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Limit theorems for discrete-time metapopulation models. (English) Zbl 1194.60024
Summary: 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.

MSC:
60F05 Central limit and other weak theorems
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
92B05 General biology and biomathematics
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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