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On deterministic approximation for nearly critical branching processes with dependent immigration

Author

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  • Rahimov, I.
  • Sharipov, S.O.

Abstract

In this paper, we investigate the asymptotic behavior of a triangular array of branching processes with non-stationary immigration. In the nearly critical case, we prove weak convergence of properly normalized and scaled branching processes with immigration to a deterministic function when the immigration process is generated by dependent random variables.

Suggested Citation

  • Rahimov, I. & Sharipov, S.O., 2024. "On deterministic approximation for nearly critical branching processes with dependent immigration," Statistics & Probability Letters, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:stapro:v:208:y:2024:i:c:s0167715223002547
    DOI: 10.1016/j.spl.2023.110031
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    References listed on IDEAS

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    1. Rahimov, I., 2009. "Bootstrap of the offspring mean in the critical process with a non-stationary immigration," Stochastic Processes and their Applications, Elsevier, vol. 119(11), pages 3939-3954, November.
    2. Guo, Hongsong & Zhang, Mei, 2014. "A fluctuation limit theorem for a critical branching process with dependent immigration," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 29-38.
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