Quenched large deviations in renewal theory

Stochastic Processes and their Applications, vol. 175, pp. 104414

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.

Authors 2

1. Frank den Hollander Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch Instituut, Universiteit Leiden, Einsteinweg 55, 2333 CC Leiden, The Netherlands

2. Marco Zamparo corresponding

   Istituto Nazionale di Fisica Nucleare, Sezione di Bari · University of Bari Aldo Moro

   Affiliation as printed

   Dipartimento di Fisica, Università degli Studi di Bari e Istituto Nazionale di Fisica Nucleare, Sezione di Bari, via Amendola 173, 70126 Bari, Italy