Entropy and convergence in dynamics and demography (Q1802939)
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scientific article; zbMATH DE number 219779
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Entropy and convergence in dynamics and demography |
scientific article; zbMATH DE number 219779 |
Statements
Entropy and convergence in dynamics and demography (English)
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29 June 1993
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The paper starts with a review of some results by \textit{S. Goldstein} and \textit{O. Penrose} [J. Stat. Phys. 24, 325-342 (1981; Zbl 0516.70021)] on the relation between convergence rate, Kullback information, and Kolmogorov-Sinai entropy for irreducible, aperiodic finite Markov chains (including the effects of time-scaling and of coarse-graining of the state space). Elementary proofs of such results are provided. The transformation of the standard demographic Leslie projection model into a Markov chain is reviewed. An expression for the entropy in terms of the eigenvalues of the Leslie matrix is obtained. When there is a stable age distribution, the demographic meaning of the entropy is discussed in connection with the convergence rate. Finally, imprimitive and periodic limits and the relation to population entropy are discussed.
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demography
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convergence rate
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Kullback information
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Kolmogorov-Sinai entropy
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irreducible, aperiodic finite Markov chains
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time-scaling
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coarse-graining
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demographic Leslie projection model
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eigenvalues
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stable age distribution
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imprimitive and periodic limits
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population entropy
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