Journal article
A law of large numbers approximation for Markov population processes with countably many types
AD Barbour, MJ Luczak
Probability Theory and Related Fields | SPRINGER | Published : 2012
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. © 2011 Springer-Verlag.
Grants
Awarded by Engineering and Physical Sciences Research Council
Funding Acknowledgements
A.D. Barbour was supported in part by Schweizerischer Nationalfonds Projekt Nr. 20-107935/1. M.J. Luczak was supported in part by a STICERD grant.