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Some passage-time generating functions for discrete-time and continuous-time finite Markov chains

Published online by Cambridge University Press:  14 July 2016

J. N. Darroch  and
K. W. Morris
J. N. Darroch
Affiliation:
Flinders University of South Australia
K. W. Morris
Affiliation:
University of Adelaide
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Abstract

Let T denote a subset of the possible transitions between the states of a finite Markov chain and let Yk denote the time of the kth occurrence of a T-transition. Formulae are derived for the generating functions of Yk, of Yj + k — Yj and of Yj + k — Yj in the limit as j → ∞, for both discrete-time and continuoustime chains. Several particular cases are briefly discussed.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 3 , November 1967 , pp. 496 - 507
Copyright
Copyright © Applied Probability Trust 

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References

Bartlett, M. S. (1962) Stochastic Processes. 2nd edition. Cambridge U. Press.Google Scholar
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