Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces

Abstract

We describe quantization designs which lead to asymptotically and order optimal functional quantizers for Gaussian processes in a Hilbert space setting. Regular variation of the eigenvalues of the covariance operator plays a crucial role to achieve these rates. For the development of a constructive quantization scheme we rely on the knowledge of the eigenvectors of the covariance operator in order to transform the problem into a finite dimensional quantization problem of normal distributions. © EDP Sciences, SMAI, 2010.