The oscillating random walk on $\mathbb{Z}$
Probability
2022-01-06 v1
Abstract
The paper is concerned with a new approach for the recurrence property of the oscillating process on in Kemperman's sense. In the case when the random walk is ascending on and descending on , we determine the invariant measure of the embedded process of successive crossing times and then prove a necessary and sufficient condition for recurrence. Finally, we make use of this result to show that the general oscillating process is recurrent under some H{\"o}lder-typed moment assumptions.
Cite
@article{arxiv.2201.01515,
title = {The oscillating random walk on $\mathbb{Z}$},
author = {D Vo},
journal= {arXiv preprint arXiv:2201.01515},
year = {2022}
}