Extension of a theorem of Wschebor to free and matrix Brownian motions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914179189833728 |
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| author | Donati-Martin, Catherine Rouault, Alain |
| author_facet | Donati-Martin, Catherine Rouault, Alain |
| contents | In 1992, M. Wschebor proved a theorem on the convergence of small increments of the Brownian motion. Since then, it has been extended to various processes. We prove a version of this theorem for the Hermitian Brownian motion and the free Brownian motion. Since these theorems deal with a convergence to a deterministic limit, we prove also the convergence in distribution of the corresponding fluctuations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21014 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extension of a theorem of Wschebor to free and matrix Brownian motions Donati-Martin, Catherine Rouault, Alain Probability In 1992, M. Wschebor proved a theorem on the convergence of small increments of the Brownian motion. Since then, it has been extended to various processes. We prove a version of this theorem for the Hermitian Brownian motion and the free Brownian motion. Since these theorems deal with a convergence to a deterministic limit, we prove also the convergence in distribution of the corresponding fluctuations. |
| title | Extension of a theorem of Wschebor to free and matrix Brownian motions |
| topic | Probability |
| url | https://arxiv.org/abs/2505.21014 |