Quick search | Browse volumes | |

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

Comment: This article contains joint work with K. Harzallah

Keywords: Covariance, Riemannian manifold, Riemannian distance, Lévy Brownian motions, Several parameter Brownian motions

Nature: Original

Retrieve article from Numdam

X: 06, 78-85, LNM 511 (1976)

**MANDREKAR, Vidyadhar**

Germ-field Markov property for multiparameter processes (Miscellanea)

The paper studies the relations between several Markov properties of a process indexed by an open set of $**R**^n$

Comment: To be completed

Keywords: Several parameter Brownian motions, Several parameter processes

Nature: Original

Retrieve article from Numdam

Introduction à l'étude des mouvements browniens à plusieurs paramètres (Gaussian processes)

Settles in particular a disagreement between statements of Lévy (

Comment: More recent work of Cartier on covariances appeared in the L.~Schwartz volume

Keywords: Several parameter Brownian motions, Covariance

Nature: New exposition of known results

Retrieve article from Numdam

VII: 09, 61-76, LNM 321 (1973)

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

Comment: This article contains joint work with K. Harzallah

Keywords: Covariance, Riemannian manifold, Riemannian distance, Lévy Brownian motions, Several parameter Brownian motions

Nature: Original

Retrieve article from Numdam

X: 06, 78-85, LNM 511 (1976)

Germ-field Markov property for multiparameter processes (Miscellanea)

The paper studies the relations between several Markov properties of a process indexed by an open set of $

Comment: To be completed

Keywords: Several parameter Brownian motions, Several parameter processes

Nature: Original

Retrieve article from Numdam