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On a multi-type critical age-dependent branching process

Published online by Cambridge University Press:  14 July 2016

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

We will consider a branching process with m > 1 distinguishable particle types as follows. At time 0, one newly born cell of type i is born (i = 1, 2, ···, m). Cell type i lives a random lifetime with continuous distribution function Gi(t), Gi(0+) = 0. At the end of its life, cell i is replaced by j1 new cells of type 1, j2 new cells of type 2, ···, jm new cells of type m with probability , and we define the generating functions for i = 1,···,m, where and . Each new daughter cell proceeds independently of the state of the system, with each cell type j governed by Gj(t) and hj(s).

Type
Research Papers
Information
Journal of Applied Probability , Volume 7 , Issue 3 , December 1970 , pp. 523 - 543
Copyright
Copyright © Applied Probability Trust 1970 

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References

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