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Stochastic stable population growth

Published online by Cambridge University Press:  14 July 2016

Kenneth Lange  and
William Holmes
Kenneth Lange*
Affiliation:
University of California
William Holmes*
Affiliation:
University of California
*
∗Postal address: Department of Biomathematics, University of California, Los Angeles, CA 90024, U.S.A.
∗Postal address: Department of Biomathematics, University of California, Los Angeles, CA 90024, U.S.A.
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Abstract

In classical demographic theory, the age structure of a population eventually stabilizes, and the population as a whole grows at a geometric rate. It is possible to prove stochastic analogues of these results if vital rates fluctuate according to a stationary stochastic process. The approach taken here is to study the action of random matrix products on random vectors. This permits the application of Hilbert's projective metric and leads to considerable simplification of the ergodic and central limit theory of population growth.

Keywords

DEMOGRAPHYHILBERT'S PROJECTIVE METRICERGODICCENTRAL LIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 325 - 334
Copyright
Copyright © Applied Probability Trust 

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Footnotes

This research supported in part by the University of California, Los Angeles; the Mailman Research Center; NIH Research Career Development Award, K04 HD00307; and NRSA Training Grant GM 7191.

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