A Central Limit Theorem for a sequence of Brownian motions in the unit sphere in RnReport as inadecuate




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* Corresponding author 1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires 2 ENS Paris - École normale supérieure - Paris 3 School of Mathematics - Department of Mathematics Manchester 4 IUF - Institut Universitaire de France

Abstract : 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





Author: Stavros Vakeroudis - Marc Yor -

Source: https://hal.archives-ouvertes.fr/



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