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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2020, Vol. 37 ›› Issue (3): 314-324.doi: 10.3969/j.issn.1005-3085.2020.03.006

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一类两性分枝过程条件均值增长率的极限性质

宋明珠, 邵  静   

  1. 铜陵学院数学与计算机学院，安徽 铜陵 244061
  • 收稿日期:2018-01-04 接受日期:2018-09-12 出版日期:2020-06-15 发布日期:2020-08-15
  • 基金资助:
    安徽省高校自然科学研究重点项目(KJ2019A0700)；国家级大学生创新创业训练计划立项项目(201910383001)；安徽省大学生创新创业训练计划立项项目(201810383173).

The Limit Properties of the Conditional Mean Growth Rate for a Kind of Bisexual Branching Process

SONG Ming-zhu, SHAO Jing   

  1. School of Mathematics and Computer Science, Tongling University, Tongling, Anhui 244061
  • Received:2018-01-04 Accepted:2018-09-12 Online:2020-06-15 Published:2020-08-15
  • Supported by:
    The Key University Science Research Project of Anhui Province (KJ2019A0700); the National Undergraduate Training Programs for Innovation and Entrepreneurship (201910383001); the Anhui Province Undergraduate Training Programs for Innovation and Entrepreneurship (201810383173).

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摘要： 本文主要研究随机环境中配对依赖人口数两性 Galton-Watson 分枝过程的条件均值增长率的极限性质．利用上可加函数的性质，得到配对单元平均增长率的极限性质和该过程条件均值的上界和下界．文中给出了关于过程条件均值增长率的两个序列，利用配对单元平均增长率的性质，获得了这两个序列的极限性质．随机环境中配对依赖人口数两性分枝过程比较复杂，本文的结论推广了现有的研究成果．

关键词: 两性分枝过程, 配对单元平均增长率, 条件均值增长率, 极限性质

Abstract: In this paper, we study the limiting behavior of the conditional mean growth rate for the bisexual Galton-Watson branching process with population-size-dependent mating in random environments. Using the properties of superadditive functions, we obtain the limit properties of the mean growth rate per mating unit, and the upper bound and lower bound of the conditional mean. We introduce two sequences on the conditional mean growth rate, whose limit properties are established by utilizing the properties of the mean growth rate per mating unit. The bisexual Galton-Watson branching process with population-size-dependent mating is rather complex, so our results improve and extend the related known works in the literature.

Key words: bisexual branching process, the mean growth rate per mating unit, conditional mean growth rate, limit properties

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