Semi-Markov processes and α-invariant distributions |
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Authors: | E Arjas E Nummelin |
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Institution: | Department of Mathematics, University of Oulu, SF-96100 Oulu 10, Finland;Institute of Mathematics, Helsinki University of Technology, SF-02150 Espoo 15, Finland |
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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 α-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. |
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