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arXiv · 2111.04043

Limit theorems for the critical Galton-Watson processes with immigration stopped at zero

Doudou Li·Mei Zhang·Xianyu Zhang
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Abstract

In this paper, we consider a critical Galton-Watson branching process with immigration stopped at zero $\mathbf{W}$. Some precise estimation on the generation function of the $n$-th population are obtained, and the tail probability of the life period of $\mathbf{W}$ is studied. Based on above results, two conditional limit theorems for $\mathbf{W}$ are established.

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Doudou Li, Mei Zhang, Xianyu Zhang. 2021-11-07. Limit theorems for the critical Galton-Watson processes with immigration stopped at zero. https://arxiv.org/abs/2111.04043

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