HAL: hal-00004668, version 1

arXiv: math.PR/0504236

DOI: 10.1016/j.jat.2006.04.006

Detailed view

Export this paper BibTeX - EndNote - TEI - RefWorks -

Journal of Approximation Theory 144, 1 (2007) 27-53 ; http://dx.doi.org/10.1016/j.jat.2006.04.006

Optimal quantizers for Radon random vectors in a Banach space

Siegried Graf 1, Harald Luschgy 2, Pagès Gilles 3

(2007)

For every integer n and evrery positive real number r > 0 and a Radon random vector X with values in a Banach space E, let e_{n,r}(X,E) = inf{(E (\min_{a \in \alpha} || X-a ||^r )^{1/r}}, where the infimum is taken over all subsets \alpha of E with card(\alpha) <= n (n-quantizers). We investigate the existence of optimal n-quantizers for this L^r-quantization propblem, derive their stationarity properties and establish for L^p-spaces E the pathwise regularity of stationary quantizers.

1:	Fakultät für Mathematik und Informatik (UNIVERSITÄT PASSAU)
	Universität Passau
2:	FB IV-Mathematik
	Universität Trier
3:	Laboratoire de Probabilités et Modèles Aléatoires (LPMA)
	CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot

Subject

:

Mathematics/Probability

Keyword(s): Functional quantization – optimal quantizer – stationary quantizer – stochastic process – intersection properties of balls

hal-00004668, version 1

http://hal.archives-ouvertes.fr/hal-00004668

oai:hal.archives-ouvertes.fr:hal-00004668

From: Gilles Pagès <>

Submitted on: Tuesday, 12 April 2005 10:10:13

Updated on: Tuesday, 2 April 2013 09:10:55