On the asymptotics of a lazy reinforced random walk
Probability
2024-02-14 v1
Abstract
Based on a martingale theory approach, we present a complete characterization of the asymptotic behaviour of a lazy reinforced random walk (LRRW) which shows three different regimes (diffusive, critical and superdiffusive). This allows us to prove versions of the law of large numbers, the quadratic strong law, the law of iterated logarithm, the almost sure central limit theorem and the functional central limit theorem in the diffusive and critical regimes. In the superdiffusive regime we obtain a strong convergence to a random variable, including a central limit theorem and a law of iterated logarithm for the fluctuations.
Keywords
Cite
@article{arxiv.2402.08033,
title = {On the asymptotics of a lazy reinforced random walk},
author = {Manuel González-Navarrete and Rodrigo Lambert and Víctor Hugo Vázquez Guevara},
journal= {arXiv preprint arXiv:2402.08033},
year = {2024}
}