Theory of Probability &Its Applications, Volume 67, Issue 2, Page 310-317, August 2022.
The paper continues the author's long-term studies on extremes of random particle scores in branching processes. It is assumed that multiplication of particles is described by an immortal supercritical discrete-time branching process, the particle scores are dependent due to general heredity, and this dependence is a function of the degree of their relationship. The case of heavy-tail distributions of scores is considered. The max-linear model for scores formation is used. We evaluate the limit probabilities of the current generation superiority to the previous generation or all previous generations, in terms of maxima of particle scores.

中文翻译：

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具有最大线性遗传的超临界分支过程中随机粒子分数的多元极值的记录和增加

概率论及其应用，第 67 卷，第 2 期，第 310-317 页，2022
年 8 月。本文延续了作者对分支过程中随机粒子分数极值的长期研究。假设粒子的倍增是由一个不朽的超临界离散时间分支过程描述的，粒子分数由于一般遗传而依赖，并且这种依赖是它们关系程度的函数。考虑分数的重尾分布的情况。使用分数形成的最大线性模型。我们根据粒子分数的最大值评估当前一代优于上一代或所有前几代的极限概率。