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August 2007 High-resolution product quantization for Gaussian processes under sup-norm distortion
Harald Luschgy, Gilles Pagès
Bernoulli 13(3): 653-671 (August 2007). DOI: 10.3150/07-BEJ6025


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.


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Harald Luschgy. Gilles Pagès. "High-resolution product quantization for Gaussian processes under sup-norm distortion." Bernoulli 13 (3) 653 - 671, August 2007.


Published: August 2007
First available in Project Euclid: 7 August 2007

zbMATH: 1131.60029
MathSciNet: MR2348745
Digital Object Identifier: 10.3150/07-BEJ6025

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability


Vol.13 • No. 3 • August 2007
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