Ester Mariucci
(University of Potsdam)

Stochastics Seminar

We consider the problem of estimating the Lévy density $f$ of a pure jump Lévy process, possibly of infinite variation, from the high frequency observation of one trajectory. We discuss two different approaches.

The first one consists in reducing the problem of the nonparametric estimation of $f$ to an easier one, namely the estimation of a drift of a Gaussian white noise model.

More precisely, we establish a global asymptotic equivalence between the experiments generated by the discrete (high frequency) or continuous observation of a path of a Lévy process and a Gaussian white noise experiment observed up to a time $T$, with $T$ tending to $\infty$. These approximations are given in the sense of the Le Cam distance, under some smoothness conditions on the unknown Lévy density. The asymptotic equivalences are established by constructing explicit equivalence mappings that can be used to reproduce one experiment from the other and to transfer estimators.

Organised by: Department of Mathematics

Contact: Mark Podolskij
Revised: 24.06.2021