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Central limit theorems for a class of polynomial hypergroups

Published online by Cambridge University Press:  01 July 2016

Michael Voit
Michael Voit*
Affiliation:
Technische Universität Munchen
*
∗Postal address: Institut für Mathematik, Technische Universität München, Arcisstr. 21, D-8000 München 2, W. Germany.
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Abstract

Central limit theorems are proved for random walks on the non-negative integers where the transition probabilities are homogeneous with respect to a sequence of orthogonal polynomials. Assuming some restrictions concerning the three-term recursion formula of these polynomials, one gets a Rayleigh distribution as limit distribution where bounds of the order of convergence can be computed explicitly. These central limit theorems are applied to generalized birth and death random walks and random walks on polynomial hypergroups. Finally some examples of polynomial hypergroups are discussed in view of the limit theorems above.

Keywords

BIRTH AND DEATH RANDOM WALKCENTRAL LIMIT THEOREMS WITH ERROR BOUNDSRAYLEIGH DISTRIBUTION
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 1 , March 1990 , pp. 68 - 87
Copyright
Copyright © Applied Probability Trust 1990 

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