The Annals of Probability

Regularite De Fonctions Aleatoires Gaussiennes a Valeurs Vectorielles

X. Fernique

Full-text: Open access

Abstract

In this paper, we give a simple condition ensuring that a Gaussian random function $X$ on a metric space $T$ with values in a Lusin topological vector space has a modification with continuous paths. This result extends previous results where $X$ was supposed to be stationary or have stationary increments. As in the stationary case, proof is based on Talagrand's theorem about the majorizing measures which permit us, if $E$ is a separable Banach space, to bound the law of the maximum on $T$ of the norm of $X$ in $E$.

Article information

Source
Ann. Probab., Volume 18, Number 4 (1990), 1739-1745.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990644

Digital Object Identifier
doi:10.1214/aop/1176990644

Mathematical Reviews number (MathSciNet)
MR1071821

Zentralblatt MATH identifier
0718.60037

JSTOR
links.jstor.org

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60B11: Probability theory on linear topological spaces [See also 28C20] 60G20: Generalized stochastic processes 28C15: Set functions and measures on topological spaces (regularity of measures, etc.)

Keywords
Gaussian random functions Gaussian random vectors Lusin space regularity of paths

Citation

Fernique, X. Regularite De Fonctions Aleatoires Gaussiennes a Valeurs Vectorielles. Ann. Probab. 18 (1990), no. 4, 1739--1745. doi:10.1214/aop/1176990644. https://projecteuclid.org/euclid.aop/1176990644


Export citation