2004/04/05 by Russell Lyons, Robin Pemantle, Yuval Peres
Mathematics · #math.PR #msc:60J80
published as Ann. Probab., 23, 1125 - 1138 (1995) · 15 pages
arxiv created 2004/04/05 · arxiv updated 2009/12/01
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.