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Limit Theorems for Critical Galton-Watson Processes with Immigration Stopped at Zero

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Abstract

In this paper, we consider a critical Galton–Watson branching process with immigration stopped at zero W. Some precise estimation on the probability generating 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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Acknowledgements

The authors are deeply grateful to the anonymous referees for their careful reading the original manuscript and helpful suggestions to improve the paper.

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Authors and Affiliations

  1. College of Statistics and Data Science, Faculty of Science, Beijing University of Technology, Beijing, 100124, P. R. China

    Dou Dou Li

  2. Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China

    Mei Zhang & Xian Yu Zhang

Authors
  1. Dou Dou Li
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  2. Mei Zhang
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  3. Xian Yu Zhang
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Correspondence to Mei Zhang.

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The authors declare no conflict of interest.

Additional information

The first author is supported by China Postdoctoral Science Foundation (Grant No. 2020M680269) and National Natural Science Foundation of China (Grant No. 12101023); the second author is supported by National Natural Science Foundation of China (Grant No. 11871103) and the National Key Research and Development Program of China (Grant No. 2020YFA0712900)

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Li, D.D., Zhang, M. & Zhang, X.Y. Limit Theorems for Critical Galton-Watson Processes with Immigration Stopped at Zero. Acta. Math. Sin.-English Ser. 40, 435–450 (2024). https://doi.org/10.1007/s10114-023-1574-3

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  • DOI: https://doi.org/10.1007/s10114-023-1574-3

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