Quenched large deviations in renewal theory

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. W...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 175; p. 104414
Main Authors den Hollander, Frank, Zamparo, Marco
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2024
Subjects
Compound Poisson processes
Pinned polymers
Quenched large deviations
Random environments
Rate functions
Renewal–reward processes
Returns of Markov chains
Compound Poisson processes
Quenched large deviations
60F10
Random environments
Renewal–reward processes
82D60
Returns of Markov chains
60K05
60K37
Rate functions
60K10
Pinned polymers
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Summary: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.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2024.104414