Nonparametric inference for discretely sampled Lévy processes

S. Gugushvili

Research output: Book/ReportReportAcademic

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Abstract

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 \rho corresponding to the process X is studied. An estimator of \rho 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 \rho over suitable classes of Lévy triplets. The corresponding lower bounds are also discussed.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages24
EditionRevision 25 May 2011 (v3)
Publication statusPublished - 2009

Publication series

NameReport Eurandom
Volume2009041
ISSN (Print)1389-2355

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