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On Cohen's stochastic generalization of the strong ergodic theorem of demography

Published online by Cambridge University Press:  14 July 2016

Kenneth Lange
Kenneth Lange*
Affiliation:
University of California, Los Angeles
*
∗ Postal address: Department of Biomathematics, School of Medicine, University of California, Los Angeles, CA 90024, U.S.A. Research supported in part by the University of California, Los Angeles and NIH Special Research Resources Grant RR-3.
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Abstract

Cohen has generalized the classical strong ergodic theorem of demography to a stochastic setting. In this setting population projection matrices are chosen according to some homogeneous Markov chain. If this Markov chain converges to the same long-run distribution regardless of its starting point, then one can define an induced Markov chain on the product space of projection matrices and age structure vectors that also has a long-run distribution independent of its starting point. The present paper gives more natural conditions under which Cohen's result holds.

Keywords

DEMOGRAPHYAGE STRUCTUREMARKOV CHAINERGODICCONVERGENCE IN DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 3 , September 1979 , pp. 496 - 504
Copyright
Copyright © Applied Probability Trust 1979 

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References

Blumenthal, R. M. and Getoor, R. K. (1968) Markov Processes and Potential Theory. Academic Press, New York.Google Scholar
Bushell, P. J. (1973) Hilbert's metric and positive contraction mappings in a Banach space. Arch. Rational Mech. Anal. 52, 330–338.Google Scholar
Cohen, J. E. (1976) Ergodicity of age structure in populations with Markovian vital rates. I: Countable states. J. Amer. Statist. Assoc. 71, 335–339.Google Scholar
Cohen, J. E. (1977a) Ergodicity of age structure in populations with Markovian vital rates. II: General states. Adv. Appl. Prob. 9, 18–37.Google Scholar
Cohen, J. E. (1977b) Ergodicity of age structure in populations with Markovian vital rates. III: Finite state moments and growth rate; an illustration. Adv. Appl. Prob. 9, 462–475.Google Scholar
Cohen, J. E. (1979) Contractive inhomogeneous products of non-negative matrices. Math. Proc. Camb. Phil. Soc. To appear.Google Scholar
Golubitsky, M., Keeler, E. B. and Rothschild, M. (1975) Convergence of the age structure: application of the projective metric. Theoret. Popn Biol. 7, 84–93.Google Scholar
Hajnal, J. (1976) On products of non-negative matrices. Math. Proc. Camb. Phil. Soc. 79, 521–530.Google Scholar
Lopez, A. (1961) Some Problems in Stable Population Theory. Office of Population Research, Princeton University, Princeton, New Jersey.Google Scholar
Parthasarathy, K. R. (1967) Probability Measures on Metric Spaces. Academic Press, New York.Google Scholar
Pollard, J. H. (1973) Mathematical Models for the Growth of Human Populations. Cambridge University Press, London.Google Scholar
Rosenblatt, M. (1971) Markov Processes: Structure and Asymptotic Behavior. Springer-Verlag, Berlin.Google Scholar