English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 109948/140897 (78%)
Visitors : 46069702      Online Users : 859
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    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
    Tsou, Chu-Yang
    Keywords: 分支過程
    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
    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

    Files in This Item:

    File Description SizeFormat
    101001.pdf347KbAdobe PDF2100View/Open

    All items in 政大典藏 are protected by copyright, with all rights reserved.

    社群 sharing

    著作權政策宣告 Copyright Announcement
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback