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A large deviations principle is established for the joint law of theempirical measure and the flow measure of a renewal Markov process on a finitegraph. We do not assume any bound on the arrival times, allowing heavy taileddistributions. In particular, the rate functional is in general degenerate (ithas a nontrivial set of zeros) and not strictly convex. These features show abehavior highly different from what one may guess with a heuristicDonsker-Varadhan analysis of the problem.

Large deviations for the empirical measure of heavy tailed Markov renewal processes