Large Deviations in Discrete-Time Renewal Theory
Probability
2023-04-24 v2
Abstract
We establish sharp large deviation principles for cumulative rewards associated with a discrete-time renewal model, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. The framework we consider is the pinning model of polymers, which amounts to a Gibbs change of measure of a classical renewal process and includes it as a special case. We first tackle the problem in a constrained pinning model, where one of the renewals occurs at a given time, by an argument based on convexity and super-additivity. We then transfer the results to the original pinning model by resorting to conditioning.
Cite
@article{arxiv.1903.03527,
title = {Large Deviations in Discrete-Time Renewal Theory},
author = {Marco Zamparo},
journal= {arXiv preprint arXiv:1903.03527},
year = {2023}
}