterated logarithm. Using a martingale approach, we study the multidimensional elephant random walk with random step sizes. For this model, we obtain several almost sure convergence results for the number of moves, including the law of large numbers, the quadratic strong law, the law of iterated logarithm and the central limit theorem. Similar convergence results are derived for the multidimensional elephant random walk with random step sizes.
Cite
@article{arxiv.2601.07502,
title = {On multidimensional elephant random walk with stops and random step sizes},
author = {Shyan Ghosh and Manisha Dhillon and Kuldeep Kumar Kataria},
journal= {arXiv preprint arXiv:2601.07502},
year = {2026}
}