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

Abstract : We derive high-resolution upper bounds for optimal product quantization of pathwise contionuous Gaussian processes respective 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 e.g. to fractional Brownian sheets and the Ornstein-Uhlenbeck process.
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https://hal.archives-ouvertes.fr/hal-00013489
Contributor : Gilles Pagès <>
Submitted on : Wednesday, September 5, 2007 - 5:24:59 PM
Last modification on : Thursday, December 10, 2020 - 10:45:38 AM
Long-term archiving on: : Tuesday, September 21, 2010 - 1:45:09 PM

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Harald Luschgy, Gilles Pagès. High-resolution product quantization for Gaussian processes under sup-norm distortion. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2007, 13 (3), 653-671 ; http://dx.doi.org/10.3150/07-BEJ6025. ⟨10.3150/07-BEJ6025⟩. ⟨hal-00013489v2⟩

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