Browse by: Author name - Classification - Keywords - Nature

2 matches found
V: 05, 58-75, LNM 191 (1971)
CARTIER, Pierre
Introduction à l'étude des mouvements browniens à plusieurs paramètres (Gaussian processes)
Settles in particular a disagreement between statements of Lévy (Processus Stochastiques et Mouvement Brownien, 1948) and McKean (Teor. Ver. i Prim. 8, 1963) on the domain of analyticity of some Gaussian random functions
Comment: More recent work of Cartier on covariances appeared in the L.~Schwartz volume Mathematical Analysis and Applications, A, Academic Press 1981
Keywords: Several parameter Brownian motions, Covariance
Nature: New exposition of known results
Retrieve article from Numdam
VII: 09, 61-76, LNM 321 (1973)
FARAUT, Jacques
Fonction brownienne sur une variété riemannienne (Miscellanea, Gaussian processes)
As defined originally by Lévy in the case of spheres and euclidian spaces, a Brownian motion indexed by a point of a metric space $E$ is a centered Gaussian process $(X_t)_{t\in E}$ such that $E[(X_t-X_s)^2]=d(s,t)$, the distance. In a Riemannian manifold $d$ is understood to be the geodesic distance. The results of this paper imply that Brownian motions exist on spheres and Euclidean spaces (Lévy's original result), on real hyperbolic spaces, but not on quaternionic hyperbolic spaces