A probabilistic proof of Stein’s factors

Abstract

We provide a probabilistic proof of the Stein’s factors based on properties of birth and death Markov chains, solving a tantalizing puzzle in using Markov chain knowledge to view the celebrated Stein-Chen method for Poisson approximations. This work complements the work of Barbour (1988) for the case of Poisson random variable approximation. © 1999 Applied Probability Trust.