Nonparametric estimation of the Lévy density - Institut Élie Cartan de Lorraine

Date/heure
1 décembre 2022
10:45 - 11:45

Oratrice ou orateur
Ester Mariucci (Université de Versailles)

Catégorie d'évènement
Séminaire Probabilités et Statistique

Résumé

We consider the problem of estimating the Lévy density of a pure jump Lévy process, possibly of infinite variation, from the high frequency observation of one trajectory. To directly construct an estimator of the Lévy density, we use a compound Poisson approximation and we build a linear wavelet estimator. Its performance is studied in terms of $L_{p}$ loss functions, $p \geq 1$ , over Besov balls. To show that the resulting rates are minimax-optimal for a large class of Lévy processes, we propose new non-asymptotic bounds of the cumulative distribution function of Lévy processes with Lévy density bounded from above by the density of an alpha-stable type Lévy process in a neighbourhood of the origin. It is a joint work with Céline Duval.