Abstract
The Kesten-Stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an $L \log L$ condition is decisive. In critical and subcritical cases, results of Kolmogorov and later authors give the rate of decay of the probability that the process survives at least $n$ generations. We give conceptual proofs of these theorems based on comparisons of Galton-Watson measure to another measure on the space of trees. This approach also explains Yaglom's exponential limit law for conditioned critical branching processes via a simple characterization of the exponential distribution.
Citation
Russell Lyons. Robin Pemantle. Yuval Peres. "Conceptual Proofs of $L$ Log $L$ Criteria for Mean Behavior of Branching Processes." Ann. Probab. 23 (3) 1125 - 1138, July, 1995. https://doi.org/10.1214/aop/1176988176
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