Central limit theorems for a heavy-tailed subcritical Galton-Watson process with state-dependent immigration

Xiaodan Luo; Mei Zhang

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arXiv · 2608.12070

Central limit theorems for a heavy-tailed subcritical Galton-Watson process with state-dependent immigration

Xiaodan Luo·Mei Zhang

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Abstract

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.

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BibTeX RIS

Xiaodan Luo, Mei Zhang. 2026-08-12. Central limit theorems for a heavy-tailed subcritical Galton-Watson process with state-dependent immigration. https://arxiv.org/abs/2608.12070

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