Large deviations in discrete-time renewal theory

Marco Zamparo

Stochastic Processes and their Applications, 2021, vol. 139, issue C, 80-109

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.

Keywords: Large deviations; Cramér’s theorem; Renewal processes; Polymer pinning models; Renewal–reward processes; Banach space valued random variables (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spa.2021.04.014

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