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2006 High Resolution Quantization and Entropy Coding for Fractional Brownian Motion
Steffen Dereich, Michael Scheutzow
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Electron. J. Probab. 11: 700-722 (2006). DOI: 10.1214/EJP.v11-344


We establish the precise asymptotics of the quantization and entropy coding errors for fractional Brownian motion with respect to the supremum norm and $L^p [0,1]$-norm distortions. We show that all moments in the quantization problem lead to the same asymptotics. Using a general principle, we conclude that entropy coding and quantization coincide asymptotically. Under supremum-norm distortion, our proof uses an explicit construction of efficient codebooks based on a particular entropy constrained coding scheme.


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Steffen Dereich. Michael Scheutzow. "High Resolution Quantization and Entropy Coding for Fractional Brownian Motion." Electron. J. Probab. 11 700 - 722, 2006.


Accepted: 27 August 2006; Published: 2006
First available in Project Euclid: 31 May 2016

zbMATH: 1110.60030
MathSciNet: MR2242661
Digital Object Identifier: 10.1214/EJP.v11-344

Primary: 60G35
Secondary: 41A25 , 94A29

Keywords: Complexity , Distortion rate function , Entropy , High-resolution quantization , stochastic process

Vol.11 • 2006
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