# Nonparametric estimation of the Lévy density

#### 11.07.2022, 10:00  –  Campus Golm, 2.09.2.22 (hybrid) Forschungsseminar Statistik

Céline Duval (Université de Lille)

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, $$p\geq1$$, 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 Ester Mariucci.

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