Optimal estimation of the local time and the occupation time measure for an α-stable Lévy process
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- dc.contributor.author Amorino, Chiara
- dc.contributor.author Jaramillo, Arturo
- dc.contributor.author Podolskij, Mark
- dc.date.accessioned 2025-11-04T13:56:28Z
- dc.date.available 2025-11-04T13:56:28Z
- dc.date.issued 2024
- dc.date.updated 2025-11-04T13:56:28Z
- dc.description.abstract A 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.
- dc.description.sponsorship The authors gratefully acknowledge financial support of ERC Consolidator Grant 815703 "STAMFORD: Statistical Methods for High Dimensional Diffusions."
- dc.format.mimetype application/pdf
- dc.identifier.citation Amorino 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-VMSTA243
- dc.identifier.doi http://dx.doi.org/10.15559/24-VMSTA243
- dc.identifier.issn 2351-6046
- dc.identifier.uri http://hdl.handle.net/10230/71763
- dc.language.iso eng
- dc.publisher VTeX
- dc.relation.ispartof Modern Stochastics: Theory and Applications. 2024;11(2):149-168
- dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/815703
- dc.rights © 2024 The Author(s). Published by VTeX. Open access article under the CC BY license.
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.rights.uri http://creativecommons.org/licenses/by/4.0/
- dc.subject.keyword High frequency data
- dc.subject.keyword Local time
- dc.subject.keyword Mixed normal distribution
- dc.subject.keyword Occupation time
- dc.subject.keyword Stable Lévy processes
- dc.title Optimal estimation of the local time and the occupation time measure for an α-stable Lévy process
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/publishedVersion