This article is cited in 85 papers

On asymptotics of the probability of nonextinction for a critical branching process in random environment

M. V. Kozlov

Moscow

Abstract: For critical branching processes in random environment, under some slight restrictions, the following inequalities for the tails of the extinction time distribution are proved:
\begin{equation} c_1/\sqrt n\le\mathbf P(T>n)\le c_2/\sqrt n. \end{equation}

In the case of fractional linear generating functions, (1) is replaced by
$$ \mathbf P(T>n)\sim c/\sqrt n,\qquad n\to\infty. $$


Received: 08.04.1976

 English version: Theory of Probability and its Applications, 1977, 21:4, 791–804

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