Large deviations in discrete-time renewal theory

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:139

Article

Zamparo, Marco¹ 

[1] Politecn Torino, Dipartimento Sci Applicata & Tecnol, Corso Duca Abruzzi 24, I-10129 Turin, Italy

关键词: Large deviations;    Cramer's theorem;    Renewal processes;    Polymer pinning models;    Renewal-reward processes;    Banach space valued random variables;   

DOI  :  10.1016/j.spa.2021.04.014

来源: Elsevier

【 摘 要 】

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. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free