Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces

Harald Luschgy , Gilles Pagès , Benedikt Wilbertz

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.

Mots clés: Functional quantization; Gaussian process; Brownian motion; Riemann-Liouville process; optimal quantizer

Harald Luschgy, Gilles Pagès, Benedikt Wilbertz. Asymptotically optimal quantization schemes for Gaussian processes on Hilbert spaces. ESAIM: Probability and Statistics, 2010, 14, pp.93-116. ⟨10.1051/ps:2008026⟩. ⟨hal-00591695⟩