  Assuming that a stochastic process $X=(X_t)_{t\geq 0}$ is a sum of a compound
Poisson process $Y=(Y_t)_{t\geq 0}$ with known intensity $\lambda$ and unknown
jump size density $f,$ and an independent Brownian motion $Z=(Z_t)_{t\geq 0},$
we consider the problem of nonparametric estimation of $f$ from low frequency
observations from $X.$ The estimator of $f$ is constructed via Fourier
inversion and kernel smoothing. Our main result deals with asymptotic normality
of the proposed estimator at a fixed point.
