A martingale approach for the elephant random walk
Probability
2018-01-17 v1 Data Analysis, Statistics and Probability
Abstract
The purpose of this paper is to establish, via a martingale approach, some refinements on the asymptotic behavior of the one-dimensional elephant random walk (ERW). The asymptotic behavior of the ERW mainly depends on a memory parameter which lies between zero and one. This behavior is totally different in the diffusive regime , the critical regime , and the superdiffusive regime . Notwithstanding of this trichotomy, we provide some new results on the almost sure convergence and the asymptotic normality of the ERW.
Cite
@article{arxiv.1707.04130,
title = {A martingale approach for the elephant random walk},
author = {Bernard Bercu},
journal= {arXiv preprint arXiv:1707.04130},
year = {2018}
}