Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-06T06:22:26.635Z Has data issue: false hasContentIssue false
  • English
  • Français

Conditional moments in a critical age-dependent branching process

Published online by Cambridge University Press:  14 July 2016

Howard J. Weiner
Howard J. Weiner*
Affiliation:
University of California, Davis
Get access Rights & Permissions [Opens in a new window]

Abstract

Let X(t), N(t) respectively denote the number of cells alive at t and the total number of cells born by t in a critical age-dependent Bellman-Harris branching process.

The asymptotic behavior of the conditional moments, for 0 < α ≦ 1, E(Nn(αt) | X(t) > 0), E(Nn(t) |X(αt) > 0), is obtained.

Keywords

CONDITIONAL MOMENTSCRITICAL AGE-DEPENDENT BRANCHING PROCESSINTEGRAL EQUATIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 3 , September 1975 , pp. 581 - 587
Copyright
Copyright © Applied Probability Trust 1975 

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] Athreya, K. and Ney, P. (1972) Branching Processes. Springer-Verlag, New York.CrossRefGoogle Scholar
[2] Esty, W. (1973) Critical age dependent branching processes , Technical Report CSUMD 16, Cleveland State University, Cleveland, Ohio.Google Scholar
[3] Weiner, H. (1965) Asymptotic properties of an age dependent branching process. Ann. Math. Statist. 36, 1565–1568.CrossRefGoogle Scholar
[4] Weiner, H. (1969) Sums of lifetimes in age-dependent branching processes. J. Appl. Prob. 6, 195–200.CrossRefGoogle Scholar