Abstract:
The almost critical branching processes $Z_{k,n}$ in a random environment is considered. It was shown that the survival probabilities for the processes $Z_{n,n}$ and $Z_n$ are equivalent under rather natural assumptions on the closeness of $Z_{k,n}$ and $Z_k$. This paper contains examples of applications of this result and justifies the need for imposed conditions.
Keywords:random walks, branching processes, random environments.
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