Fractal functional quantization of mean-regular stochastic processes

We investigate the functional quantization problem for stochastic processes with respect to L-p(IRd, 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(IRd, mu).