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Semi-Markov processes and [alpha]-invariant distributions

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  • Arjas, E.
  • Nummelin, E.

Abstract

A semi-Markov process is easily made Markov by adding some auxiliary random variables. This paper discusses the I-type quasi-stationary distributions of such "extended" processes, and the [alpha]-invariant distributions for the corresponding Markov transition probabilities; and we show that there is an intimate relation between the two. The results have relevance in the study of the time to "absorption" or "death" of semi-Markov processes. The particular case of a terminating renewal process is studied as an example.

Suggested Citation

  • Arjas, E. & Nummelin, E., 1977. "Semi-Markov processes and [alpha]-invariant distributions," Stochastic Processes and their Applications, Elsevier, vol. 6(1), pages 53-64, November.
    • Handle: RePEc:eee:spapps:v:6:y:1977:i:1:p:53-64
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