Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Sharp asymptotics of the Kolmogorov entropy for Gaussian measures

Auteur(s):

Code(s) de Classification MSC:

Résumé: Let $U$ denote the unit ball of the Cameron-Martin space of a Gaussian measure on a Hilbert space. The sharp asymptotics for the Kolmogorov (metric) entropy numbers of $U$ is derived. The condition imposed is regular variation of the eigenvalues of the covariance operator. A consequence is a precise link including constants to the functional quantization problem.

Mots Clés: Metric entropy ; ellipsoid ; Gaussian process ; functional quantization ; Shannon entropy

Date: 2003-06-04

Prépublication numéro: PMA-824