Large deviation principles for renewal-reward processes
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Publication:6381974
DOI10.1016/J.SPA.2022.11.009arXiv2111.01679MaRDI QIDQ6381974
Publication date: 2 November 2021
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 Cram'er's theorem. We also exhibit sufficient conditions for exponential tightness of renewal-reward processes, which leads to a full large deviation principle.
Interacting random processes; statistical mechanics type models; percolation theory (60K35) Large deviations (60F10) Renewal theory (60K05)
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