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Critical branching processes in random environment: The probability of extinction at a given moment. (English. Russian original) Zbl 0977.60088
Discrete Math. Appl. 7, No. 5, 469-496 (1997); translation from Diskretn. Mat. 9, No. 4, 100-126 (1997).
The author describes in detail the way in which a Galton-Watson branching process may be regarded as a probability distribution over a set of hyper-trees, and the correspondence which exist between concepts in the conventional and tree-based approaches. He then quotes various limit theorems, as \(n\to\infty\), conditional on the total progeny of the branching process being equal to \(n\), and translates them into the tree context. Most of these theorems have their origins in a paper of D. P. Kennedy [J. Appl. Probab. 12, 800-806 (1975; Zbl 0322.60072)].

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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[1] Valulin, Theory Probab Appi Dyakonova Kozlov A random walk on the line with stochastic structure Theory Probab Solomon Random walk in random environment Probab Kesten Kozlov and Spitzer A limit law for random walk in a random environment, Appl 11 pp 513– (1966)
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