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- W2020590411 abstract "The weak ergodic theorems of mathematical demography state that the age distribution of a closed population is asymptotically independent of the initial distribution. In this paper, we provide a new proof of the weak ergodic theorem of the multistate population model with continuous time. The main tool to attain this purpose is a theory of multiplicative processes, which was mainly developed by Garrett Birkhoff, who showed that ergodic properties generally hold for an appropriate class of multiplicative processes. First, we construct a general theory of multiplicative processes on a Banach lattice. Next, we formulate a dynamical model of a multistate population and show that its evolution operator forms a multiplicative process on the state space of the population. Subsequently, we investigate a sufficient condition that guarantees the weak ergodicity of the multiplicative process. Finally, we prove the weak and strong ergodic theorems for the multistate population and resolve the consistency problem." @default.
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- W2020590411 date "1989-10-01" @default.
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- W2020590411 title "Weak ergodicity of population evolution processes" @default.
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- W2020590411 doi "https://doi.org/10.1016/0025-5564(89)90059-x" @default.
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