The Ergodic Theorems of Demography: A Simple Proof

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/1742 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/1742 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/1742 archive 351 disk0/00/00/17/09 2016-01-15 01:50:10 2021-08-27 17:10:26 2016-01-15 01:50:10 monograph show 3 Arthur W.B. 518 The Ergodic Theorems of Demography: A Simple Proof pub iis_met iis_pop prog_sds Standard proofs of the ergodic theorems of demography rely on theorems borrowed from positive matrix theory, tauberian theory, and the theory of time-inhomogeneous Markov matrices. But while these proofs are efficient and expedient, they give little direct insight into the mechanism that causes ergodicity. This paper proposes a simple and unified proof of the two ergodic theorems. It is shown that the birth dynamics can be decomposed into a smoothing process that progressively levels out past fluctuations in the birth sequence and a reshaping process that accounts for current period-to-period changes in vital rates. The smoothing process, which causes the birth sequence to lose information on its past shape, is shown to be the ergodic mechanism behind both theorems. 1981-04 published WP-81-052 WP-81-052 1694 public working_paper IIASA, Laxenburg, Austria 13 FALSE info:eu-repo/semantics/book