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Conditional moments in a critical age-dependent branching process

Published online by Cambridge University Press:  14 July 2016

Howard J. Weiner
Howard J. Weiner*
Affiliation:
University of California, Davis
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Abstract

Let X(t), N(t) respectively denote the number of cells alive at t and the total number of cells born by t in a critical age-dependent Bellman-Harris branching process.

The asymptotic behavior of the conditional moments, for 0 < α ≦ 1, E(Nn(αt) | X(t) > 0), E(Nn(t) |X(αt) > 0), is obtained.

Keywords

CONDITIONAL MOMENTSCRITICAL AGE-DEPENDENT BRANCHING PROCESSINTEGRAL EQUATIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 581 - 587
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Athreya, K. and Ney, P. (1972) Branching Processes. Springer-Verlag, New York.CrossRefGoogle Scholar
[2] Esty, W. (1973) Critical age dependent branching processes , Technical Report CSUMD 16, Cleveland State University, Cleveland, Ohio.Google Scholar
[3] Weiner, H. (1965) Asymptotic properties of an age dependent branching process. Ann. Math. Statist. 36, 1565–1568.CrossRefGoogle Scholar
[4] Weiner, H. (1969) Sums of lifetimes in age-dependent branching processes. J. Appl. Prob. 6, 195–200.CrossRefGoogle Scholar