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Limit Theorems for a Strongly Supercritical Branching Process with Immigration in Random Environment

Author

Listed:
  • Afanasyev Valeriy Ivanovich

    (Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkin St., Moscow, 119991, Russia)

Abstract

We consider a strongly supercritical branching process in random environment with immigration stopped at a distant time 𝑛. The offspring reproduction law in each generation is assumed to be geometric. The process is considered under the condition of its extinction after time 𝑛. Two limit theorems for this process are proved: the first one is for the time interval from 0 till 𝑛, and the second one is for the time interval from 𝑛 till +∞+\infty.

Suggested Citation

  • Afanasyev Valeriy Ivanovich, 2021. "Limit Theorems for a Strongly Supercritical Branching Process with Immigration in Random Environment," Stochastics and Quality Control, De Gruyter, vol. 36(2), pages 129-143, December.
  • Handle: RePEc:bpj:ecqcon:v:36:y:2021:i:2:p:129-143:n:6
    DOI: 10.1515/eqc-2021-0036
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