Nonparametric inference for discretely sampled Lévy processes
Given a sample from a discretely observed Lévy process = ( )≥0 of the finite jump activity, the problem of nonparametric estimation of the Lévy density corresponding to the process is studied. An estimator of is proposed that is based on a suitable inversion of the Lévy–Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of over suitable classes of Lévy triplets. The corresponding lower bounds are also discussed.