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Asymptotic growth of a class of size-and-age-dependent birth processes

Published online by Cambridge University Press:  14 July 2016

W. A. O'N. Waugh
W. A. O'N. Waugh*
Affiliation:
The University of Toronto
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Abstract

A class of binary fission stochastic population models is described, in which the fission probabilities may depend on the age of an individual and the total population size. Age-dependent binary branching processes with Erlangian lifelength distributions are a special case. An asymptotic expression for the growth of the population size is developed, which generalizes known theorems about the asymptotic exponential growth of a branching process.

Keywords

BRANCHING PROCESSESAGE-DEPENDENTERLANGIAN DISTRIBUTIONSSOJOURN TIMESASYMPTOTIC GROWTHIMBEDDED PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 2 , June 1974 , pp. 248 - 254
Copyright
Copyright © Applied Probability Trust 1974 

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References

Clifford, P. and Sudbury, A. (1972) The linear cell-size-dependent branching process. J. Appl. Prob. 9, 687–696.Google Scholar
Cox, D. R. and Smith, W. L. (1961) Queues. Methuen, London.Google Scholar
Harris, T. E. (1963) The Theory of Branching Processes. Springer, Berlin.Google Scholar
Kendall, D. G. (1948) On the role of a variable generation time in the development of a stochastic birth process. Biometrika 35, 316–330.Google Scholar
Waugh, W. A. O'N. (1974) Modes of growth of counting processes with increasing arrival rates. J. Appl. Prob. 11, 237–247.Google Scholar
Weiner, H. J. (1966) Applications of the age distribution in age dependent branching processes. J. Appl. Prob. 3, 179–201.CrossRefGoogle Scholar