R\'egularit\'e ergodique de quelques classes de Donsker
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 766-784
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We use a weak decoupling inequality in ergodic theory for maximal operators. We apply this inequality to the study of the property for a set of functions to be a Donsker class. The sets we examine are built from a sequence of $L^2$-operators and naturally appear in the study of the almost sure regularity properties of these. We obtain new individual necessary conditions (for a given $f\in L^2(\mu)$) and new global necessary conditions. The latter conditions are of uniform type and have a natural translation on the regularity properties of the canonical Gaussian process $Z$ defined on $L^2(\mu)$.
Keywords:
ergodic maximal operator, almost sure convergence, Gaussian processes, decoupling inequality, entropy numbers.
@article{TVP_2003_48_4_a6,
author = {M. Weber},
title = {R\'egularit\'e ergodique de quelques classes de {Donsker}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {766--784},
publisher = {mathdoc},
volume = {48},
number = {4},
year = {2003},
language = {fr},
url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a6/}
}
M. Weber. R\'egularit\'e ergodique de quelques classes de Donsker. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 766-784. http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a6/