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Central limit approximations for Markov population processes with countably many types. (English) Zbl 1284.92079

Summary: 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 diseases. In this paper, we prove central limit theorems for quite general systems of this kind, together with bounds on the rate of convergence in an appropriately chosen weighted \(\ell_1\) norm.

MSC:

92D25 Population dynamics (general)
92D30 Epidemiology
60F05 Central limit and other weak theorems
60J27 Continuous-time Markov processes on discrete state spaces
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