Open Access
November, 1985 A Martingale Approach to Supercritical (CMJ) Branching Processes
Harry Cohn
Ann. Probab. 13(4): 1179-1191 (November, 1985). DOI: 10.1214/aop/1176992803


A new method of tackling convergence properties of random processes turns out to be applicable to finite mean supercritical age-dependent branching processes. If $\{Z^\phi_t\}$ is a Crump-Mode-Jagers process counted with general characteristics $\phi$, convergence in probability of $\{e^{-\alpha t} Z^\phi_t\}$ follows from convergence in distribution. Under some mild restrictions on $\phi$, norming constants $\{C(t)\}$ are identified such that $\{C^{-1}(t)Z^\phi_t\}$ converges almost surely to a nondegenerate limit.


Download Citation

Harry Cohn. "A Martingale Approach to Supercritical (CMJ) Branching Processes." Ann. Probab. 13 (4) 1179 - 1191, November, 1985.


Published: November, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0587.60086
MathSciNet: MR806216
Digital Object Identifier: 10.1214/aop/1176992803

Primary: 60K99
Secondary: 60J80

Keywords: convergence , functional equation , martingale , Supercritical (CMJ) branching process

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 4 • November, 1985
Back to Top