Year: 2019
Type: preprint
Abstract: We consider random walks perturbed at zero which behave like (possibly different) random walks with i.i.d. increments on each half lines and restarts at $0$ whenever they cross that point. We show that the perturbed random walk, after being rescaled in a proper way, converges to a skew Brownian motion whose parameter is defined by renewal functions of the simple random walks and the transition probabilities from $0$.
Source: arXiv (Cornell University)
Authors: Ngo, Hoang-Long, Peigne, Marc
Institutions: Université de Tours, Université d'Orléans, Institut Denis Poisson
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2947280506