Quasistationarity in continuous-time Markov chains with positive drift

Pauline Coolen-Schrijner, Andrew Hart and Phil Pollett

Abstract: We shall consider continuous-time Markov chains on Z_+, which are both irreducible and transient, and which exhibit discernable stationarity before drift to infinity `sets in'. After demonstrating this quasistationary behaviour with reference to several examples of birth-death chains, we will show how it can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By defining a dual chain, obtained by killing the original process on last exit from 0, we can invoke standard theory on quasistationarity for absorbing Markov chains, thus obtaining new results on the existence of limiting conditional distributions for irreducible transient chains.

Acknowledgement: This worked was funded by the Australian Research Council.

The authors:

Last modified: 12th November 1998