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Sums of Lifetimes in Age Dependent Branching Processes

Published online by Cambridge University Press:  14 July 2016

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

Consider a Bellman-Harris [1] age dependent branching process. At t = 0, a cell is born, has lifetime distribution function G(t), G(0) = 0, assumed to be absolutely continuous with density g(t). At the death of the cell, k new cells are born, each proceeding independently and identically as the parent cell, and independent of past history. Denote by h(s) = Σk=0 ∞pk s k and suppose h(1) ≡ m, and assume h”(1) < ∞. Additional assumptions will be added as required.

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Type
Short Communications
Information
Journal of Applied Probability , Volume 6 , Issue 1 , April 1969 , pp. 195 - 200
Copyright
Copyright © Applied Probability Trust 

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References

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