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A local limit theorem for the critical age-dependent branching process
Published online by Cambridge University Press: 14 July 2016
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→∞.
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- Copyright © Applied Probability Trust 1978
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
[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
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