Extension of a theorem of Wschebor to free and matrix Brownian motions

Catherine Donati-Martin; Alain Rouault

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arXiv · 2505.21014

Extension of a theorem of Wschebor to free and matrix Brownian motions

Catherine Donati-Martin·Alain Rouault

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Abstract

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.

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Catherine Donati-Martin, Alain Rouault. 2025-05-27. Extension of a theorem of Wschebor to free and matrix Brownian motions. https://arxiv.org/abs/2505.21014

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