Article contents
On the almost sure convergence of controlled branching processes
Published online by Cambridge University Press: 14 July 2016
Abstract
An almost sure convergence result for the normed population size of a supercritical controlled branching process is proved.
Keywords
- Type
- Short Communications
- Information
- Copyright
- Copyright © Applied Probability Trust 1986
References
[1]
Asmussen, S. (1978) Some martingale methods in the limit theory of supercritical branching processes. In Branching Processes, eds. Joffe, A. and Ney, P., Marcel Dekker, New York.Google Scholar
[2]
Chow, Y. S. and Teicher, H. (1978) Probability Theory: Independence, Interchangeability, Martingales.
Springer-Verlag, New York.Google Scholar
[3]
Foster, J. I. (1971) A limit theorem for a branching process with state-independent immigration. Ann. Math. Statist.
42, 1773–1776.Google Scholar
[4]
Jagers, P. (1975) Branching Processes with Biological Applications.
Wiley, New York.Google Scholar
[5]
Sevastyanov, B. A. and Zubkov, A. M. (1974) Controlled branching processes. Theory Prob. Appl.
19, 14–24.CrossRefGoogle Scholar
[7]
Zubkov, A. M. (1974) Analogies between Galton–Watson processes and ? -branching processes. Theory Prob. Appl.
19, 309–331.CrossRefGoogle Scholar
- 6
- Cited by