Large deviations for renewal processes

R. Lefevere (1) , M. Mariani , L. Zambotti (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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]

R. Lefevere, M. Mariani, L. Zambotti. Large deviations for renewal processes. Stochastic Processes and their Applications, 2011, 121 (10), pp.2243-2271. ⟨10.1016/j.spa.2011.06.005⟩. ⟨hal-00623074⟩