Nonparametric inference for discretely sampled Lévy processes

S. Gugushvili

Nonparametric inference for discretely sampled Lévy processes

S. Gugushvili

Eurandom

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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 language	English
Place of Publication	Eindhoven
Publisher	Eurandom
Number of pages	24
Edition	Revision 25 May 2011 (v3)
Publication status	Published - 2009

Publication series

Name	Report Eurandom
Volume	2009041
ISSN (Print)	1389-2355

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title = "Nonparametric inference for discretely sampled L{\'e}vy processes",

abstract = "Given a sample from a discretely observed L{\'e}vy process $ X = (X_t)_{t \geq 0} $ of the finite jump activity, the problem of nonparametric estimation of the L{\'e}vy 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{\'e}vy-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{\'e}vy triplets. The corresponding lower bounds are also discussed.",

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AB - 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.

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