Functional Quantization and Entropy for Stochastic Processes

Authors Harald Luschgy, Gilles Pagès

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Harald Luschgy
Gilles Pagès

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Harald Luschgy and Gilles Pagès. Functional Quantization and Entropy for Stochastic Processes. In Algorithms and Complexity for Continuous Problems. Dagstuhl Seminar Proceedings, Volume 4401, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)


Let X be a Gaussian process and let U denote the Strassen ball of X. A precise link between the L^2-quantization error of X and the Kolmogorov (metric) entropy of U in a Hilbert space setting is established. In particular, the sharp asymptotics of the Kolmogorov entropy problem is derived. The condition imposed is regular variation of the eigenvalues of the covariance operator. Good computable quantizers for Gaussian and diffusion processes and their numerical efficieny are discussed. This is joint work with G. Pagès, Université de Paris 6.
  • Functional quantization
  • entropy
  • product quantizers


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