Subcritical Sevastyanov branching processes with nonhomogeneous Poisson immigration

J Appl Probab. 2017 Jun;54(2):569-587. doi: 10.1017/jpr.2017.18. Epub 2017 Jun 22.

Abstract

We consider a class of Sevastyanov branching processes with non-homogeneous Poisson immigration. These processes relax the assumption required by the Bellman-Harris process which imposes the lifespan and offspring of each individual to be independent. They find applications in studies of the dynamics of cell populations. In this paper, we focus on the subcritical case and examine asymptotic properties of the process. We establish limit theorems, which generalize classical results due to Sevastyanov and others. Our key findings include novel LLN and CLT which emerge from the non-homogeneity of the immigration process.

Keywords: 60J85; 62P10; Branching processes; Immigration; Limit theorems; Poisson process; Primary 60J80; Secondary 60F05.