Large deviations for the empirical measure of Markov renewal processes

Abstract : A large deviations principle is established for the joint law of the empirical measure and the flow measure of a renewal Markov process on a finite graph. We do not assume any bound on the arrival times, allowing heavy tailed distributions. In particular, the rate functional is in general degenerate (it has a nontrivial set of zeros) and not strictly convex. These features show a behavior highly different from what one may guess with a heuristic Donsker-Varadhan analysis of the problem.
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https://hal.archives-ouvertes.fr/hal-00706802
Contributor : Lorenzo Zambotti <>
Submitted on : Monday, June 11, 2012 - 3:43:11 PM
Last modification on : Tuesday, January 14, 2020 - 10:42:38 AM

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  • HAL Id : hal-00706802, version 1
  • ARXIV : 1203.5930

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Mauro Mariani, Yuhao Shen, Lorenzo Zambotti. Large deviations for the empirical measure of Markov renewal processes. 2012. ⟨hal-00706802⟩

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