  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.
