Estimation for Lévy processes from high frequency data within a long time interval
长时间区间内基于高频数据的 Lévy 过程估计
In this paper, we study nonparametric estimation of the Lévy density for Lévy processes, with and without Brownian component. For this, we consider n discrete time observations with step Δ. The asymptotic framework is: n tends to infinity, Δ=Δn tends to zero while nΔn tends to infinity. We use a Fourier approach to construct an adaptive nonparametric estimator of the Lévy density and to provide a bound for the global ${\mathbb{L}}^{2}$-risk. Estimators of the drift and of…