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A critical branching process with immigration in varying environments

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  • Mitov, Kosto V.

Abstract

The paper studies a critical Bienaymé–Galton–Watson branching processes with immigration in varying environments. Assuming that the offspring variance is infinite and the mean number of immigrants is either finite or infinite is proved the asymptotic formulas for the probability for non extinction. The proper limiting distributions under the appropriate normalization are also proved.

Suggested Citation

  • Mitov, Kosto V., 2021. "A critical branching process with immigration in varying environments," Statistics & Probability Letters, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:stapro:v:168:y:2021:i:c:s0167715220302315
    DOI: 10.1016/j.spl.2020.108928
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    References listed on IDEAS

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    1. Mitov, Kosto V. & Pakes, Anthony G. & Yanev, George P., 2003. "Extremes of geometric variables with applications to branching processes," Statistics & Probability Letters, Elsevier, vol. 65(4), pages 379-388, December.
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    Cited by:

    1. Wang, Han & Liao, Haitao & Ma, Xiaobing, 2022. "Stochastic Multi-phase Modeling and Health Assessment for Systems Based on Degradation Branching Processes," Reliability Engineering and System Safety, Elsevier, vol. 222(C).

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