On the center of mass of the elephant random walk

Our goal is to investigate the asymptotic behavior of the center of mass of the elephant random walk, which is a discrete-time random walk on integers with a complete memory of its whole history. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated log...

Full description

Saved in:
Bibliographic Details
Published inStochastic processes and their applications Vol. 133; pp. 111 - 128
Main Authors Bercu, Bernard, Laulin, Lucile
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2021
Elsevier
Subjects
Almost sure convergence
Asymptotic normality
Center of mass
Elephant random walk
Mathematics
Multi-dimensional martingales
Probability
secondary
Almost sure convergence
Asymptotic normality
Center of mass
Elephant random walk
Multi-dimensional martingales
primary
Online AccessGet full text

Cover

More Information
Summary:Our goal is to investigate the asymptotic behavior of the center of mass of the elephant random walk, which is a discrete-time random walk on integers with a complete memory of its whole history. In the diffusive and critical regimes, we establish the almost sure convergence, the law of iterated logarithm and the quadratic strong law for the center of mass of the elephant random walk. The asymptotic normality, properly normalized, is also provided. Finally, we prove a strong limit theorem for the center of mass in the superdiffusive regime. All our analysis relies on asymptotic results for multi-dimensional martingales.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2020.11.004