A universal scaling limit for diffusive amnesic step-reinforced random walks
Probability
2024-02-15 v1
Abstract
We introduce a variation of the step-reinforced random walk with general memory. For the diffusive regime, we establish a functional invariance principle and show that, given suitable conditions on the memory sequence, the arising limiting processes are always the sum of a noise reinforced Brownian motion and a (not independent) Brownian motion.
Cite
@article{arxiv.2402.09202,
title = {A universal scaling limit for diffusive amnesic step-reinforced random walks},
author = {Marco Bertenghi and Lucile Laulin},
journal= {arXiv preprint arXiv:2402.09202},
year = {2024}
}
Comments
20 pages, comments welcome !