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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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2010
Deposited On:04 Feb 2010 14:54
Last Modified:27 Nov 2013 18:20
Publisher:Springer
ISSN:1387-5841
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:10.1007/s11009-009-9124-8
Related URLs:http://arxiv.org/abs/0902.0884

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