Semi-Markov processes and [alpha]-invariant distributions

E. Arjas and E. Nummelin

Stochastic Processes and their Applications, 1977, vol. 6, issue 1, 53-64

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.

Date: 1977
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