A Central Limit Theorem for a sequence of Brownian motions in the unit sphere in Rn

Stavros Vakeroudis; Marc Yor

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arXiv · 1107.3230

A Central Limit Theorem for a sequence of Brownian motions in the unit sphere in Rn

Stavros Vakeroudis·Marc Yor

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Abstract

We use a Stochastic Differential Equation satisfied by Brownian motion taking values in the unit sphere $S_{n-1}subsetmathbb{R}^{n}$ and we obtain a Central Limit Theorem for a sequence of such Brownian motions. We also generalize the results to the case of the $n$-dimensional Ornstein-Uhlenbeck processes.

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Stavros Vakeroudis, Marc Yor. 2011-07-16. A Central Limit Theorem for a sequence of Brownian motions in the unit sphere in Rn. https://arxiv.org/abs/1107.3230

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