本文選題：分支過程 + 分支樹�。� 參考：《南京大學》2017年碩士論文

【摘要】：本文對分支過程的基本理論進行了介紹,主要介紹分支過程的定義、概率母函數(shù),生成后代數(shù)量的均值或均值矩陣與滅絕概率之間的關(guān)系,判斷分支過程是否可約的方法等。在兩物種分支過程中,我們詳細介紹了分支樹的構(gòu)造,分支樹與隨機游走間的聯(lián)系,以及與兩物種分支樹相對應的由變異節(jié)點組成的分支樹,并說明了兩者之間的關(guān)聯(lián)。本文探究在最終必然滅絕的臨界或是下臨界分支過程中,各種類的粒子總數(shù)的分布。在兩物種情形下,對可約的分支過程,各種類的粒子總數(shù)的概率分布已有相應的研究成果。結(jié)合分支樹的相關(guān)理論性質(zhì),本文給出在不可約條件下各種類的粒子總數(shù)的概率分布。然后類比單物種分支過程中樹葉的分布,本文給出在兩物種過程中類似的分布。最后,同樣類比單物種分支過程中后代數(shù)不多于k個的粒子個數(shù)的分布性質(zhì),本文給出在兩物種過程中后代數(shù)不多于(k1,k2)的粒子個數(shù)的分布性質(zhì)。
[Abstract]:In this paper, the basic theory of branching process is introduced, including the definition of branching process, the probability generating function, the relationship between the mean value or mean matrix of generating the number of offspring and the extinction probability, and the method of judging whether the branching process is reducible or not. In the process of two species branching, we introduce in detail the structure of branch tree, the relation between branch tree and random walk, and the branch tree which is composed of mutation nodes corresponding to branch tree of two species, and explain the relation between them. This paper explores the distribution of the total number of particles in the critical or lower critical branching processes of eventual extinction. In the case of two species, the probability distribution of the total number of particles in the reducible branching process has been studied. In this paper, the probability distribution of the total number of particles of various classes under irreducible conditions is given in combination with the related theoretical properties of branching trees. Then the distribution of leaves in the process of single species branching is compared, and the similar distribution in the process of two species is given in this paper. Finally, similar to the distribution properties of the number of particles with no more than k offspring in the process of single species branching, this paper gives the distribution properties of the number of particles not more than (k1k2) in the process of two species.
【學位授予單位】：南京大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O211.65

【參考文獻】

相關(guān)期刊論文 前1條

1 Hua Ming WANG;;On Total Progeny of Multitype Galton-Watson Process and the First Passage Time of Random Walk on Lattice[J];Acta Mathematica Sinica(English Series);2014年12期

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本文編號：2095637