We consider a class of Sevastyanov branching processes with nonhomogeneous 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 a novel law of large numbers and a central limit theorem which emerge from the nonhomogeneity of the immigration process.

中文翻译：

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具有非均匀泊松迁移的亚临界 Sevastyanov 分支过程

我们考虑一类具有非齐次泊松迁移的 Sevastyanov 分支过程。这些过程放宽了贝尔曼-哈里斯过程所要求的假设，该过程强制每个人的寿命和后代是独立的。他们在细胞群动力学研究中找到了应用。在本文中，我们关注亚临界情况并检查过程的渐近特性。我们建立了极限定理，它概括了 Sevastyanov 等人的经典结果。我们的主要发现包括一个新的大数定律和一个从移民过程的非同质性中出现的中心极限定理。