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Please use this identifier to cite or link to this item:
https://nccur.lib.nccu.edu.tw/handle/140.119/146299
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| 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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