AI 中文总结
本文针对仅当前一代为空时发生移民的重尾次临界Galton-Watson过程，建立直至时间n总后代的中心极限定理，扩展了有限方差模型的已有结果。
AI 中文摘要
本文研究带状态依赖移民的次临界Galton-Watson过程，仅当前一代为空时发生移民。在后代与移民分布满足重尾假设下，建立了直至时间n的总后代的中心极限定理，扩展了文献中有限方差模型的现有结果。
英文摘要
In this paper, we study a subcritical Galton-Watson process with state-dependent immigration, where immigration occurs only if the preceding generation is empty. Under heavy-tailed assumptions on the offspring and immigration distributions, we establish central limit theorems for the total progeny up to time $n$, thereby extending existing results for the finite-variance model in the literature.
