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High Resolution Quantization and Entropy Coding for Fractional Brownian Motion


 
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1. Title Title of document High Resolution Quantization and Entropy Coding for Fractional Brownian Motion
 
2. Creator Author's name, affiliation, country Steffen Dereich; TU Berlin
 
2. Creator Author's name, affiliation, country Michael Scheutzow; TU Berlin
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) High-resolution quantization; complexity; stochastic process; entropy; distortion rate function
 
3. Subject Subject classification 60G35; 41A25; 94A29
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2006-08-27
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/344
 
10. Identifier Digital Object Identifier 10.1214/EJP.v11-344
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 11
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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