Bernoulli

  • Bernoulli
  • Volume 13, Number 3 (2007), 653-671.

High-resolution product quantization for Gaussian processes under sup-norm distortion

Harald Luschgy and Gilles Pagès

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Abstract

We derive high-resolution upper bounds for optimal product quantization of pathwise continuous Gaussian processes with respect to the supremum norm on [0, T]d. Moreover, we describe a product quantization design which attains this bound. This is achieved under very general assumptions on random series expansions of the process. It turns out that product quantization is asymptotically only slightly worse than optimal functional quantization. The results are applied to fractional Brownian sheets and the Ornstein–Uhlenbeck process.

Article information

Source
Bernoulli, Volume 13, Number 3 (2007), 653-671.

Dates
First available in Project Euclid: 7 August 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1186503481

Digital Object Identifier
doi:10.3150/07-BEJ6025

Mathematical Reviews number (MathSciNet)
MR2348745

Zentralblatt MATH identifier
1131.60029

Keywords
Gaussian process high-resolution quantization product quantization series expansion

Citation

Luschgy, Harald; Pagès, Gilles. High-resolution product quantization for Gaussian processes under sup-norm distortion. Bernoulli 13 (2007), no. 3, 653--671. doi:10.3150/07-BEJ6025. https://projecteuclid.org/euclid.bj/1186503481


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