| dc.contributor.advisor | 洪芷漪 | zh_TW |
| dc.contributor.advisor | Hong, Jyy-I | en_US |
| dc.contributor.author (Authors) | 鄒礎揚 | zh_TW |
| dc.contributor.author (Authors) | Tsou, Chu-Yang | en_US |
| dc.creator (作者) | 鄒礎揚 | zh_TW |
| dc.creator (作者) | Tsou, Chu-Yang | en_US |
| dc.date (日期) | 2023 | en_US |
| dc.date.accessioned | 2-Aug-2023 13:02:26 (UTC+8) | - |
| dc.date.available | 2-Aug-2023 13:02:26 (UTC+8) | - |
| dc.date.issued (上傳時間) | 2-Aug-2023 13:02:26 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0109751010 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/146299 | - |
| 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) | 109751010 | zh_TW |
| dc.description.abstract (摘要) | 在 2013 年，Athreya 和 Hong 指出，在後代子孫數目期望值大於一的分 支隨機漫步中，當 n 趨近於無窮大時，第 n 代個體位置的比例分配會收斂到 伯努利分配。同時，如果我們隨機在第 n 代中隨機挑選一個個體，在 n 越來 越大時，其位置的分配會收斂到標準常態分配。在這篇論文中，我們將考慮爆炸性折扣分支隨機漫步，研究第 n 代個 體的位置比例分配與任選之單一個體的位置分配在 n 趨近無窮大時的漸近 行為，並分別得到其收斂至伯努利分配與標準常態分配的結果。 | zh_TW |
| dc.description.abstract (摘要) | In 2013, Athreya and Hong showed that, in the supercritical and explosive regular branching random walk, the empirical distribution of the positions in the nth generation converges to a Bernoulli distribution, and the position of any randomly chosen individual in the nth generation converges to a normal distribution as n → ∞.In this thesis, we consider the explosive discounted branching random walk, investigate the asymptotic behaviors of the positions of the individuals in the nth generation as n → ∞, and obtain their convergence in distribution. | en_US |
| dc.description.tableofcontents | 中文摘要 iAbstract iiContents iii1 Introduction 11.1 Galton-Watsonbranchingprocess ........................ 11.2 TheCoalescenceproblem............................. 41.3 BranchingRandomWalk............................. 72 The Positions in Explosive Discounted Branching Random Walks 102.1 Themainresultsinthepositionproblems .................... 10 2.2 TheProofofTheorem2.1.1 11 2.3 TheProofofTheorem2.1.2 143 Conclusion 21References 23 | zh_TW |
| dc.format.extent | 355813 bytes | - |
| dc.format.mimetype | application/pdf | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0109751010 | en_US |
| dc.subject (關鍵詞) | 分支過程 | zh_TW |
| dc.subject (關鍵詞) | 爆炸型 | zh_TW |
| dc.subject (關鍵詞) | 溯祖問題 | zh_TW |
| dc.subject (關鍵詞) | 分支隨機漫步 | zh_TW |
| dc.subject (關鍵詞) | 折扣分支隨 機漫步 | zh_TW |
| dc.subject (關鍵詞) | Branching Process | en_US |
| dc.subject (關鍵詞) | Explosive Case | en_US |
| dc.subject (關鍵詞) | Colascence Problem | en_US |
| dc.subject (關鍵詞) | Branching Random Wark | en_US |
| dc.subject (關鍵詞) | Discounted Branching Random Walk | en_US |
| dc.title (題名) | 爆炸性折扣分支隨機漫步的位置分佈 | zh_TW |
| dc.title (題名) | The limiting distribution of the position in explosive discounted 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] P. L. Davies. The simple branching process: a note on convergence when the mean is infinite. Journal of Applied Probability, 15(3):466–480, 1978.[3] KB Athreya. Coalescence in the recent past in rapidly growing populations. Stochastic Processes and their Applications, 122(11):3757–3766, 2012.[4] Jui-Lin Chi and Jyy-I Hong. The range of asymmetric branching random walk. Statistics & Probability Letters, 193:109705, 2023.[5] KB Athreya. Branching random walks. The Legacy of Alladi Ramakrishnan in the Mathematical Sciences, pages 337–349, 2010.[6] Krishna B Athreya and Jyy-I Hong. An application of the coalescence theory to branching random walks. Journal of Applied Probability, 50(3):893–899, 2013. | zh_TW |
