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Convergence of general branching processes and functionals thereof

Published online by Cambridge University Press:  14 July 2016

Peter Jagers
Peter Jagers*
Affiliation:
University of Gothenburg, Sweden
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Abstract

With each individual in a branching population associate a random function of the age. Count the population by the values of these functions. Different choices yield different processes. In the supercritical case a unified treatment of the asymptotics is possible for a wide class, including for example the number of individuals having some random age dependent property or integrals of branching processes. As an application, the demographic concept of average age at childbearing is given a rigorous interpretation.

Keywords

ALMOST SURE CONVERGENCEGENERAL BRANCHING PROCESSES

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974, pp. 471 - 478
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Brockwell, P. J. and Trucco, E. (1970) On the decomposition by generations of the PLM-function. J. Theoret. Biol. 26, 149–179.Google Scholar
[2] Crump, K. S. and Mode, C. J. (1968), (1969) A general age-dependent branching process I, II. J. Math. Anal. Appl. 24, 494–508, and 25, 8–17.CrossRefGoogle Scholar
[3] Doney, R. A. (1971) The progeny of a branching process. J. Appl. Prob. 8, 407–412.Google Scholar
[4] Harris, T. E. (1963) The Theory of Branching Processes. Springer, Berlin.Google Scholar
[5] Jagers, P. (1967) Integrals of branching processes. Biometrika 54, 263–271.Google Scholar
[6] Jagers, P. (1968) Renewal theory and the almost sure convergence of branching processes. Ark. Mat. 7, 495–504.CrossRefGoogle Scholar
[7] Jagers, P. (1969) A general stochastic model for population development. Skand. Aktuar. Tidskr. 52, 84–103.Google Scholar
[8] Jagers, P. (1970) The composition of branching populations: a mathematical result and its application to determine the incidence of death in cell proliferation. Math. Biosci. 8, 227–238.CrossRefGoogle Scholar
[9] Jagers, P. (1973) A ruin problem for the insurance of expanding portfolios. Skand. Aktuar. Tidskr. 55, 187–190.Google Scholar
[10] Keiding, N. (1973) Lecture Notes on the Stochastic Population Model. Institute of Mathematical Statistics, University of Copenhagen.Google Scholar
[11] Keyfitz, N. (1968) Introduction to the Mathematics of Population. Addison-Wesley, Reading, Mass.Google Scholar
[12] Pakes, A. G. (1972) A limit theorem for the integral of a critical age-dependent branching process. Math. Biosci. 13, 109–112.Google Scholar
[13] Weiner, H. J. (1969) Sums of lifetimes in age dependent branching processes. J. Appl. Prob. 6, 195–200.Google Scholar
[14] Weiner, H. J. (1966) Applications of the age distribution in age-dependent branching processes. J. Appl. Prob. 3, 179–201.CrossRefGoogle Scholar