Translated Poisson approximation to equilibrium distributions of Markov population processes

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.

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.

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.

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics Physical Sciences > Statistics and Probability Physical Sciences > General Mathematics English 2010 04 Feb 2010 14:54 29 Jul 2020 20:48 Springer 1387-5841 The original publication is available at www.springerlink.com Green https://doi.org/10.1007/s11009-009-9124-8 http://arxiv.org/abs/0902.0884