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The ergodic theorems of demography: a simple proof.
- Source :
- Demography (Springer Nature); Nov1982, Vol. 19 Issue 4, p439-445, 7p
- Publication Year :
- 1982
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00703370
- Volume :
- 19
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Demography (Springer Nature)
- Publication Type :
- Academic Journal
- Accession number :
- 16799428
- Full Text :
- https://doi.org/10.2307/2061011