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

TitleHigh-resolution product quantization for Gaussian processes under sup-norm distortion
Publication TypeMiscellaneous
Year of Publication2005
AuthorsHarald Luschgy, and Gilles Pagès
KeywordsGaussian process, High-resolution quantization, product quantization, series expansion
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.