# Central limit approximations for Markov population processes with countably many types

Barbour, A D; Luczak, Malwina (2012). Central limit approximations for Markov population processes with countably many types. Electronic Journal of Probability, 17(90):1-16.

## Abstract

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch, this leads to systems in which there are countably infinitely many possible types of entity. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove central limit theorems for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted $\ell_1$ norm.

## Abstract

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch, this leads to systems in which there are countably infinitely many possible types of entity. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove central limit theorems for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted $\ell_1$ norm.

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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 2012 28 Dec 2017 14:38 18 Feb 2018 03:28 Institute of Mathematical Statistics 1083-6489 Schweizerischer Nationalfonds Hybrid Publisher DOI. An embargo period may apply. https://doi.org/10.1214/EJP.v17-1760

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