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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-58136

Barbour, A D; Luzcak, M J (2012). A law of large numbers approximation for Markov population processes with countably many types. Probability Theory and Related Fields, 153(3-4):727-757.

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Abstract

When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since the population size has no natural upper limit, this leads to systems in which there are countably infinitely many possible types of individual. Analogous considerations apply in the transmission of parasitic diseases. In this paper, we prove a law of large numbers for quite general systems of this kind, together with a rather sharp bound on the rate of convergence in an appropriately chosen weighted ℓ 1 norm.

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3 citations in Web of Science®
3 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
DDC:510 Mathematics
Language:English
Date:2012
Deposited On:17 Feb 2012 20:02
Last Modified:07 Jun 2014 07:21
Publisher:Springer
ISSN:0178-8051 (P) 1432-2064 (E)
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:10.1007/s00440-011-0359-2
Related URLs:http://arxiv.org/abs/1001.0044

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