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

Fuente: arXiv
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Main Authors: Amorino, Chiara, Jaramillo, Arturo, Podolskij, Mark
Format: Preprint
Published: 2022
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author Amorino, Chiara
Jaramillo, Arturo
Podolskij, Mark
author_facet Amorino, Chiara
Jaramillo, Arturo
Podolskij, Mark
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2210_07672
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Optimal estimation of local time and occupation time measure for an α-stable Levy process
Amorino, Chiara
Jaramillo, Arturo
Podolskij, Mark
Probability
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.
title Optimal estimation of local time and occupation time measure for an α-stable Levy process
topic Probability
url https://arxiv.org/abs/2210.07672