Nonparametric inference for discretely sampled Lévy processes

Details Nonparametric inference for discretely sampled Lévy processes Nonparametric inference for discretely sampled Lévy processes

2009-08-21

arxiv.org/abs/0908.3121v3

Mathematics

Statistics Theory

38 pages

Scientific paper

Given a sample from a discretely observed L\'evy process $X=(X_t)_{t\geq 0}$ of the finite jump activity, the problem of nonparametric estimation of the L\'evy density $\rho$ corresponding to the process $X$ is studied. An estimator of $\rho$ is proposed that is based on a suitable inversion of the L\'evy-Khintchine formula and a plug-in device. The main results of the paper deal with upper risk bounds for estimation of $\rho$ over suitable classes of L\'evy triplets. The corresponding lower bounds are also discussed.

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