Translated Poisson Approximation to Equilibrium Distributions of Markov Population Processes

Sanda N. Socoll () and A. D. Barbour
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Sanda N. Socoll: Universität Zürich-Irchel
A. D. Barbour: Universität Zürich-Irchel

Methodology and Computing in Applied Probability, 2010, vol. 12, issue 4, 567-586

Abstract: 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.

Keywords: Continuous-time Markov process; Equilibrium distribution; Total-variation distance; Infinitesimal generator; Stein–Chen method; Point process; 60J75; 62E17 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s11009-009-9124-8

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