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 MODAL'X - Modélisation aléatoire de Paris X
4 IUF - Institut universitaire de France

We use a Stochastic Differential Equation satisfied by Brownian motion taking values in the unit sphere Sn−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 $n$-dimensional Ornstein-Uhlenbeck processes.

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

Domaines: Probabilités [math.PR]

Stavros Vakeroudis, Marc Yor. A Central Limit Theorem for a sequence of Brownian motions in the unit sphere in Rn. 2011. ⟨hal-00608880v1⟩