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Ergodic theorems in demography
Author(s):
Joel E.
Cohen
Journal:
Bull. Amer. Math. Soc.
1
(1979),
275-295.
MSC (1970):
Primary 15A48, 60J20;
Secondary 92A15, 60B15
MathSciNet review:
520076
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Additional information
References:
- David R. Anderson, Optimal exploitation strategies for an animal population in a Markovian environment: a theory and an example, Ecology 56 (1975), 1281-1297.
- K. B. Athreya and S. Karlin, On branching processes with random environments: I. Extinction probabilities: II. Limit theorems, Ann. Math. Statist. 42 (1971), 1499-1520, 1843-1858. MR 298780
- Garrett Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ., no. 25, Amer. Math. Soc., Providence, R. I., 1967. MR 227053
- J. Bourgeois-Pichat, The concept of a stable population: application to the study of populations of countries with incomplete demographic statistics, United Nations, New York, ST/SOA/SER.A/39, 1968.
- A. L. Bowley, Births and population of Great Britain, J. Roy. Econom. Soc. 34 (1924), 188-192.
- Mark S. Boyce, Population growth with stochastic fluctuations in the life table, Theoret. Population Biology 12 (1977), 366-373.
- Edwin Cannan, The probability of a cessation of the growth of population in England and Wales during the next century, The Economic Journal 5 (1895), 505-515.
- Ansley J. Coale, How the age distribution of a human population is determined, Cold Spring Harbor Symposia on Quantitative Biology (ed. K. B. Warren) 22 (1957), 83-89.
- Ansley J. Coale, The use of Fourier analysis to express the relation between time variations in fertility and the time sequence of births in a closed human population, Demography 7 (1970), 93-120.
- Ansley J. Coale, The growth and structure of human populations, Princeton Univ. Press, Princeton, N. J., 1972.
- A. J. Coale and Paul Demeny, Methods of estimating basic demographic measures from incomplete data, United Nations Manual IV on Methods of Estimating Population, ST/SOA/Ser.A/42, United Nations, New York, 1969.
- Joel E. Cohen, Ergodicity of age structure in populations with Markovian vital rates. I: Countable states, J. Amer. Statist. Assoc. 71 (1976), 335-339. MR 408881
- Joel E. Cohen, Ergodicity of age structure in populations with Markovian vital rates. II: General states, Advances in Appl. Probability 9 (1977a), 18-37. MR 429175
- Joel E. Cohen, Ergodicity of age structure in populations with Markovian vital rates, III: Finite-state moments and growth rates; illustration, Advances in Appl. Probability 9 (1977b), 462-475. MR 465278
- Joel E. Cohen, Derivatives of the spectral radius as a function of nonnegative matrix elements, Math. Proc. Cambridge Philos. Soc. 83 (1978a), 183-190. MR 466178
- Joel E. Cohen, Long-run growth rates of discrete multiplicative processes in Markovian environments, J. Math. Anal. Appl. (1978b). MR 535294
- Joel E. Cohen, The cumulative distance from an observed to a stable age structure, SIAM J. Appl. Math. (to appear). MR 519192
- Joel E. Cohen, Comparative statics and stochastic dynamics of age-structured populations, Theoret. Population Biology (submitted). MR 552137
- Peter R. Cox, Demography, 4th ed., Cambridge Univ. Press, London and New York, 1970.
- Lloyd Demetrius, The sensitivity of population growth rate to perturbations in the life cycle components, Math. Biosciences 4 (1969), 129-136.
- Lloyd Demetrius, Demographic parameters and natural selection, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 4645-4647. MR 392032
- Lloyd Demetrius, Adaptedness and fitness, Amer. Natur. 111 (1977), 1163-1168.
- Harold F. Dorn, Pitfalls in population forecasts and projections, J. Amer. Statist. Assoc. 45 (1950), 311-334.
- H. Furstenberg and H. Kesten, Products of random matrices, Ann. Math. Statist. 31 (1960), 457-469. MR 121828
- Martin Golubitsky, Emmett B. Keeler and Michael Rothschild, Convergence of the age structure: Applications of the projective metric, Theoret. Population Biology 7 (1975), 84-93. MR 371433
- Leo A. Goodman, Stochastic models for the population growth of the sexes, Biometrika 55 (1968), 469-487. MR 238579
- Leo A. Goodman, On the sensitivity of the intrinsic growth rate to changes in the age-specific birth and death rates, Theoret. Population Biology 2 (1971), 339-354.
- John V. Grauman, Success and failure in population forecasts in the 1950's; a general appraisal, Proc. World Population Conf., Belgrade, August 30-September 10, 1965, United Nations, New York, 1967.
- David Griffeath, Uniform coupling of non-homogeneous Markov chains, J. Appl. Probability 12 (1975), 753-762. MR 386018
- John Hajnal, The prospects for population forecasts, J. Amer. Statist. Assoc. 50 (1955), 309-322.
- John Hajnal, On products of nonnegative matrices, Math. Proc. Cambridge Philos. Soc. 79 (1976), 521-530. MR 396628
- Louis Henry and Hector Gutierrez, Qualité des prévisions démographiques à court terme. Étude de l'extrapolation de la population totale des départements et villes de France 1821-1975, Population 32 (1977), 625-647.
- Frank Hoppensteadt, Mathematical theories of populations: demographics, genetics and epidemics, Society for Industrial and Applied Mathematics, Philadelphia, Penn., 1975. MR 526771
- Tosio Kato, Perturbation theory for linear operators, 2nd ed., Springer-Verlag, New York, 1976. MR 407617
- Nathan Keyfitz, An introduction to the mathematics of population, Addison-Wesley, Reading, Mass., 1968.
- Nathan Keyfitz, Linkages of intrinsic to age-specific rates, J. Amer. Statist. Assoc. 66 (1971a), 275-281.
- Nathan Keyfitz, On the momentum of population growth, Demography 8 (1971b), 71-80.
- Nathan Keyfitz, On future population, J. Amer. Statist. Assoc. 67 (1972a), 347-363.
- Nathan Keyfitz, Population Waves, Population Dynamics, T. N. E. Greville (ed.), 1-38, Academic Press, New York, 1972b. MR 411694
- Nathan Keyfitz, Applied mathematical demography, Wiley, New York, 1977. MR 682611
- Y. J. Kim and Z. M. Sykes, An experimental study of weak ergodicity in human populations, Theoret. Population Biology 10 (1976), 150-172.
- J. F. C. Kingman, Review of Stochastic processes in queueing theory, by A. A. Borovkov, Bull. Amer. Math. Soc. 83 (1977), 317-318.
- Kenneth Lange, The momentum of a population whose birth rates gradually change to replacement levels, Math. Biosciences (in press).
- Kenneth Lange, On Cohen's stochastic generalization of the strong ergodic theorem of demography, Advances in Appl. Probability (in press b).
- Ronald Demos Lee, Forecasting births in post-transition populations: stochastic renewal with serially correlated fertility, J. Amer. Statist. Assoc. 69 (1974), 607-617.
- Ronald Demos Lee, Natural fertility, population cycles and the spectral analysis of births and marriage, J. Amer. Statist. Assoc. 70 (1975), 295-304.
- P. H. Leslie, Some further notes on the use of matrices in population mathematics, Biometrika 35 (1948), 213-245. MR 27991
- Alvaro Lopez, Problems in stable population theory, Office of Population Research, Princeton, N. J., 1961.
- Alfred J. Lotka, Théorie analytique des associations biologiques. Part II. Analyse démographique avec application particulière à l'espèce humaine, Actualités Sci. Indust., No. 780, Hermann, Paris, 1939.
- Donald Ludwig, Stochastic population theories, Lecture Notes in Biomath., vol. 3, Springer-Verlag, New York, 1974. MR 373658
- Robert H. MacArthur, Selection for life tables in periodic environments, Amer. Natur. 102 (1968), 381-383.
- George W. Mackey, Ergodic theory and its significance for statistical mechanics and probability theory, Advances in Math. 12 (1974), 178-268. MR 346131
- Ingo Morgenstern, Kurt Binder, and Artur Baumgärtner, Statistical mechanics of Ising chains in random magnetic fields, J. Chem. Phys. 69 (1978), 253-262.
- John H. Pollard, Mathematical models for the growth of human populations, Cambridge Univ. Press, London and New York, 1973.
- Chris Rorres, Stability of an age specific population with density dependent fertility, Theoret. Population Biology 10 (1976), 26-46. MR 418963
- J. L. M. Saboia, Autoregressive integrated moving average (ARIMA) models for birth forecasting, J. Amer. Statist. Assoc. 72 (1977), 264-270.
- Tore Schweder, The precision of population projections studied by multiple prediction methods, Demography 8 (1971), 441-450.
- Eugene Seneta, Non-negative matrices, Allen and Unwin, London, 1973. MR 389944
- David Smith and Nathan Keyfitz, Mathematical demography: Selected Readings, Biomathematics, vol. 6, Springer-Verlag, New York, 1977. MR 682611
- Walter L. Smith, Necessary conditions for almost sure extinction of a branching process with random environment, Ann. Math. Statist. 39 (1968), 2136-2140. MR 237006
- W. L. Smith and William E. Wilkinson, Branching processes in Markovian environments, Duke Math. J. 38 (1971), 749-763. MR 288885
- Mortimer Spiegelman, Introduction to demography, rev. ed., Harvard Univ. Press, Cambridge, Mass., 1968.
- Zenas M. Sykes, On discrete stable population theory, Biometrics 25 (1969a), 285-293.
- Zenas M. Sykes, Some stochastic versions of the matrix model for population dynamics, J. Amer. Statist. Assoc. 64 (1969b), 111-130. MR 395934
- S. M. Ulam, Adventures of a mathematician, Charles Scribner's Sons, New York, 1976. MR 485098
- Kenneth M. Weiss and P. A. Ballonoff (eds.), Demographic genetics, Benchmark Papers in Genetics, vol. 3, Dowden, Hutchinson & Ross, Stroudsburg, Penn., 1975. MR 389260
- P. K. Whelpton, An empirical method of calculating future population, J. Amer. Statist. Assoc. 31 (1936), 457-473.
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Additional Information:
DOI:
10.1090/S0273-0979-1979-14594-4
PII:
S 0273-0979(1979)14594-4
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