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

2021/11/07 by Li, Doudou, Zhang, Mei, Zhang, Xianyu
#60F10 #60J80 #FOS: Mathematics #G.3 #Probability (math.PR)

paper · doi:10.48550/arxiv.2111.04043

Abstract

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

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