| 中文题名： | 由 Lévy 过程驱动的随机微分方程解的Feller 性 |
| 姓名： | |
| 保密级别： | 公开 |
| 论文语种： | 中文 |
| 学科代码： | 070103 |
| 学科专业： | |
| 学生类型： | 硕士 |
| 学位： | 理学硕士 |
| 学位类型： | |
| 学位年度： | 2021 |
| 校区： | |
| 学院： | |
| 研究方向： | 分枝过程 |
| 第一导师姓名： | |
| 第一导师单位： | |
| 提交日期： | 2021-06-10 |
| 答辩日期： | 2021-05-31 |
| 外文题名： | The Feller Property of Solutions of Stochastic Differential Equations driven by Lévy process. |
| 中文关键词： | |
| 外文关键词： | Feller property ; stochastic differential equations ; Lévy process ; Ito formula |
| 中文摘要： |
本文主要对由 Lévy 过程驱动的随机微分方程解的 Feller 性进行研究. 首先对随机微分方程的相关基础理论以及应用做了简单的介绍, 描述了国内外对随机微分方程及其解的性质的研究进展. 同时简单说明了由 Lévy 过程驱动的随机微分方程解的存在唯一性以及 Feller 性的研究结果, 并说明了本论文的研究价值. 然后简单介绍了 Lévy 过程与 α-稳定过程的估计. 接着研究了 Lévy 过程驱动的随机微分方程以及其解的矩估计. 最后证明了一类随机微分方程解的 Cb-Feller 性以及给出了关于解的C0-Feller 性的一些性质.
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主要结果有两个, 一是在 Takeuchi 和 Tsukada [9] 论文的基础上, 通过带跳的 Ito 公式以及 Gronwall’s 不等式, 证明出在系数满足一定条件下, 由一维 Lévy 过程驱动的随机微分方程的解是 Cb-Feller 的. 二是给出了一个右连续马氏过程是 C0-Feller 过程的充分条件, 最后, 应用 Ito 公式, 通过研究对系数的限制，证明了与解的 C0-Feller 性相关的一些性质. |
| 外文摘要： |
In this paper, we mainly study the Feller property of solutions of stochastic differential equations driven by Lévy process.
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Firstly, the basic theory and application of stochastic differential equations are briefly introduced, and the research progress of stochastic differential equations and their solutions at home and abroad is described. At the same time, the existence and uniqueness of solutions of stochastic differential equations driven by Lévy process and there Feller property are briefly explained. Then, the estimation of Lévy process and α-stable process are briefly introduced. Also, we studied the stochastic differential equation driven by Lévy process and the moment estimation of its solution. Finally, the Cb-Feller property of the solution of a class of stochastic differential equation and some properties of C0-Feller property is given. There are two main works in this paper. One is based on the paper of Takeuchi and Tsukada [9], by using the It? formula with jumps and Gronwall’s inequality, it is proved that the solution of stochastic differential equation driven by one-dimensional Lévy process is Cb-Feller under certain conditions. Secondly, we give the condition that a right continuous Markov process is a C0-Feller process. At the same time, by using the it? formula, and by studying the restriction on the coeffcient, we proved some properties related to the C0-Feller property of the solution. |
| 参考文献总数： | 14 |
| 馆藏号： | 硕070103/21007 |
| 开放日期： | 2022-06-10 |
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