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We consider a strongly supercritical branching process in random environment with immigration stopped at a distant time . The offspring reproduction law in each generation is assumed to be geometric. The process is considered under the condition of its extinction after time . Two limit theorems for this process are proved: the first one is for the time interval from 0 till , and the second one is for the time interval from  till+∞+\infty.

Limit Theorems for a Strongly Supercritical Branching Process with Immigration in Random Environment