Large deviations for the empirical measure of heavy tailed Markov renewal processes
Probability
2014-02-18 v2
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.
Keywords
Cite
@article{arxiv.1203.5930,
title = {Large deviations for the empirical measure of heavy tailed Markov renewal processes},
author = {Mauro Mariani and Lorenzo Zambotti},
journal= {arXiv preprint arXiv:1203.5930},
year = {2014}
}