Document Detail


The ergodic theorems of demography: a simple proof.
MedLine Citation:
PMID:  7173465     Owner:  NLM     Status:  MEDLINE    
Abstract/OtherAbstract:
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. These proofs are efficient and expedient, but 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.
Authors:
W B Arthur
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Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Demography     Volume:  19     ISSN:  0070-3370     ISO Abbreviation:  Demography     Publication Date:  1982 Nov 
Date Detail:
Created Date:  1983-02-25     Completed Date:  1983-02-25     Revised Date:  2004-11-17    
Medline Journal Info:
Nlm Unique ID:  0226703     Medline TA:  Demography     Country:  UNITED STATES    
Other Details:
Languages:  eng     Pagination:  439-45     Citation Subset:  IM    
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MeSH Terms
Descriptor/Qualifier:
Birth Rate
Demography*
Fertility
Humans
Mathematics*
Mortality

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine


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