Large deviation principles for renewal–reward processes

Marco Zamparo

Stochastic Processes and their Applications, 2023, vol. 156, issue C, 226-245

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.

Keywords: Large deviations; Cramér’s theorem; Renewal processes; Renewal–reward processes; Banach space valued random variables (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2022.11.009

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