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In this paper, we study nonparametric estimation of the L\'{e}vy density forL\'{e}vy processes, with and without Brownian component. For this, we consider$n$ discrete time observations with step $\Delta$. The asymptotic framework is:$n$ tends to infinity, $\Delta=\Delta_n$ tends to zero while $n\Delta_n$ tendsto infinity. We use a Fourier approach to construct an adaptive nonparametricestimator of the L\'{e}vy density and to provide a bound for the global${\mathbb{L}}^2$-risk. Estimators of the drift and of the variance of theGaussian component are also studied. We discuss rates of convergence and giveexamples and simulation results for processes fitting in our framework.

Estimation for L\'{e}vy processes from high frequency data within a long time interval