Time-Homogeneous Birth-Death Processes with Probability Intervals and Absorbing State

Abstract

This paper concerns discrete-time time-homogeneous birth-death processes on a finite state space, containing a single absorbing state, with interval-valued transition probabilities. As absorption is certain, the quasi-stationary behaviour of the process is studied with the distribution of the process conditional on non-absorption. It is shown that the set of all possible limiting conditional distributions is the set of all possible quasi-stationary distributions. An approximation of the possibly infinite set of conditional distributions at time n is presented, together with an example.