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

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

2009-12-30

arxiv.org/abs/1001.0044v3

Mathematics

Probability

revised version in response to referee comments, 34 pages

Scientific paper

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 rather general systems of this kind, together with a rather sharp bound on the rate of convergence in an appropriately chosen weighted $\ell_1$ norm.

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