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

Optimal estimation of local time and occupation time measure for an {\alpha}-stable Levy process