Large deviations for the empirical measure of Markov renewal processes

Mauro Mariani (1) , Yuhao Shen (2) , Lorenzo Zambotti (2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Domaines: Probabilités [math.PR]

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