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| 研究生： |
紀瑞麟 Chi, Jui-Lin |
|---|---|
| 論文名稱： |
非對稱分支隨機漫步的範圍 The Range of Asymmetric Branching Random Walk |
| 指導教授： |
洪芷漪
Hong, Jyy-I |
| 口試委員: |
陳隆奇
Chen, Lung-Chi 陳美如 Chen, May-Ru 洪芷漪 Hong, Jyy-I |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2021 |
| 畢業學年度： | 109 |
| 語文別： | 中文 |
| 論文頁數： | 29 |
| 中文關鍵詞： | 分支隨機過程 、分支過程 、隨機漫步 |
| 外文關鍵詞： | Branching random walk, Random walk, Galton-Watson process |
| DOI URL： | http://doi.org/10.6814/NCCU202100827 |
| 相關次數： | 點閱：84 下載：56 |
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考慮一個分支過程且族群中的每個個體在出生時皆在實數線上移動, 作一非對稱的隨機漫步, 並記錄每一個個體的位置。︀ 在本篇論文中, 我們證明了當時間趨近於無限大時,實數線上有個體佔據的位置將會是一個區間。︀
We consider a Galton-Watson branching process in which each individual performs an asymmetric random walk on the real line and record the positions of all individuals in each generation. In this thesis, we show that the set of occupied positions is eventually an interval.
致謝ii
中文摘要iii
Abstract iv
Contents v
List of Figures vi
1 Preliminary 1
1.1 Introduction 1
1.2 Galton-Watson branching process 2
1.2.1 Model setting 2
1.2.2 Classial results 3
1.3 Branching random walk 4
1.31 Model setting 4
2 Properties on local population 6
2.1 Local extinction probabilities 6
2.2 Population at extreme points 13
3 Main results on occupied positions 18
3.1 Main theorems 18
3.2 Proofs of main theorems 18
Bibliography 29
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