Large Deviations in Discrete-Time Renewal Theory

Marco Zamparo

doi:10.1016/j.spa.2021.04.014

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arXiv · 1903.03527

Large Deviations in Discrete-Time Renewal Theory

Marco Zamparo

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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.

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Marco Zamparo. 2019-03-08. Large Deviations in Discrete-Time Renewal Theory. https://doi.org/10.1016/j.spa.2021.04.014

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