Optimal estimation of the local time and the occupation time measure for an α-stable Lévy process

A novel theoretical result on estimation of the local time and the occupation time measure of an alpha-stable Levy process with alpha is an element of (1, 2) is presented. The approach is based upon computing the conditional expectation of the desired quantities given high frequency data, which is an L2-optimal statistic by construction. The corresponding stable central limit theorems are proved and a statistical application is discussed. In particular, this work extends the results of [20], which investigated the case of the Brownian motion.