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,
CovarianceNature: 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 motionsNature: Original Retrieve article from Numdam
VII: 10, 77-94, LNM 321 (1973)
HEINKEL, Bernard
Une condition suffisante pour la continuité presque sûre des trajectoires de certains processus gaussiens (
Gaussian processes)
It is shown that a continuity criterion due to Preston (1972) can be deduced from a theorem of Dudley (1967)
Comment: To be completed
Keywords: Continuity of paths of Gaussian processesNature: Original Retrieve article from Numdam
VIII: 12, 155-171, LNM 381 (1974)
HEINKEL, Bernard
Théorèmes de dérivation du type de Lebesgue et continuité presque sûre de certains processus gaussiens (
Gaussian processes)
To be completed
Comment: To be completed
Keywords: Continuity of paths of Gaussian processesNature: Original Retrieve article from Numdam
IX: 14, 318-335, LNM 465 (1975)
FERNIQUE, Xavier
Des résultats nouveaux sur les processus gaussiens (
Gaussian processes)
Given a centered Gaussian process indexed by an arbitrary set~$T$, a major problem has been to find conditions implying that the sample functions are a.s. bounded, or a.s. continuous in the natural metric associated with the covariance. Here new necessary conditions for boundedness are given, which turn out to be sufficient in the case of stationary processes on $
R^n$. The conditions given here involve the existence of a majorizing measure, an idea which became crucial in the theory
Comment: For a systematic account of the theory around the time this paper was written, see Fernique's lectures in
École d'Été de Saint-Four~IV, LNM
480, 1974. For the definitive solution, see chapter 11 of Ledoux-Talagrand
Probability in Banach spaces, Springer 1991
Keywords: Gaussian processes,
Sample path regularityNature: Original Retrieve article from Numdam
XI: 13, 196-256, LNM 581 (1977)
WEBER, Michel
Classes uniformes de processus gaussiens stationnaires (
Gaussian processes)
To be completed
Comment: See the long and interesting review by Berman in
Math. Reviews, 56,
13343Nature: Exposition,
Original additions Retrieve article from Numdam
XII: 44, 567-690, LNM 649 (1978)
NANOPOULOS, Constantin;
NOBELIS, Photis
Régularité et propriétés limites des fonctions aléatoires (
Miscellanea,
Gaussian processes)
This paper extends to the non-Gaussian case methods to study the regularity of sample paths which have proved useful in the Gaussian case, notably that of majorizing measures (to be completed)
Comment: To be completed
Keywords: Sample path regularity,
Majorizing measuresNature: Original Retrieve article from Numdam
XII: 45, 691-706, LNM 649 (1978)
FERNIQUE, Xavier
Caractérisation de processus à trajectoires majorées ou continues (
Miscellanea,
Gaussian processes)
The methods which lead the author to necessary and sufficient conditions for boundedness or continuity of stationary Gaussian processes are extended and applied to non-stationary Gaussian processes and non-Gaussian processes
Keywords: Sample path regularityNature: Original Retrieve article from Numdam
XIV: 01, 1-16, LNM 784 (1980)
HEINKEL, Bernard
Deux exemples d'utilisation de mesures majorantes (
Gaussian processes)
From the introduction: ``our purpose is to study in detail two examples to which the method of majorizing measures, but not the entropy method, can be applied''
Nature: Original Retrieve article from Numdam
XIV: 02, 17-17, LNM 784 (1980)
GINÉ, Evarist
Corrections to ``Domains of attraction in Banach spaces'' (
Gaussian processes)
Contains three minor corrections to
1303Nature: Correction Retrieve article from Numdam
XIV: 46, 475-488, LNM 784 (1980)
WEBER, Michel
Sur un théorème de Maruyama (
Gaussian processes,
Ergodic theory)
Given a stationary centered Gaussian process $X$ with spectral measure $\mu$, a new proof is given of the fact that if $\mu$ is continuous, the flow of $X$ is weakly mixing
Keywords: Stationary processesNature: Original Retrieve article from Numdam
XXVI: 24, 322-347, LNM 1526 (1992)
JEULIN, Thierry;
YOR, Marc
Une décomposition non-canonique du drap brownien (
Brownian sheet,
Gaussian processes)
In
2415, the authors have introduced a transform of Brownian motion. Here, a similar transform is defined on the Brownian sheet; this transform is shown to be strongly mixing
Comment: This work was motivated by Föllmer's article on Martin boundaries on Wiener space (in
Diffusion processes and related problems in analysis, vol.~I, Birkhäuser 1990)
Keywords: Brownian motion,
Several parameter processesNature: Original Retrieve article from Numdam
XLII: 13, 365-381, LNM 1978 (2009)
ERRAOUI, M.;
ESSAKY, E. H.
Canonical representation for Gaussian processes (
Theory of Gaussian processes)
Nature: Original
