随机环境中伴有移民且配对依赖人口数的两性分枝过程

作者:宋明珠 ;向亚云 刊名:工程数学学报 上传者:陈鸿英[1]

【摘要】本文首先介绍了两性分枝过程的发展情况,在前人研究的基础上,本文建立了更符合自然界两性生物繁衍规律的模型,配对依赖当前人口数且伴有移民的两性分枝过程.利用上可加函数的性质,得到了平均增长率的极限.在一定的条件,推导出此过程以概率1灭绝的一个充要条件,进而推广了前人的研究成果.

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Feb. 2018 CHINESE JOURNAL OF ENGINEERING MATHEMATICS Vol. 35 No. 1 doi: 10.3969/j.issn.1005-3085.2018.01.011 Article ID: 1005-3085(2018)01-0110-13 Limiting Behavior of the Bisexual Galton-Watson Branching Process with Immigration and Population-size-dependent Mating in Random Environments∗ SONG Ming-zhu, XIANG Ya-yun (Department of Mathematics and Computer Science, Tongling University, Tongling 244000) Abstract: Firstly, this paper introduces the development of bisexual Galton-Watson branching process. On the basis of past achievements, a model with population size dependent mating and immigration (BIPSDM) is established in random environments, that is more conform to the fact about bisexual biological reproduction. Then, applying some classical results on superadditive functions, the limit of mean growth rate per mating unit is obtained. Through discussing extinct probability of BIPSDM, a necessary and sufficient condition for BIPSDM to become extinct with probability one was found under certain conditions. Some properties known are enlarged in this article. Keywords: Galton-Watson branching process; bisexual Galton-Watson branching process; immigration; population size dependent mating; growth rate; extinction proba- bility Classification: AMS(2010) 60F37; 60J80 CLC number: O211.65 Document code: A 1 Introduction Daley[1] introduced the bisexual Galton-Watson branching process as a two-type branching model {(F ∗n ,M∗n), n = 1, 2, · · · } defined recursively Z∗0 = N, (F ∗ n+

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