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

Stavros Vakeroudis; Marc Yor

paper

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

arXiv:1107.3230

Abstract

We use a Stochastic Differential Equation satisfied by Brownian motion taking values in the unit sphere $S_{n - 1} s u b se t ma t hbb R^{n}$ 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.