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https://nccur.lib.nccu.edu.tw/handle/140.119/136485
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| Title: | 非對稱分支隨機漫步的範圍
The Range of Asymmetric Branching Random Walk |
| Authors: | 紀瑞麟
Chi, Jui-Lin |
| Contributors: | 洪芷漪
Hong, Jyy-I
紀瑞麟
Chi, Jui-Lin |
| Keywords: | 分支隨機過程
分支過程
隨機漫步
Branching random walk
Random walk
Galton-Watson process |
| Date: | 2021 |
| Issue Date: | 2021-08-04 15:40:12 (UTC+8) |
| Abstract: | 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. |
| Reference: | [1] John D Biggins. Martingale convergence in the branching random walk. Journal of Applied
Probability, pages 25–37, 1977.
[2] John D Biggins. Growth rates in the branching random walk. Zeitschrift für
Wahrscheinlichkeitstheorie und Verwandte Gebiete, pages 17–34, 1979.
[3] John D Biggins. Uniform convergence of martingales in the branching random walk. The
Annals of Probability, pages 137–151, 1992.
[4] Maury D Bramson. Minimal displacement of branching random walk. Zeitschrift für
Wahrscheinlichkeitstheorie und verwandte Gebiete, pages 89–108, 1978.
[5] Frederik Michel Dekking and Bernard Host. Limit distributions for minimal displacement
of branching random walks. Probability theory and related fields, pages 403–426, 1991.
[6] Karl Grill. The range of simple branching random walk. Statistics & probability letters,
pages 213–218, 1996.
[7] Theodore Edward Harris et al. The theory of branching processes, volume 6. Springer
Berlin, 1963.
[8] Torrey Johnson. On the support of the simple branching random walk. Statistics &
Probability Letters, pages 107–109, 2014. |
| Description: | 碩士
國立政治大學
應用數學系
108751003 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0108751003 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU202100827 |
| Appears in Collections: | [應用數學系] 學位論文
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Files in This Item:
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Size | Format | |
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| 100301.pdf | | 486Kb | Adobe PDF2 | 83 | View/Open |
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