- 學位論文
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
On uniqueness and existence of stochastic differential equations with non-Lipschitz coefficients and Levy noise
摘要
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。
並列摘要
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.
參考文獻
[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.
[5]D.W.Stroock.(1975) Diffusion processes associated with L′evy generators. Z.f.Wahrscheinlichkeitstheorie vol.32,pp.209-244.
[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.
延伸閱讀
- Lin, C. Y. (2007). 在非Lipschitz係數條件及L′evy過程下隨機微分方程之特性 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2007.01618
- Chen, K. P. (2008). 某類網格型微分方程行波解的存在性，唯一性及穩定性 [master's thesis, National Central University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0031-0207200917352393
- Lu, H. C., & Hwang, D. Y. (2013). 關於可微分函數的加權辛普森不等式和高階動差的隨機變數之應用. 馬偕學報, (11), 71-90. https://www.airitilibrary.com/Article/Detail?DocID=20725396-201308-201310290018-201310290018-71-90
- 洪翊書（2013）。Marcinkiewicz-Zygmund型強大數法則在隨機變數為成對獨立且有相同分佈結構下之研究〔碩士論文，國立清華大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0016-2511201311341630
- Diop, M. A., Ezzinbi, K., & Lo, M. (2012). Existence and Uniqueness of Mild Solutions to Some Neutral Stochastic Partial Functional Integrodifferential Equations with Non-Lipschitz Coefficients. International Journal of Mathematics and Mathematical Sciences, 2012(), 322-333-128. https://doi.org/10.1155/2012/748590