Asymptotic behaviour of the survival probability of almost critical branching processes in a random environment

A generalization of the well-known result concerning the survival probability of a critical branching process in random environment $Z_k$ is considered. The triangular array scheme of branching processes in random environment $Z_{k,n}$ that are close to $Z_k$ for large $n$ is studied. The equivalence of the survival probabilities for the processes $Z_{n,n}$ and $Z_n$ is obtained under rather natural assumptions on the closeness of $Z_{k,n}$ and $Z_k$. Bibliography: 7 titles.