Abstract
The asymptotic behavior of the survival probability of an intermediate subcritical branching process $Z_n$ in a random environment is found when a transformation of the reproduction law of the offspring number is attracted to a stable law $\alpha\in (1,2]$. It is shown that the distribution of the random variable $\{Z_n\}$ given $Z_n>0$ converges to a nondegenerate distribution as $n\to\infty$.
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