姜祖恕臺灣大學：數學研究所黃勝郁Huang, Sheng-YuSheng-YuHuang2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/59452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。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.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............... . . 33462590 bytesapplication/pdfen-USLevy過程Levy型隨機微分方程pathwise uniquenessLevy processSDE driven by Levy processthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/59452/1/ntu-96-R94221039-1.pdf