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

Stavros Vakeroudis; Marc Yor

hal-00608880, version 1

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

Abstract: 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.

1: Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot
2: Ecole Normale Supérieure de Paris (ENS)
Ecole normale supérieure de Paris - ENS Paris
3: Modélisation aléatoire de Paris X (MODAL'X)
Université Paris X - Paris Ouest Nanterre La Défense
4: Institut Universitaire de France (IUF)
Ministère de l'Enseignement Supérieur et de la Recherche Scientifique

hal-00608880, version 1
http://hal.archives-ouvertes.fr/hal-00608880
oai:hal.archives-ouvertes.fr:hal-00608880
From: Stavros Vakeroudis <>
Submitted on: Friday, 15 July 2011 15:47:14
Updated on: Thursday, 15 September 2011 17:31:22

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arXiv: 1107.3230

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