Limit theorems of branching processes with immigration

Abstract

In this paper, we introduce some references on the limit behaviors of Galton-Watson branching process with immigration in subcritical, critical and supercritical cases. Some research work and new progress of the author and collaborators are presented and discussed, including the large deviation and upper deviation for the branching processes with immigration in critical case; the harmonic moment, large deviation and lower deviation for the branching processes with immigration in supercritical case.