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Direct analytical methods for determining quasistationary distributions for continuous-time Markov chains. (English) Zbl 0858.60067
Heyde, C. C. (ed.) et al., Athens conference on applied probability and time series analysis, Athens, Greece, March 22–26, 1995. Vol. I: Applied probability. In honor of J. M. Gani. Berlin: Springer. Lect. Notes Stat., Springer-Verlag. 114, 116-126 (1996).
Summary: We shall be concerned with the problem of determining the quasistationary distributions of an absorbing continuous-time Markov chain directly from the transition-rate matrix $Q$. We shall present conditions which ensure that any finite $\mu$-invariant probability measure for $Q$ is a quasistationary distribution. Our results will be illustrated with reference to birth and death processes.
##### MSC:
 60J27 Continuous-time Markov processes on discrete state spaces