# Critical dimension for quadratic functional quantization

Abstract : In this paper we tackle the asymptotics of the critical dimension for quadratic functional quantization of Gaussian stochastic processes as the quantization level goes to infinity, $i.e.$ the smallest dimensional truncation of an optimal quantization of the process which is ''fully" quantized. We first establish a lower bound for this critical dimension based on the regular variation index of the eigenvalues of the Karhunen-Loève expansion of the process. This lower bound is consistent with the commonly shared sharp rate conjecture (and supported by extensive numerical experiments). Moreover, we show that, conversely, constructive optimized quadratic functional quantizations based on this critical dimension rate are always asymptotically optimal (strong admissibility result).
Mots-clés :
Type de document :
Pré-publication, Document de travail
16 pages. 2012
Domaine :
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00731523
Contributeur : Gilles Pagès <>
Soumis le : jeudi 13 septembre 2012 - 09:21:10
Dernière modification le : mardi 11 octobre 2016 - 13:55:31
Document(s) archivé(s) le : vendredi 14 décembre 2012 - 03:55:38

### Fichiers

LUPA7.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : hal-00731523, version 1

### Citation

Harald Luschgy, Gilles Pagès. Critical dimension for quadratic functional quantization. 16 pages. 2012. <hal-00731523>

Consultations de
la notice

## 139

Téléchargements du document