Asymptotically optimal quantization schemes for Gaussian processes

Details Asymptotically optimal quantization schemes for Gaussian processes Asymptotically optimal quantization schemes for Gaussian processes

2008-02-26

arxiv.org/abs/0802.3761v1

Mathematics

Probability

25

Scientific paper

We describe quantization designs which lead to asymptotically and order optimal functional quantizers. 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. Furthermore we derive a high-resolution formula for the $L^2$-quantization errors of Riemann-Liouville processes.

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