Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T01:35:46.475Z Has data issue: false hasContentIssue false
  • English
  • Français

Diffusion limits of critical branching processes conditioned on extinction in the near future

Published online by Cambridge University Press:  14 July 2016

Warren W. Esty
Warren W. Esty*
Affiliation:
Cleveland State University
*
*Now at Montana State University, Bozeman, Montana.
Get access Rights & Permissions [Opens in a new window]

Abstract

Limit laws and limiting diffusions are obtained for critical branching processes, either Galton-Watson or age-dependent, conditioned on extinction in the interval (T, cT], 1 < c, as T→∞, and also as T→∞ and c ↓ 1.

Keywords

BRANCHING PROCESSDIFFUSIONCRITICAL BRANCHING PROCESSGALTON-WATSON PROCESSAGE-DEPENDENT BRANCHING PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 247 - 254
Copyright
Copyright © Applied Probability Trust 1976 

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. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, Heidelberg.Google Scholar
[2] Esty, W. W. (1975) Critical age-dependent branching processes. Ann. Prob. 3, 49–60.Google Scholar
[3] Esty, W. W. (1975) Critical age-dependent branching process diffusions. Stoch. Proc. Appl. To appear.CrossRefGoogle Scholar
[4] Esty, W. W. (1975) The reverse Galton-Watson process. J. Appl. Prob. 12, 574–580.Google Scholar
[5] Gikhman, I. I. and Skorokhod, A. V. (1969) Introduction to the Theory of Random Processes. W. B. Saunders Co., Philadelphia.Google Scholar