Conceptual Proofs of L log L Criteria

Details Conceptual Proofs of L log L Criteria Conceptual Proofs of L log L Criteria

2004-04-05

arxiv.org/abs/math/0404083v1

Ann. Probab., 23, 1125 - 1138 (1995)

Mathematics

Probability

15 pages

Scientific paper

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.

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