Functional quantization and metric entropy for Riemann-Liouville processes

Harald Luschgy; Gilles Pagès

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arXiv · math/0502375

Functional quantization and metric entropy for Riemann-Liouville processes

Harald Luschgy·Gilles Pagès

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Abstract

We derive a high-resolution formula for the $L^2$-quantization errors of Riemann-Liouville processes and the sharp Kolmogorov entropy asymptotics for related Sobolev balls. We describe a quantization procedure which leads to asymptotically optimal functional quantizers. Regular variation of the eigenvalues of the covariance operator plays a crucial role.

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Harald Luschgy, Gilles Pagès. 2005-02-17. Functional quantization and metric entropy for Riemann-Liouville processes. https://arxiv.org/abs/math/0502375

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