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A law of large numbers approximation for Markov population processes with countably many types


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.

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.

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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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:2012
Deposited On:17 Feb 2012 20:02
Last Modified:07 Dec 2017 12:12
Publisher:Springer
ISSN:0178-8051 (P) 1432-2064 (E)
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s00440-011-0359-2
Related URLs:http://arxiv.org/abs/1001.0044

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Download PDF  'A law of large numbers approximation for Markov population processes with countably many types'.
Preview
Content: Accepted Version
Filetype: PDF (Version 3)
Size: 308kB