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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/146299
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/146299


    Title: 爆炸性折扣分支隨機漫步的位置分佈
    The limiting distribution of the position in explosive discounted branching random walks
    Authors: 鄒礎揚
    Tsou, Chu-Yang
    Contributors: 洪芷漪
    Hong, Jyy-I
    鄒礎揚
    Tsou, Chu-Yang
    Keywords: 分支過程
    爆炸型
    溯祖問題
    分支隨機漫步
    折扣分支隨 機漫步
    Branching Process
    Explosive Case
    Colascence Problem
    Branching Random Wark
    Discounted Branching Random Walk
    Date: 2023
    Issue Date: 2023-08-02 13:02:26 (UTC+8)
    Abstract: 在 2013 年,Athreya 和 Hong 指出,在後代子孫數目期望值大於一的分 支隨機漫步中,當 n 趨近於無窮大時,第 n 代個體位置的比例分配會收斂到 伯努利分配。同時,如果我們隨機在第 n 代中隨機挑選一個個體,在 n 越來 越大時,其位置的分配會收斂到標準常態分配。
    在這篇論文中,我們將考慮爆炸性折扣分支隨機漫步,研究第 n 代個 體的位置比例分配與任選之單一個體的位置分配在 n 趨近無窮大時的漸近 行為,並分別得到其收斂至伯努利分配與標準常態分配的結果。
    In 2013, Athreya and Hong showed that, in the supercritical and explosive regular branching random walk, the empirical distribution of the positions in the nth generation converges to a Bernoulli distribution, and the position of any randomly chosen individual in the nth generation converges to a normal distribution as n → ∞.
    In this thesis, we consider the explosive discounted branching random walk, investigate the asymptotic behaviors of the positions of the individuals in the nth generation as n → ∞, and obtain their convergence in distribution.
    Reference: [1] Krishna B Athreya, Peter E Ney, and PE Ney. Branching processes. Courier Corporation, 2004.
    [2] P. L. Davies. The simple branching process: a note on convergence when the mean is infinite. Journal of Applied Probability, 15(3):466–480, 1978.
    [3] KB Athreya. Coalescence in the recent past in rapidly growing populations. Stochastic Processes and their Applications, 122(11):3757–3766, 2012.
    [4] Jui-Lin Chi and Jyy-I Hong. The range of asymmetric branching random walk. Statistics & Probability Letters, 193:109705, 2023.
    [5] KB Athreya. Branching random walks. The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, pages 337–349, 2010.
    [6] Krishna B Athreya and Jyy-I Hong. An application of the coalescence theory to branching random walks. Journal of Applied Probability, 50(3):893–899, 2013.
    Description: 碩士
    國立政治大學
    應用數學系
    109751010
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0109751010
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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