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A note on a generalized Ehrenfest urn model: another look at the mean transition times

Part of: Combinatorial probability Markov processes

Published online by Cambridge University Press:  21 June 2016

Eve D. Lathrop ,
Isaac H. Goldstein  and
Yung-Pin Chen
Eve D. Lathrop*
Affiliation:
Oregon State University
Isaac H. Goldstein*
Affiliation:
Lewis & Clark College
Yung-Pin Chen*
Affiliation:
Lewis & Clark College
*
* Postal address: College of Engineering, 1691 SW Campus Way, Oregon State University, Corvallis, OR 97331, USA.
** Postal address: Department of Mathematical Sciences, 0615 S.W. Palatine Hill Road, Lewis & Clark College, MSC 110, Portland, OR 97219, USA.
** Postal address: Department of Mathematical Sciences, 0615 S.W. Palatine Hill Road, Lewis & Clark College, MSC 110, Portland, OR 97219, USA.
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Abstract

This note is motivated by Blom's work in 1989. We consider a generalized Ehrenfest urn model in which a randomly-chosen ball has a positive probability of moving from one urn to the other urn. We use recursion relations between the mean transition times to derive formulas in terms of finite sums, which are shown to be equivalent to the definite integrals obtained by Blom.

Keywords

Ehrenfest urn modeltransition time

MSC classification

Primary: 60C05: Combinatorial probability
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Short Communications
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 630 - 632
Copyright
Copyright © Applied Probability Trust 2016 

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References

[1]Blom, G. (1989).Mean transition times for the Ehrenfest urn model.Adv. Appl. Prob. 21, 479–480.CrossRefGoogle Scholar
[2]Palacios, J. L. (1994).Another look at the Ehrenfest urn via electric networks.Adv. Appl. Prob. 26, 820–824.CrossRefGoogle Scholar