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

Abstract: We present a novel theoretical result on estimation of local time and occupation time measure of an {\alpha}-stable L\'evy process with {\alpha} in (1, 2). Our approach is based upon computing the conditional expectation of the desired quantities given high frequency data, which is an L^2-optimal statistic by construction. We prove the corresponding stable central limit theorems and discuss a statistical application. In particular, this work extends the results of [Ivanovs and i Podolskij (2021)], which investigated the case of the Brownian motion.