Large deviations for renewal processes

Details Large deviations for renewal processes Large deviations for renewal processes

2010-09-14

arxiv.org/abs/1009.2659v2

Mathematics

Probability

Scientific paper

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.

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