CONCEPTUAL PROOFS OF L-LOG-L CRITERIA FOR MEAN-BEHAVIOR OF BRANCHING-PROCESSES
CONCEPTUAL PROOFS OF L-LOG-L CRITERIA FOR MEAN-BEHAVIOR OF BRANCHING-PROCESSES
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DOI：
10.1214/aop/1176988176
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发表时间：
1995-07-01
影响因子：
2.3
通讯作者：
PERES, Y
中科院分区：
文献类型：
--
作者：
LYONS, R;PEMANTLE, R;PERES, Y
Kesten-Stigum 定理是超临界分支过程增长率的基本标准，证明 L log L 条件是决定性的。在临界和亚临界情况下，柯尔莫哥洛夫和后来作者的结果给出了该过程至少存活n代的概率的衰减率。我们基于高尔顿-沃森测度与树空间上的另一种测度的比较，给出了这些定理的概念证明。该方法还通过指数分布的简单表征解释了条件临界分支过程的 Yaglom 指数极限定律。
The Kesten-Stigum theorem is a fundamental criterion for the rate of growth of a supercritical branching process, shelving 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.