A Lévy process is observed at time points of distance Δ until time T. We construct an estimator of the Lévy-Khinchine characteristics of the process and derive optimal rates of convergence simultaneously in T and Δ. Thereby, ...

For a Lévy process X having finite variation on compact sets and finite first moments, µ( dx) = xv( dx) is a finite signed measure which completely describes the jump dynamics. We construct kernel estimators for linear ...