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Large deviations in discrete-time renewal theory

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  • Zamparo, Marco

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.

Suggested Citation

  • Zamparo, Marco, 2021. "Large deviations in discrete-time renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 80-109.
    • Handle: RePEc:eee:spapps:v:139:y:2021:i:c:p:80-109
    DOI: 10.1016/j.spa.2021.04.014
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    References listed on IDEAS

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    1. Serfozo, Richard F., 1974. "Large deviations of renewal processes," Stochastic Processes and their Applications, Elsevier, vol. 2(3), pages 295-301, July.
    2. Lefevere, Raphaël & Mariani, Mauro & Zambotti, Lorenzo, 2011. "Large deviations for renewal processes," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2243-2271, October.
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    Cited by:

    1. Zamparo, Marco, 2023. "Large deviation principles for renewal–reward processes," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 226-245.
    2. Cattiaux, Patrick & Colombani, Laetitia & Costa, Manon, 2023. "Asymptotic deviation bounds for cumulative processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 85-105.

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