Reinforced random walks under memory lapses
Probability
2021-09-22 v1 Mathematical Physics
math.MP
Abstract
We introduce a one-dimensional random walk, which at each step performs a reinforced dynamics with probability and with probability , the random walk performs a step independent of the past. We analyse its asymptotic behaviour, showing a law of large numbers and characterizing the diffusive and superdiffusive regions. We prove central limit theorems and law of iterated logarithm based on the martingale approach.
Cite
@article{arxiv.2109.10301,
title = {Reinforced random walks under memory lapses},
author = {Manuel González-Navarrete and Ranghely Hernández},
journal= {arXiv preprint arXiv:2109.10301},
year = {2021}
}