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<p>Let (<i>Z</i><sub><i>n</i></sub>) be a supercritical branching process with immigration in a random environment. The small positive values and some lower deviation inequalities for <i>Z</i><sub><i>n</i></sub> are investigated. Based on these results, the central limit theorem of log <i>Z</i><sub><i>n</i></sub> and the Edgeworth expansion are obtained. The study is taken under the assumption that each individual produces 0 offspring with a positive probability.</p>

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Small Positive Values and Limit Theorems for Supercritical Branching Processes with Immigration in Random Environment

  • 期刊论文

  • 发表日期：

    2026年2月15日

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  • Yinxuan Zhao,
  • Mei Zhang

摘要

Let (Zn) be a supercritical branching process with immigration in a random environment. The small positive values and some lower deviation inequalities for Zn are investigated. Based on these results, the central limit theorem of log Zn and the Edgeworth expansion are obtained. The study is taken under the assumption that each individual produces 0 offspring with a positive probability.