Regularite De Fonctions Aleatoires Gaussiennes a Valeurs Vectorielles

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 $E$.