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 language | English |
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Place of Publication | Eindhoven |
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Publisher | Eurandom |
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Number of pages | 24 |
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Edition | Revision 25 May 2011 (v3) |
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Publication status | Published - 2009 |
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Name | Report Eurandom |
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Volume | 2009041 |
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ISSN (Print) | 1389-2355 |
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