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Gaussian fluctuations and a law of the iterated logarithm for Nerman’s martingale in the supercritical general branching process
In his, by now, classical work from 1981, Nerman made extensive use of a crucial martingale (Wt)t≥0 to prove convergence in probability, in mean and almost surely, of supercritical general branching processes (also known as Crump-Mode-Jagers branching processes) counted with a general characteristic. The martingale terminal value W figures in …