Quenched large deviations in renewal theory
type: Item
instance of: scholarly article
title: Quenched large deviations in renewal theory
author: F. den Hollander
author: Marco Zamparo
published in: Stochastic Processes and their Applications
publication date: 2024-09-02T00:00:00Z
review text: The aim of this study is to develop \textit{large deviation principles} for \textit{renewal-reward processes in random environments}. In the studied class of models, identified as generalized \textit{pinning models} with general rewards, the authors assume that each renewal involves a reward taking a value in a real separable Banach space. In contrast to the random walks in random environments and random potentials with bounded increments, which are typically analyzed in the literature, renewal times with possibly unbounded and heavy-tailed increments are here considered. Under some specific assumptions (involving the waiting-time distribution, the potential and the reward probability measures), the quenched fluctuations of the total reward over time are characterized. \par The main theoretical results of this study are applied to the following three examples: compound Poisson processes in random environments, pinning of polymers at interfaces with disorder and returns of Markov chains in dynamic random enviroments.
reviewed by: Eugen Paltanea
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60K37
Mathematics Subject Classification ID: 82D60
zbMATH DE Number: 7904811
zbMATH Keywords: random environments
zbMATH Keywords: renewal-reward processes
zbMATH Keywords: quenched large deviations
zbMATH Keywords: rate functions
zbMATH Keywords: compound Poisson processes
zbMATH Keywords: pinned polymers
zbMATH Keywords: returns of Markov chains
MaRDI profile type: Publication
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Quenched large deviations in renewal theory (DOI)
DOI: 10.1016/J.SPA.2024.104414