一個G-W分枝過程的特例的相關性質研究
發(fā)布時間：2018-09-07 06:44
【摘要】：本文討論了Galton-Watson過程(后文簡稱G-W過程)的一個特例的相關問題,這個特例我們可以稱為幾何分布,這是目前唯一一個可以明確計算出fn(s)的例子。G-W過程是定義在非負整數集上的一類馬爾可夫鏈,該過程有利于研究類似于姓氏消亡的許多問題,在物理學和生物學方面有很多應用。這篇文章主要計算了特例的擬平穩(wěn)分布,其他情況下的極限定理,以及討論了fn(s)的收斂速率問題。第一章是緒論部分,這部分介紹了G-W過程的研究背景與意義、研究歷史與現狀以及本文的主要結論。第二章是預備知識,主要介紹了后文需要用到的定義和性質。第三章是論文的核心部分,介紹了特例的表達式,滅絕概率,比率定理,擬平穩(wěn)分布,fn(s)的收斂速率等,并計算出了在該模型下對應的具體數值。第四章是總結,對本文的主要結果作一個綜合性的總結。
[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.
【學位授予單位】：湘潭大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O211.65
本文編號：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.
【學位授予單位】：湘潭大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O211.65
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