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Zbl 0994.60095
Geiger, J.; Kersting, G.
The survival probability of a critical branching process in a random environment.
(English)
[J] Theory Probab. Appl. 45, No.3, 517-525 (2000) and Teor. Veroyatn. Primen. 45, No.3, 607-615 (2000). ISSN 0040-585X; ISSN 1095-7219/e

There are determined the asymptotic behavior of the survival probability of a critical branching process in a random environment. In the special case of independent identically distributed geometric offspring distributions, and the somewhat more general case of offspring distributions with linear fractional generating functions, {\it M. V. Kozlov} [Theory Probab. Appl. 21(1976), 791-804 (1977); translation from Teor. Veroyatn. Primen. 21, 813-825 (1976; Zbl 0384.60058)] proved that, as $n\to\infty$, the probability of nonextinction at generation $n$ is proportional to $n^{-1/2}$. There are established Kozlov's asymptotic for general independent identically distributed offspring distributions.
[Valentin Topchii (Omsk)]
MSC 2000:
*60K37 Processes in random environments
60J80 Branching processes
60G50 Sums of independent random variables

Keywords: branching processes; random environments; conditioned random walks

Citations: Zbl 0384.60058

Cited in: Zbl 1068.60096

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