Non parametric estimation of the measure associated with the Lévy–Khintchine canonical representation

Abstract

Given a Lévy process observed on a finite time interval [0, R], we consider the non parametric estimation of the function H, sometimes called the jump function, associated with the Lévy–Khintchine canonical representation over an interval [c, d] where −∞ < c < d < ∞. In particular, we shall assume a high-frequency framework and apply the method of sieves to estimate H. We also show that under certain conditions the estimator enjoys asymptotic normality and consistency. The dimension of the sieve will also be investigated.