Workshop on Structure Adapting Methods - Abstract

Gugushvili, Shota

Nonparametric inference for discretely sampled Lévy processes

Given a sample from a discretely observed Lévy process $X=(X_t)_tgeq 0$ of the finite jump activity, we study the problem of nonparametric estimation of the Lévy density $rho$ corresponding to the process $X.$ Our estimator of $rho$ is based on a suitable inversion of the Lévy-Khintchine formula and a plug-in device. The main result of the paper deals with an upper bound on the mean square error of the estimator of $rho$ at a fixed point $x.$ We also show that the estimator attains the minimax convergence rate over a suitable class of Lévy densities.