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Large deviations for the empirical measure of heavy-tailed Markov renewal processes. (English) Zbl 1351.60031

Summary: A large deviations principle is established for the joint law of the empirical measure and the flow measure of a Markov renewal process on a finite graph. We do not assume any bound on the arrival times, allowing heavy-tailed distributions. In particular, the rate function is in general degenerate (it has a nontrivial set of zeros) and not strictly convex. These features show a behaviour highly different from what one may guess with a heuristic Donsker-Varadhan analysis of the problem.

MSC:

60F10 Large deviations
60K15 Markov renewal processes, semi-Markov processes
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