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On a generalization of the ehrenfest urn model

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Holger Dette
Holger Dette*
Affiliation:
Technische Universität Dresden
*
∗Postal address: Institut für Mathematische Stochastik, Abteilung Mathematik, Technische Universität Dresden, Mommsenstr. 13, 01062 Dresden, Germany.
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Abstract

Krafft and Schaefer [14] considered a two-parameter Ehrenfest urn model and found the n-step transition probabilities using representations by Krawtchouk polynomials. For a special case of the model Palacios [17] calculated some of the expected first-passage times. This note investigates a generalization of the two-parameter Ehrenfest urn model where the transition probabilities pi,i+1 and pi,i+1 are allowed to be quadratic functions of the current state i. The approach used in this paper is based on the integral representations of Karlin and McGregor [9] and can also be used for Markov chains with an infinite state space.

Keywords

HAHN POLYNOMIALSEXPECTED FIRST-PASSAGE TIMESn-STEP TRANSITION PROBABILITIES

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 930 - 939
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research supported in part by the Deutsche Forschungsgemeinschaft.

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