Rate of Convergence in the Functional Central Limit Theorem for Stable Processes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908927090753536 |
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| author | Huang, Lorick Decreusefond, Laurent Coutin, Laure |
| author_facet | Huang, Lorick Decreusefond, Laurent Coutin, Laure |
| contents | In this article, we quantify the functional convergence of the rescaled random walk with heavy tails to a stable process.This generalizes the Generalized Central Limit Theorem for stable random variables infinite dimension. We show that provided we have a control between the randomwalk or the limiting stable process and their respective affine interpolation, we canlift the rate of convergence obtained for multivariate distributions to a rateof convergence in some functional spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16834 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rate of Convergence in the Functional Central Limit Theorem for Stable Processes Huang, Lorick Decreusefond, Laurent Coutin, Laure Probability In this article, we quantify the functional convergence of the rescaled random walk with heavy tails to a stable process.This generalizes the Generalized Central Limit Theorem for stable random variables infinite dimension. We show that provided we have a control between the randomwalk or the limiting stable process and their respective affine interpolation, we canlift the rate of convergence obtained for multivariate distributions to a rateof convergence in some functional spaces. |
| title | Rate of Convergence in the Functional Central Limit Theorem for Stable Processes |
| topic | Probability |
| url | https://arxiv.org/abs/2401.16834 |