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On the equivalence of [mu]-invariant measures for the minimal process and its q-matrix

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  • Pollett, P. K.

Abstract

In this paper we obtain necessary and sufficient conditions for a measure or vector that is [mu]-invariant for a q-matrix, Q, to be [mu]-invariant for the family of transition matrices, {P(t)}, of the minimal process it generates. Sufficient conditions are provided in the case when Q is regular and these are shown not to be necessary. When [mu]-invariant measures and vectors can be identified, they may be used, in certain cases, to determine quasistationary distributions for the process.

Suggested Citation

  • Pollett, P. K., 1986. "On the equivalence of [mu]-invariant measures for the minimal process and its q-matrix," Stochastic Processes and their Applications, Elsevier, vol. 22(2), pages 203-221, July.
    • Handle: RePEc:eee:spapps:v:22:y:1986:i:2:p:203-221
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    Cited by:

    1. van Doorn, Erik A. & Pollett, Philip K., 2013. "Quasi-stationary distributions for discrete-state models," European Journal of Operational Research, Elsevier, vol. 230(1), pages 1-14.
    2. Phil Pollett, 2022. "Quasi-stationary distributions for queueing and other models," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 241-243, April.

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