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Distributions and expectations of singular random variables

Published online by Cambridge University Press:  14 July 2016

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.

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.

Type
Research Papers
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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