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<p>We study supercritical age-structured branching models starting from a single particle with a random lifetime, where the reproduction law depends on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. A necessary and sufficient condition is provided for the convergence of the Malthusian normalized random measures. The Malthusian type limit theory in a functional form can be strengthened to hold with probability one under some “<i>L</i> log <i>L</i>” conditions. We further prove a central limit theory with a random normalization factor.</p>

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Limit Theorems for Supercritical Remaining-lifetime Age-structured Branching Processes

  • 期刊论文

  • 发表日期：

    2026年1月15日

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  • Ziling Cheng

摘要

We study supercritical age-structured branching models starting from a single particle with a random lifetime, where the reproduction law depends on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. A necessary and sufficient condition is provided for the convergence of the Malthusian normalized random measures. The Malthusian type limit theory in a functional form can be strengthened to hold with probability one under some “L log L” conditions. We further prove a central limit theory with a random normalization factor.