# 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 :
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [13 references]

https://hal.archives-ouvertes.fr/hal-00731523
Contributor : Gilles Pagès <>
Submitted on : Thursday, September 13, 2012 - 9:21:10 AM
Last modification on : Wednesday, December 9, 2020 - 3:06:08 PM
Long-term archiving on: : Friday, December 14, 2012 - 3:55:38 AM

### Files

LUPA7.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00731523, version 1

### Citation

Harald Luschgy, Gilles Pagès. Critical dimension for quadratic functional quantization. 2012. ⟨hal-00731523⟩

Record views