Nonparametric inference for discretely sampled Lévy processes

S. Gugushvili

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17 Citations (Scopus)
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Abstract

Given a sample from a discretely observed Lévy process X = (Xt)t≥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
Original languageEnglish
Pages (from-to)282-307
JournalAnnales de l'institut Henri Poincare (B): Probability and Statistics
Volume48
Issue number1
DOIs
Publication statusPublished - 2012

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