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

Stavros Vakeroudis (1, 2, 3) , Marc Yor (1, 4)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 ENS-PSL - École normale supérieure - Paris
3 School of Mathematics - Department of Mathematics [Manchester]
4 IUF - Institut universitaire de France

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.

Keywords: Central Limit Theorem; Brownian motion in the unit sphere in Rn; Ornstein-Uhlenbeck processes

Domains: Probability [math.PR]

Stavros Vakeroudis, Marc Yor. A Central Limit Theorem for a sequence of Brownian motions in the unit sphere in Rn. 2011. ⟨hal-00608880v3⟩