A Martingale Approach to Supercritical (CMJ) Branching Processes

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