Abstract : This chapter is concerned with nonparametric estimation of the Lévy density of a Lévy process. The sample path is observed at $n$ equispaced instants with sampling interval $\Delta$. We develop several nonparametric adaptive methods of estimation based on deconvolution, projection and kernel. The asymptotic framework is: $n$ tends to infinity, $\Delta=\Delta_n$ tends to $0$ while $n\Delta_n$ tends to infinity (high frequency). Bounds for the ${\mathbb L}^2$-risk of estimators are given. Rates of convergence are discussed. Estimation of the drift and Gaussian component coefficients is studied. A specific method for the estimating the jump density of compound Poisson processes is presented. Examples and simulation results illustrate the performance of estimators.
Type de document :
Chapitre d'ouvrage
Lévy Matters IV, IV, Springer International Publishing, pp.77-177, 2015, Estimation for Discretely Observed Lévy Processes, 978-3-319-12372-1. <10.1007/978-3-319-12373-8>. <http://www.springer.com/fr/book/9783319123721#aboutBook>
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https://hal.archives-ouvertes.fr/hal-00913367
Contributeur : Fabienne Comte <>
Soumis le : mardi 3 décembre 2013 - 15:33:22
Dernière modification le : mardi 11 octobre 2016 - 13:27:54
Document(s) archivé(s) le : lundi 3 mars 2014 - 23:20:10

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Fabienne Comte, Valentine Genon-Catalot. Adaptive Estimation for Lévy processes. Lévy Matters IV, IV, Springer International Publishing, pp.77-177, 2015, Estimation for Discretely Observed Lévy Processes, 978-3-319-12372-1. <10.1007/978-3-319-12373-8>. <http://www.springer.com/fr/book/9783319123721#aboutBook>. <hal-00913367>

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