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On the generating functions of a random walk on the non-negative integers

Published online by Cambridge University Press:  14 July 2016

Holger Dette
Holger Dette*
Affiliation:
Technische Universität Dresden
*
∗Postal address: Fakultät und Institut für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany.
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Abstract

In the random walk whose state space is a subset of the non-negative integers explicit representations for the generating functions of the n-step transition and the first return probabilities are obtained. These representations involve the Stieltjes transform of the spectral measure of the process and the corresponding orthogonal polynomials. Several examples are given in order to illustrate the application of the results.

Keywords

RANDOM WALKGENERATING FUNCTIONSPECTRAL MEASURESTIELTJES TRANSFORMORTHOGONAL POLYNOMIALSEHRENFEST URN

MSC classification

Secondary: 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 1033 - 1052
Copyright
Copyright © Applied Probability Trust 1996 

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