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Passage-time generating functions for 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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Extract

Let S denote a subset of the states of a finite continuous-time Markov chain and let Y(a) denote the time that elapses until a weighted sum of a time units have been spent in S. Formulae are derived for the generating functions of Y(a) and of Y(a + b) – Y(b).

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 2 , August 1968 , pp. 414 - 426
Copyright
Copyright © Applied Probability Trust 1968 

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References

Darroch, J. N. (1966) Identities for passage times with applications to recurrent events and homogeneous differential functions. J. Appl. Prob. 3, 435–444.Google Scholar
Darroch, J. N. and Morris, K. W. (1967) Some passage-time generating functions for discrete-time and continuous-time finite Markov chains. J. Appl. Prob. 4, 496–507.Google Scholar
Takács, L. (1960) Stochastic Processes. Methuen, London.Google Scholar