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A conditional function limit theorem for a critical branching process in a random medium. (English. Russian original) Zbl 0884.60085

Dokl. Math. 52, No. 2, 164-167 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 344, No. 1, 12-15 (1995).
There are established a conditional function limit theorem for the Wilkinson-Smith branching processes under the condition that it is nondegenerate on the time interval \([0,n]\) and \(n\to \infty\). The results are connected with B. Durret’s one [Ann. Probab. 6, 798-828 (1978; Zbl 0398.60023)]. This is the main part for the proof scheme connections of the process with some random walk and special constructed Markov chain.
Reviewer: V.Topchij (Omsk)

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60F17 Functional limit theorems; invariance principles
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60G50 Sums of independent random variables; random walks
60J85 Applications of branching processes

Citations:

Zbl 0398.60023
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