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https://ah.lib.nccu.edu.tw/handle/140.119/136485| 題名: | 非對稱分支隨機漫步的範圍 The Range of Asymmetric Branching Random Walk |
作者: | 紀瑞麟 Chi, Jui-Lin |
貢獻者: | 洪芷漪 Hong, Jyy-I 紀瑞麟 Chi, Jui-Lin |
關鍵詞: | 分支隨機過程 分支過程 隨機漫步 Branching random walk Random walk Galton-Watson process |
日期: | 2021 | 上傳時間: | 4-八月-2021 | 摘要: | 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. |
參考文獻: | [1] John D Biggins. Martingale convergence in the branching random walk. Journal of Applied\nProbability, pages 25–37, 1977.\n[2] John D Biggins. Growth rates in the branching random walk. Zeitschrift für\nWahrscheinlichkeitstheorie und Verwandte Gebiete, pages 17–34, 1979.\n[3] John D Biggins. Uniform convergence of martingales in the branching random walk. The\nAnnals of Probability, pages 137–151, 1992.\n[4] Maury D Bramson. Minimal displacement of branching random walk. Zeitschrift für\nWahrscheinlichkeitstheorie und verwandte Gebiete, pages 89–108, 1978.\n[5] Frederik Michel Dekking and Bernard Host. Limit distributions for minimal displacement\nof branching random walks. Probability theory and related fields, pages 403–426, 1991.\n[6] Karl Grill. The range of simple branching random walk. Statistics & probability letters,\npages 213–218, 1996.\n[7] Theodore Edward Harris et al. The theory of branching processes, volume 6. Springer\nBerlin, 1963.\n[8] Torrey Johnson. On the support of the simple branching random walk. Statistics &\nProbability Letters, pages 107–109, 2014. | 描述: | 碩士 國立政治大學 應用數學系 108751003 |
資料來源: | http://thesis.lib.nccu.edu.tw/record/#G0108751003 | 資料類型: | thesis |
| Appears in Collections: | 學位論文 |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| 100301.pdf | 486.25 kB | Adobe PDF2 | View/Open |
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