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Additional quasi-stationary distributions for semi-Markov processes

Published online by Cambridge University Press:  14 July 2016

David C. Flaspohler  and
Paul T. Holmes
Paul T. Holmes*
Affiliation:
Clemson University
*
*Now at Xavier University, Cincinnati, Ohio.
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Abstract

Consider a semi-Markov process X(t) defined on a subset of the non-negative integers with zero as an absorbing state and the non-zero states forming an irreducible class with exit to zero being possible. Conditions are given for the existence of the limits: where Xj(t) is the amount of time prior to time t spent in state j.

The limits (which are independent of the initial state) are evaluated when the sufficient conditions are satisfied.

Keywords

QUASI-STATIONARY DISTRIBUTIONSSEMI-MARKOV PROCESSESLIMITING CONDITIONAL DISTRIBUTIONSMARKOV RENEWAL PROCESSESABSORBING PROCESSSTATIONARY CONDITIONAL DISTRIBUTIONDOUBLY LIMITING CONDITIONAL DISTRIBUTIONLIMITING CONDITIONAL MEAN RATIO
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 3 , June 1972 , pp. 671 - 676
Copyright
Copyright © Applied Probability Trust 1972 

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References

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