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

Abstract

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