In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on wheth...

Spatial birth and death processes are obtained as solutions of a system of stochastic equations. The processes are required to be locally finite, but may involve an infinite population over the full (noncompact) type space. Conditions are given for existence and uniqueness of such solutions, and for temporal and spatial ergodicity. For birth and death processes with constant death rate, a sub-c...

We provide a probabilistic proof of the Stein's factors based on properties of birth and death Markov chains, solving a tantalising puzzle in using Markov chain knowledge to view the celebrated Stein-Chen method for Poisson approximations. This paper complements the work of Barbour (1988) for the case of Poisson random variable approximation. The Stein-Chen method was introduced in Chen (1975) ...