Nonparametric adaptive estimation for pure jump Lévy processes
This paper is concerned with nonparametric estimation of the Lévy density of a pure jump Lévy process. The sample path is observed at discrete instants with fixed sampling interval. We construct a collection of estimators obtained by deconvolution methods and deduced from appropriate estimators of the characteristic function and its first derivative. We obtain a bound for the -risk, under general assumptions on the model. Then we propose a penalty function that allows to build an adaptive estimator....