Quenched large deviations in renewal theory

Frank den Hollander and Marco Zamparo

Stochastic Processes and their Applications, 2024, vol. 175, issue C

Abstract: In this paper we introduce and study renewal–reward processes in random environments where each renewal involves a reward taking values in a Banach space. We derive quenched large deviation principles and identify the associated rate functions in terms of variational formulas involving correctors. We illustrate the theory with three examples: compound Poisson processes in random environments, pinning of polymers at interfaces with disorder, and returns of Markov chains in dynamic random environments.

Keywords: Random environments; Renewal–reward processes; Quenched large deviations; Rate functions; Compound Poisson processes; Pinned polymers; Returns of Markov chains (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104414

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