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Asymptotic probabilities in a critical age-dependent branching process

Published online by Cambridge University Press:  14 July 2016

Howard J. Weiner*
University of California at Davis


Let Z(t) denote the number of cells alive at time t in a critical Bellman-Harris age-dependent branching process, that is, where the mean number of offspring per parent is one. A comparison method is used to show for k ≧ 1, and a high-order moment condition on G(t), where G(t) is the cell lifetime distribution, that lim t→∞t2P[Z(t) = k] = ak > 0, where {ak} are constants.

The method is also applied to the total progeny in the critical process.

Research Papers
Copyright © Applied Probability Trust 1976 

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