Decompounding under Gaussian noise

Abstract

Assuming that a stochastic process $X=(X_t{)}_{t\ge 0}$ is a sum of a compound Poisson process $Y=(Y_t{)}_{t\ge 0}$ with known intensity $\lambda$ and unknown jump size density $f,$ and an independent Brownian motion $Z=(Z_t{)}_{t\ge 0},$ 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.

26 pages, 6 figures

References in corpus (2)

• Deconvolution for an atomic distribution
• Nonparametric estimation for Lévy processes from low-frequency observations

Cited by in corpus (1)

• Deconvolution for an atomic distribution