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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 姜祖恕 | |
| dc.contributor.author | Sheng-Yu Huang | en |
| dc.contributor.author | 黃勝郁 | zh_TW |
| dc.date.accessioned | 2021-06-13T01:44:28Z | - |
| dc.date.available | 2007-07-18 | |
| dc.date.copyright | 2007-07-18 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-11 | |
| dc.identifier.citation | [1]Applebaum,David.(2005)L′evy processes and stochastic calculus. University Press, Cambridge.
[2]Bass,RichardF.(2003)Stochastic differential equations driven by symmetric stable processes.Seminaire de Probability′es,Springer,Berlin,XXXVI,pp.302-313. [3]Bass,Richard.F.K.Burdzy,and Z.-Q.Chen.(2004) Stochastic differential equations driven by stable processes for which pathwise uniqueness fails,Stoch.Proc.&their Applic.vol.111,pp.1-15. [4]Billingsley,Patrick.(1999) Convergence of Probability Measures.JohnWiley&Sons Inc,2nded. [5]D.W.Stroock.(1975) Diffusion processes associated with L′evy generators. Z.f.Wahrscheinlichkeitstheorie vol.32,pp.209-244. [6]I.Karatzas,S.E.Shreve.(1999)Brownian Motionand Stochastic Calculus.Springer VerlagNewYorkInc,2nded. [7]IkedaI.,WatanabeS.(1981)Stochastic differential equations and Diffsion processes. North-Holland,Amsterdam. [8]Komatsu,T.(1982) On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations of jumptype.Proc.Japan Acad.Ser.AMath.Sci. vol.58.pp.353-356. [9]Nakao,A.(1972) On the pathwiseuniqueness of solutions of one-dimensionalstochastic differential equations.OsakaJ.Math.vol.9pp.513-518. [10]Protter,P.(1990) Stochastic integration and differential equations. Springer.NewYork. [11]Rong Situ.(2005) Theroy of stochastic differential equations with jumps and applications.Springer. [12]Sato,K.I.(1999)L′evy processes and infinitely divisible distributions.University Press,Cambridge. [13]Shizan Fangand Tusheng Zhang.(2005)A study of a class of stochastic differential equations with non-Lipschitzian coeffcients.Probability Theory and Related Fields, vol.132,pp.356-390. [14]T.YamadaandS.Watanabe.(1971)On the uniqueness of solutions of stochastic differential equations.J.Math.,vol.9,pp155-167. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/30220 | - |
| dc.description.abstract | 我們在這篇論文主要探討的是Levy
擾動型隨機微分方程解的存在與唯一性的關係。我們更專注 在非Lipshcitz 條件下其解路徑唯一性的條件。其後介紹及比較近來有關路徑惟一在隨機微分方程相於對稱穩定過程的研究。 | zh_TW |
| dc.description.abstract | In this paper, we devote our attention to
the relation of existence and uniqueness of stochastic differential equations with L'evy noise. Especially, we shall be concerned with the pathwise uniqueness of SDE with L'evy noises under non-Lipschitzian coefficients. We also describe, do and compare some of the resent work on pathwise uniqueness on stochastic differential equations with symmetric alpha-stable process, 1alpha<2. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T01:44:28Z (GMT). No. of bitstreams: 1 ntu-96-R94221039-1.pdf: 462590 bytes, checksum: f873d9cd1d383ff1154272528f5228f6 (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | 謝辭 ii
中文摘要 iii Abstract iv 1 Introduction 1 2 Levy Processes and its Properties 4 2.1 Definition and Characteristic of L′evy process........ . . . . . . . . . 4 2.2 Analytic view of Levyprocesses.................... . . . . 7 3 Stochastic integration and Itふo’s formula 12 3.1 Stochastic integrals with respect to compensated Poisson processes....12 3.2 Ito’s formula for L′evy diffusion........................ 14 4 SDE with L′evy noise 16 4.1 Definition of the SDE with L′evy noise................. . . . 16 4.2 Existence and uniqueness.......................... . . 17 5 The Coeffcients of the SDE with L′evy Noise 24 5.1 Life time of SDE................................24 5.2 Non Lipschitz Coeffcients.......................... . 28 5.2.1 Some studies on pathwise uniqueness............... . . 33 | |
| dc.language.iso | en | |
| dc.subject | pathwise uniqueness | zh_TW |
| dc.subject | Levy過程 | zh_TW |
| dc.subject | Levy型隨機微分方程 | zh_TW |
| dc.subject | Levy process | en |
| dc.subject | SDE driven by Levy process | en |
| dc.subject | pathwise uniqueness | en |
| dc.title | 在非 Lipschitz係數條件及Levy noise 下隨機微分方程解存在性及唯一性 | zh_TW |
| dc.title | On uniqueness and existence of stochastic differential equations with
non-Lipschitz coefficients and Levy noise | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 許順吉,吳慶堂 | |
| dc.subject.keyword | Levy過程,Levy型隨機微分方程,pathwise uniqueness, | zh_TW |
| dc.subject.keyword | Levy process,SDE driven by Levy process,pathwise uniqueness, | en |
| dc.relation.page | 36 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-07-11 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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