On Multivariate Strong Renewal Theorem
Probability
2017-03-16 v3
Abstract
This paper takes the so-called probabilistic approach to the Strong Renewal Theorem (SRT) for multivariate distributions in the domain of attraction of a stable law. A version of the SRT is obtained that allows any kind of lattice-nonlattice composition of a distribution. A general bound is derived to control the so-called "small- contribution", which arises from random walk paths that have a relatively small number of steps but make large cumulative moves. The asymptotic negligibility of the small- contribution is essential to the SRT. Applications of the SRT are given, including some that provide a unified treatment to known results but with substantially weaker assumptions.
Cite
@article{arxiv.1412.2026,
title = {On Multivariate Strong Renewal Theorem},
author = {Zhiyi Chi},
journal= {arXiv preprint arXiv:1412.2026},
year = {2017}
}