一个G-W分枝过程的特例的相关性质研究
发布时间：2018-09-07 06:44
【摘要】：本文讨论了Galton-Watson过程(后文简称G-W过程)的一个特例的相关问题,这个特例我们可以称为几何分布,这是目前唯一一个可以明确计算出fn(s)的例子。G-W过程是定义在非负整数集上的一类马尔可夫链,该过程有利于研究类似于姓氏消亡的许多问题,在物理学和生物学方面有很多应用。这篇文章主要计算了特例的拟平稳分布,其他情况下的极限定理,以及讨论了fn(s)的收敛速率问题。第一章是绪论部分,这部分介绍了G-W过程的研究背景与意义、研究历史与现状以及本文的主要结论。第二章是预备知识,主要介绍了后文需要用到的定义和性质。第三章是论文的核心部分,介绍了特例的表达式,灭绝概率,比率定理,拟平稳分布,fn(s)的收敛速率等,并计算出了在该模型下对应的具体数值。第四章是总结,对本文的主要结果作一个综合性的总结。
[Abstract]:In this paper, we discuss a special case of Galton-Watson process (G-W process), which we can call geometric distribution. This is the only example that can explicitly calculate the fn (s). G-W process is a class of Markov chains defined on a set of non-negative integers, which is helpful to the study of many problems similar to the extinction of last names. There are many applications in physics and biology. In this paper, we mainly calculate the quasi-stationary distribution of special cases, limit theorems in other cases, and discuss the convergence rate of fn (s). The first chapter is the introduction, which introduces the background and significance of G-W process, the research history and present situation, and the main conclusions of this paper. The second chapter is the preparatory knowledge, mainly introduces the definition and nature that need to be used later. The third chapter is the core part of the paper. The expressions of special cases, extinction probability, ratio theorem, convergence rate of quasi-stationary distribution FN (s) and so on are introduced, and the corresponding numerical values under the model are calculated. The fourth chapter is a summary, a comprehensive summary of the main results of this paper.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.65
本文编号：2227500
[Abstract]:In this paper, we discuss a special case of Galton-Watson process (G-W process), which we can call geometric distribution. This is the only example that can explicitly calculate the fn (s). G-W process is a class of Markov chains defined on a set of non-negative integers, which is helpful to the study of many problems similar to the extinction of last names. There are many applications in physics and biology. In this paper, we mainly calculate the quasi-stationary distribution of special cases, limit theorems in other cases, and discuss the convergence rate of fn (s). The first chapter is the introduction, which introduces the background and significance of G-W process, the research history and present situation, and the main conclusions of this paper. The second chapter is the preparatory knowledge, mainly introduces the definition and nature that need to be used later. The third chapter is the core part of the paper. The expressions of special cases, extinction probability, ratio theorem, convergence rate of quasi-stationary distribution FN (s) and so on are introduced, and the corresponding numerical values under the model are calculated. The fourth chapter is a summary, a comprehensive summary of the main results of this paper.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.65
【参考文献】
相关期刊论文 前4条
1 ;Markov branching processes with immigration-migration and resurrection[J];Science China(Mathematics);2011年05期
2 陈安岳;李俊平;;两参数广义碰撞分枝过程[J];中国科学(A辑:数学);2009年08期
3 付君丽;;Markov链在生命科学中的应用[J];保定学院学报;2008年04期
4 徐群芳;;一类特殊的两性G-W分支过程及其谱半径[J];大学数学;2008年02期
相关硕士学位论文 前3条
1 陈度华;变化环境下受控制的两性G-W分支过程[D];湘潭大学;2011年
2 房镜;分支过程及其应用研究[D];重庆师范大学;2007年
3 王勇;两性分支过程[D];太原理工大学;2003年
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