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The survival probability of a critical branching process in a random environment. (English) Zbl 0994.60095
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, 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, 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.

60K37Processes in random environments
60J80Branching processes
60G50Sums of independent random variables; random walks