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Large deviation principles for renewal–reward processes

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  • Zamparo, Marco

Abstract

We establish a sharp large deviation principle for renewal–reward processes, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. In fact, we demonstrate a weak large deviation principle without assuming any exponential moment condition on the law of waiting times and rewards by resorting to a sharp version of Cramér’s theory. We also exhibit sufficient conditions for exponential tightness of renewal–reward processes, which leads to a full large deviation principle.

Suggested Citation

  • Zamparo, Marco, 2023. "Large deviation principles for renewal–reward processes," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 226-245.
    • Handle: RePEc:eee:spapps:v:156:y:2023:i:c:p:226-245
    DOI: 10.1016/j.spa.2022.11.009
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    References listed on IDEAS

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    1. Zamparo, Marco, 2021. "Large deviations in discrete-time renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 80-109.
    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. 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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