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Distributions and expectations of singular random variables

Part of: Distribution theory - Probability Communication, information

Published online by Cambridge University Press:  14 July 2016

L. L. Campbell ,
A. L. McKellips  and
P. H. Wittke
L. L. Campbell*
Affiliation:
Queen's University
A. L. McKellips*
Affiliation:
Queen's University
P. H. Wittke*
Affiliation:
Queen's University
*
∗Postal addresses: Department of Mathematics and Statistics and
∗Postal addresses: Department of Mathematics and Statistics and
∗∗Department of Electrical Engineering, Queen's University, Kingston, Ontario, Canada K7L 3N6.
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Abstract

Intersymbol and cochannel interference in a communications channel can often be modelled as the sum of an infinite series of random variables with weights which decay fairly rapidly. Frequently, this yields a random variable which is singular but non-atomic. The Hausdorff dimension of the distribution is estimated and methods for calculating expectations are studied. A connection is observed between the dimension and the complexity of the calculation of an expectation.

Keywords

SINGULAR DISTRIBUTIONSDIMENSION OF SUPPORTEXPECTATIONS

MSC classification

Primary: 60E99: None of the above, but in this section
Secondary: 94A14: Modulation and demodulation 94A40: Channel models (including quantum)
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1032 - 1040
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

This research was supported by the Natural Sciences and Engineering Research Council of Canada through Grants OGP0002151 and OGP0003391 to Campbell and Wittke, and through a scholarship to McKellips.

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