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Quenched large deviations in renewal theory

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  • den Hollander, Frank
  • Zamparo, Marco

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.

Suggested Citation

  • den Hollander, Frank & Zamparo, Marco, 2024. "Quenched large deviations in renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 175(C).
    • Handle: RePEc:eee:spapps:v:175:y:2024:i:c:s0304414924001200
    DOI: 10.1016/j.spa.2024.104414
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    References listed on IDEAS

    as
    1. Zamparo, Marco, 2021. "Large deviations in discrete-time renewal theory," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 80-109.
    2. Zamparo, Marco, 2023. "Large deviation principles for renewal–reward processes," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 226-245.
    3. Bazaes, Rodrigo & Mukherjee, Chiranjib & Ramírez, Alejandro F. & Saglietti, Santiago, 2023. "The effect of disorder on quenched and averaged large deviations for random walks in random environments: Boundary behavior," Stochastic Processes and their Applications, Elsevier, vol. 158(C), pages 208-237.
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    2. Zamparo, Marco, 2023. "Large deviation principles for renewal–reward processes," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 226-245.

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