Document Detail

The ergodic theorems of demography: a simple proof.
MedLine Citation:
PMID:  7173465     Owner:  NLM     Status:  MEDLINE    
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.
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
Birth Rate

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

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