Large Deviations in Discrete-Time Renewal Theory

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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Cited by in corpus (6)

• Statistical fluctuations under resetting: rigorous results
• Large deviation principles for renewal-reward processes
• Anomalous fluctuations of renewal-reward processes with heavy-tailed distributions
• Asymptotic deviation bounds for cumulative processes
• Renewal model for dependent binary sequences
• Critical Fluctuations in Renewal Models of Statistical Mechanics