請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8442完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳逸昆 (I-Kun Chen) | |
| dc.contributor.author | YU-JUI SU | en |
| dc.contributor.author | 蘇于瑞 | zh_TW |
| dc.date.accessioned | 2021-05-20T00:54:33Z | - |
| dc.date.available | 2020-07-27 | |
| dc.date.available | 2021-05-20T00:54:33Z | - |
| dc.date.copyright | 2020-07-27 | |
| dc.date.issued | 2020 | |
| dc.date.submitted | 2020-07-21 | |
| dc.identifier.citation | [1] Borovkov, A. A., and Mogulskii, A. A. F. (2018). Integro-local limit theorems for compound renewal processes under Cramer’s condition. I. Siberian Mathematical Journal, 59(3), 383-402. [2] Borovkov, A. A., and Mogulskii, A. A. F. (2018). Integro-local limit theorems for compound renewal processes under Cramer’s condition. II. Siberian Mathematical Journal, 59(4), 578-597. [3] Borovkov, A. A. (2013). Large deviation probabilities for sums of independent random variables. In Probability Theory (pp. 239-276). Springer, London. [4] Borovkov, A. A., and Mogulskii, A. A. F. (1996). The second rate function and the asymptotic problems of renewal and hitting the boundary for multi-dimensional random walks. Siberian Mathematical Journal, 37(4), 647-682. [5] Liu, T. P., and Yu, S. H. (2008). Diffusion under gravitational and boundary effects. Bulletin of Institute of Mathematics Academia Sinica, 3(1), 167-210. [6] Serfozo, R. (2009). Basics of applied stochastic processes. Springer Science and Business Media. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8442 | - |
| dc.description.abstract | 研究的是具有散射邊界條件的漂移方程,此模型描述在上半空間裡一團接近真空的氣體。我們的工作得到了當時間趨近無窮的漸近結果。此外,研究了一些與微分方程的結構和邊界條件有關的隨機過程。漂移方程的顯式解是一個更新函數。局部極限定理是我們研究此函數的主要工具。我們問題中它有更多結構,因此,這個漸進結果在不同的時空關係下由第二速率函數的額外屬性所決定。 | zh_TW |
| dc.description.abstract | A transport equation with a diffuse boundary condition is studied for the propagation of a gas near vacuum. Our work reaches an large time asymptotic results. Also, some stochastic processes concerning the structure of the differential equation and the boundary condition were studied. The characteristic method leads to the explicit solution of the transport quation, which is a renewal function. The local limit theorem is our main tool studying this function. When turning to the specific renewal function in our problem, more structures were revealed and the space-time relationship is given by extra properties of the second rate function. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T00:54:33Z (GMT). No. of bitstreams: 1 U0001-1707202007394200.pdf: 1194092 bytes, checksum: e5a9308c9c19bdbce338ca9369d352c0 (MD5) Previous issue date: 2020 | en |
| dc.description.tableofcontents | List of Figures i 1 Introduction 1 1.1 Method of Characteristics, the Renewal Measure . . . . . . . . . . . .3 1.2 Numerical Computation . . . . . . . . . . . . . . . . . . . . . . . . .6 2 Local Limit Theorem 9 2.1 Local Limit Theorem for Sums of Independent Random Vectors . . . 9 2.2 Local Limit Theorem for the Renewal Measure . . . . . . . . . . . . . 11 3 The Second Rate Function 13 3.1 Normal and Moderate Large Deviations . . . . . . . . . . . . . . . . . 15 4 Stochastic Processes 16 References 20 | |
| dc.language.iso | en | |
| dc.title | 複合更新理論應用在散射邊界上 | zh_TW |
| dc.title | An Application of Compound Renewal Theory on a Diffuse Boundary | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 108-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.coadvisor | 黃建豪 (Chien-Hao Huang) | |
| dc.contributor.oralexamcommittee | 黃啟瑞(Chii-Ruey Hwang),郭鴻文(Hung-Wen Kuo) | |
| dc.subject.keyword | 散射邊界條件,隨機漫步,更新理論,再生過程,複合更新過程,大偏差理論,局部極限定理,第二速率函數, | zh_TW |
| dc.subject.keyword | Diffuse Boundary Condition,Random Walks,Renewal Theory,Regenerative Processes,Compound Renewal Processes,Large Deviations,Local Limit Theorem,Second Rate Function, | en |
| dc.relation.page | 20 | |
| dc.identifier.doi | 10.6342/NTU202001584 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2020-07-21 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 應用數學科學研究所 | zh_TW |
| 顯示於系所單位： | 應用數學科學研究所 | |
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|---|---|---|---|
| U0001-1707202007394200.pdf | 1.17 MB | Adobe PDF | 檢視/開啟 |
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