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

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

2005-11-08

arxiv.org/abs/math/0511208v2

Mathematics

Probability

Version publi\'ee dans la revue Bernoulli, 13(3), 653-671

Scientific paper

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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