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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/42989Full metadata record
| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 姜祖恕(Tzuu-Shuh Chiang) | |
| dc.contributor.author | Wan-Chu Chien | en |
| dc.contributor.author | 簡婉竹 | zh_TW |
| dc.date.accessioned | 2021-06-15T01:31:45Z | - |
| dc.date.available | 2009-07-30 | |
| dc.date.copyright | 2009-07-30 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-07-20 | |
| dc.identifier.citation | [1]R. Z. Khasminskii and G. Yin, On transition densities of singular perturbed diffusion with fast and slow components, SIAM Journal on Applied Mathematics, Vol. 56, No. 6 (Dec., 1996), pp. 1794-1819.
[2]R. Z. Khasminskii and G. Yin, Asymptotic series for singular perturbed Kolmogorov-Fokker-Planck equations, SIAM Journal on Applied Mathematics, Vol. 56, No. 6 (Dec., 1996), pp. 1766-1793. [3]D. G Aronson, Non-negative solutions of linear parabolic equations, Ann, Scuola Norm. Sup. Pisa C1. Sci.,XXII (1968), pp.607-694. [4]O. A Ladyahenskaia, V. A. Solonnikov, and N.Ural'tseva, Linear and quasilinear equations of parabolic type, American Mathematical Society, Providence, RI, 1968. [5]A. Bensoussan, Perturbation methods in optimal control, J. Wiley, Chichester, 1988. [6]A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, NJ, 1964. [7]R. Z. Khasminskii, Stochastic stability of differential equations, Sijthoff & Noordhoff, Groningen, the Netherlands, 1980. [8]Bernt Øksendal, Stochastic Differential Equations: An Introduction with Applications, 6th ed. 2003 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/42989 | - |
| dc.description.abstract | 這篇文章是考慮有二階擾動影響的擴散過程，並且利用漸近展開的方法來求滿足向前方程式的轉移密度函數，希望可以用一個一般項和兩個邊界項(分別是ε階層和ε^2階層)來描述解的行為。 | zh_TW |
| dc.description.abstract | This article introduces the diffusion process with second-order perturbations and match the asymptotic expansions for the solutions to forward equations. And we separate the solution by a regular term and two boundary layer terms to describe the behavior of solution. (ε-layer andε^2-layer). | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T01:31:45Z (GMT). No. of bitstreams: 1 ntu-98-R96221022-1.pdf: 577638 bytes, checksum: a8e9ff3d2d84959c660188941ba59db1 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | Contents
口試委員會審定書. . . . . . . . . . . . . . . . . . . . . . . i 誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii 中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . iii 英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . iii 1 Introduction 1 2 Basic assumptions and denitions 8 3 The regular expansions 13 3.1 The zero-order regular terms . . . . . . . . . . . . . . 13 3.2 The first-order regular terms . . . . . . . . . . . . . .17 3.3 The ith-order regular terms . . . . . . . . . . . . . . . 19 4 The boundary layer expansions 21 4.1 The second boundary layer terms . . . . . . . . . . . . . 22 4.2 The first boundary layer terms . . . . . . . . . . . . . 25 4.2.1 The zero-order of first boundary layer terms . . . . .. 25 4.2.2 The first-order of first boundary layer terms . . . . . 27 4.2.3 The ith-order of first boundary layer terms . . .. . . 29 5 Choose the initial condition 30 5.1 Special property of Green's function and the solutions . 30 5.2 Choose the initial conditions of the zero-order . . . . . 34 5.3 Choose the initial conditions of the first-order . . .. . 36 6 The error term 39 References 46 | |
| dc.language.iso | en | |
| dc.subject | 向前方程式 | zh_TW |
| dc.subject | 二階擾動 | zh_TW |
| dc.subject | forward equation | en |
| dc.subject | second-order perturbations | en |
| dc.title | 二階擾動擴散過程中轉換密度的漸近展開 | zh_TW |
| dc.title | Asymptotic Expansions to Transition Densities of Second-Order Perturbed Diffusion Process | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 許順吉(Shuenn-Jhi Sheu),韓傳祥(Chuan-Hsiang Han) | |
| dc.subject.keyword | 二階擾動,向前方程式, | zh_TW |
| dc.subject.keyword | second-order perturbations,forward equation, | en |
| dc.relation.page | 46 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-07-20 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| Appears in Collections: | 數學系 | |
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| File | Size | Format | |
|---|---|---|---|
| ntu-98-1.pdf Restricted Access | 564.1 kB | Adobe PDF |
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