Abstract
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.
Citation
Harry Cohn. "A Martingale Approach to Supercritical (CMJ) Branching Processes." Ann. Probab. 13 (4) 1179 - 1191, November, 1985. https://doi.org/10.1214/aop/1176992803
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