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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.

Keywords

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 !

R2 v1 2026-06-28T14:48:28.077Z