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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-27116

# Socoll, S N; Barbour, A D (2010). Translated Poisson approximation to equilibrium distributions of Markov population processes. Methodology and Computing in Applied Probability, 12(4):567-586.

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## Abstract

The paper is concerned with the equilibrium distributions of continuous-time density dependent Markov processes on the integers. These distributions are known typically to be approximately normal, with $O( 1 /{\sqrt{n}})$ error as measured in Kolmogorov distance. Here, an approximation in the much stronger total variation norm is established, without any loss in the asymptotic order of accuracy; the approximating distribution is a translated Poisson distribution having the same variance and (almost) the same mean. Our arguments are based on the Stein–Chen method and Dynkin’s formula.