Estimation of the characteristics of a Lévy process observed at arbitrary frequency



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, we encompass the usual low- and high-frequency assumptions and also obtain asymptotics in the mid-frequency regime.