This paper simplifies and extends previous results on the existence of an equilibrium or stationary measure for the age process associated with a semi-Markov chain: (\mathbf{I}_{(t)}, \mathbf{Z}_{(t)}) = \text{(last state entered before time t}, \text{duration of this last sojourn up to} t).
@article{1176995726,
author = {McDonald, David R.},
title = {Equilibrium Measures for Semi-Markov Processes},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 818-822},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995726}
}
McDonald, David R. Equilibrium Measures for Semi-Markov Processes. Ann. Probab., Tome 5 (1977) no. 6, pp. 818-822. http://gdmltest.u-ga.fr/item/1176995726/