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A local limit theorem for the critical age-dependent branching process

Published online by Cambridge University Press:  14 July 2016

David L. Quigg
David L. Quigg*
Affiliation:
Texas Tech University
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Abstract

Let Z(t) denote the number of particles alive at time t in a critical age-dependent branching process. It is proved that, for k ≧ 1, there exists a constant Ak > 0 such that t2P(Z(t) = k)→Ak as t→∞.

Keywords

BRANCHING PROCESSAGE-DEPENDENT BRANCHING PROCESSCRITICAL BRANCHING PROCESSLOCAL LIMIT THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 15 , Issue 1 , March 1978 , pp. 46 - 53
Copyright
Copyright © Applied Probability Trust 1978 

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References

[1] Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, Berlin.Google Scholar
[2] Buck, R. C. and Buck, E. F. (1965) Advanced Calculus. 2nd edn. McGraw-Hill, New York.Google Scholar
[3] Goldstein, M. (1971) , University of Wisconsin—Madison.Google Scholar
[4] Kesten, H., Ney, P. and Spitzer, F. (1966) The Galton–Watson process with mean one and finite variance. Theor. Prob. Appl. 11, 513–540.Google Scholar
[5] Quigg, D. (1978) On an integral equation arising in age-dependent branching processes. J. Math. Anal. Appl. To appear.CrossRefGoogle Scholar