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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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