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 $E$.
Publié le : 1990-10-14
Classification:
Gaussian random functions,
Gaussian random vectors,
Lusin space,
regularity of paths,
60G15,
60B11,
60G20,
28C15
@article{1176990644,
author = {Fernique, X.},
title = {Regularite De Fonctions Aleatoires Gaussiennes a Valeurs Vectorielles},
journal = {Ann. Probab.},
volume = {18},
number = {4},
year = {1990},
pages = { 1739-1745},
language = {fr},
url = {http://dml.mathdoc.fr/item/1176990644}
}
Fernique, X. Regularite De Fonctions Aleatoires Gaussiennes a Valeurs Vectorielles. Ann. Probab., Tome 18 (1990) no. 4, pp. 1739-1745. http://gdmltest.u-ga.fr/item/1176990644/