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What is Learnable in Valiant's Theory of the Learnable? 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Nonparametric inference for discretely sampled Lévy processes
Shota Gugushvili · 2009-08-21 · via math.ST updates on arXiv.org

Given a sample from a discretely observed Lévy process $X=(X_t)_{t\geq 0}$ of the finite jump activity, the problem of nonparametric estimation of the Lévy density $ρ$ corresponding to the process $X$ is studied. An estimator of $ρ$ 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 $ρ$ over suitable classes of Lévy triplets. The corresponding lower bounds are also discussed.

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