Amorino, ChiaraJaramillo, ArturoPodolskij, Mark2025-11-042025-11-042024Amorino C, Jaramillo A, Podolskij M. Optimal estimation of the local time and the occupation time measure for an α-stable Lévy process. Modern Stochastics: Theory and Applications. 2024;11(2):149-68. DOI: 10.15559/24-VMSTA2432351-6046http://hdl.handle.net/10230/71763A novel theoretical result on estimation of the local time and the occupation time measure of an α-stable Lévy process with α∈(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.application/pdfeng© 2024 The Author(s). Published by VTeX. Open access article under the CC BY license.info:eu-repo/semantics/article2025-11-04http://dx.doi.org/10.15559/24-VMSTA243High frequency dataLocal timeMixed normal distributionOccupation timeStable Lévy processesinfo:eu-repo/semantics/openAccess