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Mean passage times for tridiagonal transition matrices and a two-parameter ehrenfest urn model

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Olaf Krafft  and
Martin Schaefer
Olaf Krafft
Affiliation:
Aachen University of Technology
Martin Schaefer*
Affiliation:
Aachen University of Technology
*
∗ Postal address for both authors: Institut für Statistik, RWTH Aachen, Wüllnerstr 3, 52056 Aachen, Germany.
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Abstract

A two-parameter Ehrenfest urn model is derived according to the approach taken by Karlin and McGregor [7] where Krawtchouk polynomials are used. Furthermore, formulas for the mean passage times of finite homogeneous Markov chains with general tridiagonal transition matrices are given. In the special case of the Ehrenfest model they have quite a different structure as compared with those of Blom [2] or Kemperman [9].

Keywords

KRAWTCHOUK POLYNOMIALS

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Short Communications
Information
Journal of Applied Probability , Volume 30 , Issue 4 , December 1993 , pp. 964 - 970
Copyright
Copyright © Applied Probability Trust 1993 

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References

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