| dc.contributor.advisor | 洪芷漪 | zh_TW |
| dc.contributor.advisor | Hong, Jyy-I | en_US |
| dc.contributor.author (Authors) | 紀瑞麟 | zh_TW |
| dc.contributor.author (Authors) | Chi, Jui-Lin | en_US |
| dc.creator (作者) | 紀瑞麟 | zh_TW |
| dc.creator (作者) | Chi, Jui-Lin | en_US |
| dc.date (日期) | 2021 | en_US |
| dc.date.accessioned | 4-Aug-2021 15:40:12 (UTC+8) | - |
| dc.date.available | 4-Aug-2021 15:40:12 (UTC+8) | - |
| dc.date.issued (上傳時間) | 4-Aug-2021 15:40:12 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0108751003 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/136485 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學系 | zh_TW |
| dc.description (描述) | 108751003 | zh_TW |
| dc.description.abstract (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。︀ | zh_TW |
| dc.description.abstract (摘要) | 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. | en_US |
| dc.description.tableofcontents | 致謝ii中文摘要iiiAbstract ivContents vList of Figures vi1 Preliminary 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Galton-Watson branching process . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Model setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.2 Classial results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Branching random walk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.1 Model setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Properties on local population 62.1 Local extinction probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Population at extreme points . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Main results on occupied positions 183.1 Main theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 Proofs of main theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Bibliography 29 | zh_TW |
| dc.format.extent | 497918 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0108751003 | en_US |
| dc.subject (關鍵詞) | 分支隨機過程 | zh_TW |
| dc.subject (關鍵詞) | 分支過程 | zh_TW |
| dc.subject (關鍵詞) | 隨機漫步 | zh_TW |
| dc.subject (關鍵詞) | Branching random walk | en_US |
| dc.subject (關鍵詞) | Random walk | en_US |
| dc.subject (關鍵詞) | Galton-Watson process | en_US |
| dc.title (題名) | 非對稱分支隨機漫步的範圍 | zh_TW |
| dc.title (題名) | The Range of Asymmetric Branching Random Walk | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | [1] John D Biggins. Martingale convergence in the branching random walk. Journal of AppliedProbability, pages 25–37, 1977.[2] John D Biggins. Growth rates in the branching random walk. Zeitschrift fürWahrscheinlichkeitstheorie und Verwandte Gebiete, pages 17–34, 1979.[3] John D Biggins. Uniform convergence of martingales in the branching random walk. TheAnnals of Probability, pages 137–151, 1992.[4] Maury D Bramson. Minimal displacement of branching random walk. Zeitschrift fürWahrscheinlichkeitstheorie und verwandte Gebiete, pages 89–108, 1978.[5] Frederik Michel Dekking and Bernard Host. Limit distributions for minimal displacementof 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. SpringerBerlin, 1963.[8] Torrey Johnson. On the support of the simple branching random walk. Statistics &Probability Letters, pages 107–109, 2014. | zh_TW |
| dc.identifier.doi (DOI) | 10.6814/NCCU202100827 | en_US |
