# Nonparametric estimation for pure jump irregularly sampled or noisy Lévy processes

Abstract : In this paper, we study nonparametric estimation of the Lévy density for pure jump Lévy processes. We consider $n$ discrete time observations that may be irregularly sampled or possibly corrupted by a small noise independent of the main process. The case of non noisy observations with regular sampling interval has been studied by the authors in previous works which are the benchmark for the extensions proposed here. We study first the case of a regular sampling interval and noisy data, then the case of irregular sampling for non noisy data. In each case, non adaptive and adaptive estimators are proposed and risk bounds are derived.
Type de document :
Article dans une revue
Statistica Neerlandica, Wiley, 2010, 64 (3), pp.290-313. <10.1111/j.1467-9574.2010.00462.x>
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https://hal.archives-ouvertes.fr/hal-00424263
Contributeur : Fabienne Comte <>
Soumis le : mercredi 14 octobre 2009 - 16:34:06
Dernière modification le : mardi 11 octobre 2016 - 12:00:16
Document(s) archivé(s) le : mercredi 16 juin 2010 - 00:45:58

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ComteGenonNeerlandica.pdf
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### Citation

Fabienne Comte, Valentine Genon-Catalot. Nonparametric estimation for pure jump irregularly sampled or noisy Lévy processes. Statistica Neerlandica, Wiley, 2010, 64 (3), pp.290-313. <10.1111/j.1467-9574.2010.00462.x>. <hal-00424263>

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