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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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##### References:
 [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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