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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

 

 

Asymptotic quantization errors for unbounded quantizers


Author: M. Shykula
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 75 (2006).
Journal: Theor. Probability and Math. Statist. 75 (2007), 189-199
MSC (2000): Primary 60G99; Secondary 94A29, 94A34
DOI: https://doi.org/10.1090/S0094-9000-08-00725-4
Published electronically: January 25, 2008
MathSciNet review: 2321192
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Abstract:

We consider non-uniform scalar quantization for a wide class of unbounded random variables (or values of a random process sampled in time). Asymptotic stochastic structures for quantization errors are derived for two types of quantizers when the number of quantization levels tends to infinity. The corresponding results for bounded random variables are generalized. Some numerical examples illustrate the rate of convergence.


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Additional Information

M. Shykula
Affiliation: Department of Mathematics and Mathematical Statistics, Umeå University, SE-901 87 Umeå, Sweden
Email: mykola.shykula@math.umu.se

DOI: https://doi.org/10.1090/S0094-9000-08-00725-4
Keywords: Non-uniform scalar quantization, random process, stochastic structure
Received by editor(s): July 24, 2005
Published electronically: January 25, 2008
Article copyright: © Copyright 2008 American Mathematical Society