Abstract The paper studies a critical Bienayme-Galton–Watson branching processes with immigration in varying environments. Assuming that the offspring variance is infinite and the mean number of immigrants is either finite or infinite it is proved the asymptotic formulas for the probability for non extinction. The proper limiting distributions under the appropriate normalization are also proved.

中文翻译：

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在不同环境中移民的关键分支过程

摘要 本文研究了在不同环境中移民的关键 Bienayme-Galton-Watson 分支过程。假设后代方差是无限的，移民的平均数是有限的或无限的，证明了非灭绝概率的渐近公式。还证明了适当归一化下的适当极限分布。