Large deviations for renewal processes

Raphael Lefevere (1) , Mauro Mariani (2) , Lorenzo Zambotti (1)

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

We investigate large deviations for the empirical measure of the forward and backward recurrence time processes associated with a classical renewal process with arbitrary waiting-time distribution. The Donsker-Varadhan theory cannot be applied in this case, and indeed it turns out that the large deviations rate functional differs from the one suggested by such a theory. In particular, a non-strictly convex and non-analytic rate functional is obtained.

Domaines: Probabilités [math.PR]

Raphael Lefevere, Mauro Mariani, Lorenzo Zambotti. Large deviations for renewal processes. 2010. ⟨hal-00520234⟩