Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-09T12:32:14.323Z Has data issue: false hasContentIssue false
  • English
  • Français

Some limit theorems for Markov branching processes

Published online by Cambridge University Press:  14 July 2016

J. R. Leslie
J. R. Leslie*
Affiliation:
The Australian National University
Get access Rights & Permissions [Opens in a new window]

Abstract

Analogues of the central limit theorem and iterated logarithm law have recently been obtained for the Galton-Watson process; similar results are established in this paper for the temporally homogeneous Markov branching process and for the associated increasing process consisting of the number of splits in the original process up to time t.

Keywords

CENTRAL LIMIT THEOREMITERATED LOGARITHM LAWBRANCHING PROCESSTEMPORALLY HOMOGENEOUS MARKOV PROCESSSPLITTING PROCESS
Type
Research Papers
Information
Journal of Applied Probability , Volume 10 , Issue 2 , June 1973 , pp. 299 - 306
Copyright
Copyright © Applied Probability Trust 1973 

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 Karlin, S. (1967) Limit theorems for the split times of branching processes. J. Math. Mech. 17, 257–279.Google Scholar
[2] Chow, Y. S., Robbins, H. and Siegmund, D. (1971) Great Expectations: The Theory of Optimal Stopping. Houghton Mifflin, Boston.Google Scholar
[3] Harris, T. E. (1963) Theory of branching processes. Springer-Verlag, Berlin.CrossRefGoogle Scholar
[4] Heyde, C. C. (1971) Some central limit analogues for super-critical Galton-Watson processes. J. Appl. Prob. 8, 52–59.CrossRefGoogle Scholar
[5] Heyde, C. C. (1971) Some almost sure convergence theorems for branching processes. Zeit. Wahrscheinlichkeitsth. 20, 189–192.CrossRefGoogle Scholar
[6] Heyde, C. C. and Leslie, J. R. (1971) Improved classical limit analogues for Galton-Watson processes with or without immigration. Bull. Austral. Math. Soc. 5, 145–155.CrossRefGoogle Scholar