Law of large numbers and central limit approximations for Markov population processes with countably many types

Malwina Luczak (Queen Mary, University of London)

Frank Adams 2,

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 disease. In a sequence of papers, we prove a law of large numbers and a central limit theorem for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted \(\ell_1\)-norm.

This is joint work with Andrew Barbour.

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