The Annals of Probability

Regularite De Fonctions Aleatoires Gaussiennes a Valeurs Vectorielles

X. Fernique

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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

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

First available in Project Euclid: 19 April 2007

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Zentralblatt MATH identifier


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.)

Gaussian random functions Gaussian random vectors Lusin space regularity of paths


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

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