From persistent random walks to the telegraph noise
Probability
2008-10-06 v1
Abstract
We study a family of memory-based persistent random walks and we prove weak convergences after space-time rescaling. The limit processes are not only Brownian motions with drift. We have obtained a continuous but non-Markov process which can be easely expressed in terms of a counting process . In a particular case the counting process is a Poisson process, and permits to represent the solution of the telegraph equation. We study in detail the Markov process .
Cite
@article{arxiv.0810.0650,
title = {From persistent random walks to the telegraph noise},
author = {Samuel Herrmann and Pierre Vallois},
journal= {arXiv preprint arXiv:0810.0650},
year = {2008}
}