Persistent random walks
Probability
2015-09-15 v1 Statistics Theory
Statistics Theory
Abstract
We consider a walker that at each step keeps the same direction with a probabilitythat depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent random walk and give the conditions of recurrence or transience in terms of "transition" probabilities to keep on the same direction or to change, without assuming that the latter admits any stationary probability. Examples are exhibited when this process is recurrent even if the random walk is not symmetric.
Cite
@article{arxiv.1509.03882,
title = {Persistent random walks},
author = {Peggy Cénac and Basile De Loynes and Arnaud Le Ny and Yoann Offret},
journal= {arXiv preprint arXiv:1509.03882},
year = {2015}
}