Sample-path large deviations for unbounded additive functionals of the reflected random walk
Probability
2023-10-03 v3
Abstract
We prove a sample path large deviation principle (LDP) with sub-linear speed for unbounded functionals of certain Markov chains induced by the Lindley recursion. The LDP holds in the Skorokhod space equipped with the topology. Our technique hinges on a suitable decomposition of the Markov chain in terms of regeneration cycles. Each regeneration cycle denotes the area accumulated during the busy period of the reflected random walk. We prove a large deviation principle for the area under the busy period of the MRW, and we show that it exhibits a heavy-tailed behavior.
Cite
@article{arxiv.2003.14381,
title = {Sample-path large deviations for unbounded additive functionals of the reflected random walk},
author = {Mihail Bazhba and Jose Blanchet and Chang-Han Rhee and Bert Zwart},
journal= {arXiv preprint arXiv:2003.14381},
year = {2023}
}