Volume 12, April 2008
|Page(s)||127 - 153|
|Published online||23 January 2008|
Distortion mismatch in the quantization of probability measures
Universität Passau, Fakultät für Informatik und Mathematik, 94030
Passau, Germany; firstname.lastname@example.org
2 Universität Trier, FB IV-Mathematik, 54286 Trier, Germany; email@example.com
3 Laboratoire de Probabilités et Modèles aléatoires, UMR 7599, Université Paris 6, case 188, 4, pl. Jussieu, 75252 Paris cedex 5, France; firstname.lastname@example.org
Revised: 24 November 2006
We elucidate the asymptotics of the Ls-quantization error induced by a sequence of Lr-optimal n-quantizers of a probability distribution P on when s > r. In particular we show that under natural assumptions, the optimal rate is preserved as long as s < r+d (and for every s in the case of a compactly supported distribution). We derive some applications of these results to the error bounds for quantization based cubature formulae in numerical integration on and on the Wiener space.
Mathematics Subject Classification: 60G15 / 60G35 / 41A25
Key words: Optimal quantization / Zador Theorem
© EDP Sciences, SMAI, 2008
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