Limit theorems for strongly and intermediately supercritical branching processes in random environment with linear fractional offspring distributions

摘要

In the present paper, we characterize the behavior of supercritical branchingprocesses in random environment with linear fractional offspring distributions,conditioned on having small, but positive values at some large generation. Asit has been noticed in previous works, there is a phase transition in thebehavior of the process. Here, we examine the strongly and intermediatelysupercritical regimes The main result is a conditional limit theorem for therescaled associated random walk in the intermediately case.