Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-29T04:18:30.827Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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∞pksk and suppose h(1) ≡ m, and assume h”(1) < ∞. Additional assumptions will be added as required.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag, Berlin (American edition by Prentice-Hall).CrossRefGoogle Scholar
[2] Puri, P. (1966) On the homogeneous birth and death process and its integral. Biometrika 53, 61–71.CrossRefGoogle ScholarPubMed
[3] Weiner, ?. J. (1966) On age dependent branching processes. J. Appl. Prob. 3, 383–402.Google Scholar
[4] Weiner, H. J. (1965) An integral equation in age dependent branching processes. Ann. Math. Statist. 36, 1569–1573.CrossRefGoogle Scholar
[5] Weiner, H. J. (1965) Asymptotic properties of an age dependent branching process. Ann. Math. Statist. 36, 1565–1568.Google Scholar
[6] Weiner, H. J. (1966) Monotone convergence of moments in age dependent branching processes. Ann. Math. Statist. 37, 1806–1808.Google Scholar
[7] Jagers, P. (1967) Integrals of branching processes. Biometrika 54, 263–272.CrossRefGoogle ScholarPubMed
[8] Mode, C. J. (1967) A renewal density theorem in a multidimensional case. J. Appl. Prob. 4, 62–76.CrossRefGoogle Scholar