The Annals of Probability

Sharp asymptotics of the functional quantization problem for Gaussian processes

Harald Luschgy and Gilles Pagès

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Abstract

The sharp asymptotics for the L2-quantization errors of Gaussian measures on a Hilbert space and, in particular, for Gaussian processes is derived. The condition imposed is regular variation of the eigenvalues.

Article information

Source
Ann. Probab. Volume 32, Number 2 (2004), 1574-1599.

Dates
First available in Project Euclid: 18 May 2004

Permanent link to this document
http://projecteuclid.org/euclid.aop/1084884863

Digital Object Identifier
doi:10.1214/009117904000000324

Mathematical Reviews number (MathSciNet)
MR2060310

Zentralblatt MATH identifier
1049.60029

Subjects
Primary: 60E99: None of the above, but in this section 60G15: Gaussian processes 94A24: Coding theorems (Shannon theory) 94A34: Rate-distortion theory

Keywords
High-resolution quantization product quantization Shannon entropy Gaussian process

Citation

Luschgy, Harald; Pagès, Gilles. Sharp asymptotics of the functional quantization problem for Gaussian processes. Ann. Probab. 32 (2004), no. 2, 1574--1599. doi:10.1214/009117904000000324. http://projecteuclid.org/euclid.aop/1084884863.


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