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Optimal estimation of local time and occupation time measure for an α-stable Levy process
Chiara Amorino, Arturo Jaramillo, Mark Podolskij · 2022-10-14 · via math.PR updates on arXiv.org

We present a novel theoretical result on estimation of local time and occupation time measure of an α-stable Lévy process with α 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.

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