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Expected population size in the generation-dependent branching process

Published online by Cambridge University Press:  14 July 2016

J. D. Biggins  and
Thomas Götz
J. D. Biggins*
Affiliation:
University of Sheffield
Thomas Götz
Affiliation:
University of Heidelberg
*
∗Postal address: Department of Probability and Statistics, The University, Sheffield S3 7RH, England.
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Abstract

A Malthusian parameter for the generation-dependent general branching process is introduced and some asymptotics of the expected population size, counted by a general non-negative characteristic, are discussed. Processes both with and without immigration are considered.

Keywords

IMMIGRATIONMALTHUSIAN PARAMETER
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 304 - 314
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

∗∗

Present address: J. P. Sharp GmbH, Myliusstr. 45, 6000 Frankfurt/Main, W. Germany. Supported in part by Deutsche Forschungsgemeinschaft (SFB 123).

References

Edler, L. (1978) Strict supercritical generation-dependent Crump–Mode–Jagers branching processes. Adv. Appl. Prob. 10, 744–763.CrossRefGoogle Scholar
Fearn, D. H. (1976) Supercritical age-dependent branching processes with generation dependence. Ann. Prob. 4, 27–37.CrossRefGoogle Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications Vol. 2, 2nd edn. Wiley, New York.Google Scholar
Fildes, R. (1971) An age-dependent branching process with variable lifetime distributions. Adv. Appl. Prob. 4, 453–474.CrossRefGoogle Scholar
Fildes, R. (1974) An age-dependent branching process with variable lifetime distributions: The generation size. Adv. Appl. Prob. 6, 291–308.CrossRefGoogle Scholar
Jagers, P. (1975) Branching Processes with Biological Applications. Wiley, New York.Google Scholar
Smith, W. L. (1962) On some general renewal theorems for non-identically distributed variables. Proc. 4th Berkeley Symp. Math. Statist. Prob. II, 467–514.Google Scholar
Smith, W. L. (1967) On the weak law of large numbers and the generalized elementary renewal theorem. Pacific J. Math. 22, 171–188.CrossRefGoogle Scholar