  We study the nonparametric estimation of the jump density of a renewal reward
process from one discretely observed sample path over [0,T]. We consider the
regime when the sampling rate goes to 0. The main difficulty is that a renewal
reward process is not a Levy process: the increments are non stationary and
dependent. We propose an adaptive wavelet threshold density estimator and study
its performance for the Lp loss over Besov spaces. We achieve minimax rates of
convergence for sampling rates that vanish with T at polynomial rate. In the
same spirit as Buchmann and Gr\"ubel (2003) and Duval (2012), the estimation
procedure is based on the inversion of the compounding operator. The inverse
has no closed form expression and is approached with a fixed point technique.
