Optimal estimation of local time and occupation time measure for an α-stable Levy process
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910310254772224 |
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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 |