Open Access
October, 1990 Regularite De Fonctions Aleatoires Gaussiennes a Valeurs Vectorielles
X. Fernique
Ann. Probab. 18(4): 1739-1745 (October, 1990). DOI: 10.1214/aop/1176990644


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 $E$.


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X. Fernique. "Regularite De Fonctions Aleatoires Gaussiennes a Valeurs Vectorielles." Ann. Probab. 18 (4) 1739 - 1745, October, 1990.


Published: October, 1990
First available in Project Euclid: 19 April 2007

zbMATH: 0718.60037
MathSciNet: MR1071821
Digital Object Identifier: 10.1214/aop/1176990644

Primary: 60G15
Secondary: 28C15 , 60B11 , 60G20

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

Rights: Copyright © 1990 Institute of Mathematical Statistics

Vol.18 • No. 4 • October, 1990
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