@article {51,
title = {Fractal functional quantization of mean-regular stochastic processes},
journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
year = {2010},
abstract = {We investigate the functional quantization problem for stochastic processes with respect to $L^p(\mathbb{R}^d, \mu)$-norms, where $\mu$ is a fractal measure namely, $\mu$ is self-similar or a homogeneous Cantor measure. The derived functional quantization upper rate bounds are universal depending only on the mean-regularity index of the process and the quantization dimension of $\mu$ and as universal rates they are optimal. Furthermore, for arbitrary Borel probability measures $\mu$ we establish a (nonconstructive) link between the quantization errors of $\mu$ and the functional quantization errors of the process in the space $L^p(\mathbb{R}^d, \mu)$.},
author = {Harald Luschgy and Siegfried Graf and Gilles Pag{\`e}s}
}