| dc.contributor.advisor | 洪芷漪 | zh_TW |
| dc.contributor.advisor | Hong, Jyy-I | en_US |
| dc.contributor.author (Authors) | 王柏崴 | zh_TW |
| dc.contributor.author (Authors) | Wang, Po-Wei | en_US |
| dc.creator (作者) | 王柏崴 | zh_TW |
| dc.creator (作者) | Wang, Po-Wei | en_US |
| dc.date (日期) | 2025 | en_US |
| dc.date.accessioned | 1-Jul-2025 14:40:55 (UTC+8) | - |
| dc.date.available | 1-Jul-2025 14:40:55 (UTC+8) | - |
| dc.date.issued (上傳時間) | 1-Jul-2025 14:40:55 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0111751009 | en_US |
| dc.identifier.uri (URI) | https://nccur.lib.nccu.edu.tw/handle/140.119/157751 | - |
| 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) | 111751009 | zh_TW |
| dc.description.abstract (摘要) | 我們研究一種分支過程, 其中每個個體沿著實數線進行非對稱隨機漫步。在本篇論文中, 我們探討在每個局部位置的族群的一些性質, 包括其期望值、變異數及其他相關性質。我們同時也探討一些由這些在局部位置上的族群數目所衍生出的平賭過程。 | zh_TW |
| dc.description.abstract (摘要) | We study a Galton-Watson branching process in which each individual follows an asymmetric random walk along the real line. In this thesis, we study the properties of the local population including the expectation, variance and other second-order properties and introduce some associated martingales. | en_US |
| dc.description.tableofcontents | 致謝 i
中文摘要 ii
Abstract iii
Contents iv
1 Introduction 1
1.1 Background of branching processes 1
1.1.1 Galton-Watson branching processes 2
1.1.2 The probability of extinction and limit theorems 2
1.2 Branching random walks 4
2 Local population in asymmetric branching random walks 6
2.1 The expectation of λ(n, k) 7
2.2 The second-order properties of λ(n, k) 12
2.3 Martingales related to local population λ(n, k) 24
2.3.1 The case of p<q 24
2.3.2 The case of p>q 32
3 Conclusions and Open Problems 35
Reference 36 | zh_TW |
| dc.format.extent | 440909 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0111751009 | en_US |
| dc.subject (關鍵詞) | 分支過程 | zh_TW |
| dc.subject (關鍵詞) | 分支隨機漫步 | zh_TW |
| dc.subject (關鍵詞) | 平賭 | zh_TW |
| dc.subject (關鍵詞) | Galton-Watson Branching Process | en_US |
| dc.subject (關鍵詞) | Branching Random Walk | en_US |
| dc.subject (關鍵詞) | Martingale | en_US |
| dc.title (題名) | 非對稱分支隨機漫步中局部族群分佈之探討 | zh_TW |
| dc.title (題名) | Local Populations in Asymmetric Branching Random Walks | en_US |
| dc.type (資料類型) | thesis | en_US |
| dc.relation.reference (參考文獻) | [1] Krishna B Athreya, Peter E Ney, and PE Ney. Branching processes. Courier Corporation, 2004.
[2] Jui-Lin Chi and Jyy-I Hong. The range of asymmetric branching random walk. Statistics Probability Letters, 193:109705, 2023.
[3] Peter L. Davies. The simple branching process: a note on convergence when the mean is infinite. Journal of Applied Probability, 15(3):466–480, 1978.
[4] Karl Grill. The range of simple branching random walk. Statistics & probability letters, 26(3):213–218, 1996. | zh_TW |
