Nonparametric inference for discretely sampled L\'evy processes

Given a sample from a discretely observed Levy process X = (Xt)t�0 of the finite jump activity, the problem of nonparametric estimation of the Levy density ρ corresponding to the process X is studied. An estimator of ρ is proposed that is based on a suitable inversion of the Levy-Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of ρ over suit- able classes of Levy triplets. The corresponding lower bounds are also discussed.

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