  Given a sample from a discretely observed compound Poisson process, we
consider estimation of the density of the jump sizes. We propose a kernel type
nonparametric density estimator and study its asymptotic properties. An order
bound for the bias and an asymptotic expansion of the variance of the estimator
are given. Pointwise weak consistency and asymptotic normality are established.
The results show that, asymptotically, the estimator behaves very much like an
ordinary kernel estimator.
