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 Probability Surveys > Vol. 7 (2010) open journal systems 

Limit theorems for discrete-time metapopulation models

Fionnuala M. Buckley, University of Queensland
Philip K. Pollett, University of Queensland

We describe a class of one-dimensional chain binomial models of use in studying metapopulations (population networks). Limit theorems are established for time-inhomogeneous Markov chains that share the salient features of these models. We prove a law of large numbers, which can be used to identify an approximating deterministic trajectory, and a central limit theorem, which establishes that the scaled fluctuations about this trajectory have an approximating autoregressive structure.

AMS 2000 subject classifications: Primary 60J10, 92B05; secondary 60J80.

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Buckley, Fionnuala M., Pollett, Philip K., Limit theorems for discrete-time metapopulation models, Probability Surveys, 7, (2010), 53-83 (electronic). DOI: 10.1214/10-PS158.


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