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

We use a Stochastic Differential Equation satisfied by Brownian motion taking values in the unit sphere Sn−1⊂RnSn−1⊂Rn and we obtain a Central Limit Theorem for a sequence of such Brownian motions. We also generalize the results to the case of the nn-dimensional Ornstein–Uhlenbeck processes.