| 刘广应,张新生.带跳的Gauss积分过程幂变差的渐近行为[J].数学年刊A辑,2012,33(2):247~260 |
| 带跳的Gauss积分过程幂变差的渐近行为 |
| Asymptotic Properties for Power Variation of Gaussian Integral Processes with Jumps |
| |
| DOI： |
| 中文关键词: Gauss过程 Lévy过程 幂变差 高频数据 中心极限定理 大数定律 |
| 英文关键词:Gaussian processes, L′evy processes, Power variation, High
frequency data, Central limit theorems, Large number law |
| 基金项目:国家自然科学基金，教育部人文社会科学基金，江苏省自然科学基金，江苏省高校自然科学基金 |
| Author Name | Affiliation | E-mail | | LIU Guangying | School of Mathematics and Statistics, Nanjing Audit University, Nanjing
210029, China
Department of Statistics, School of Management, Fudan University,
Shanghai 200433, china | liugying2007@gmail.com | | ZHANG Xinsheng | Department of Statistics, School of Management, Fudan University, Shanghai
200433, china | xszhang@fudan.edu.cn |
|
| Hits: 1172 |
| Download times: 788 |
| 中文摘要: |
| 研究了$X_t=\int_0^t \phi_s{\rm d} G_s+\xi_t$已实现幂变差的渐近理论,
其中$G$为平稳增量Gauss过程,$\phi$为随机过程,$\xi$为与$G$独立的非Gauss L\'{e}vy过程,
而积分为按路径Riemann-Stietjes积分.
给出了经适当规范化后已实现幂变差的概率极限定理以及相应的中心极限定理,这些结果将为处理长期记忆跳过程的统计问题提供理论基础. |
| 英文摘要: |
| This paper deals with the limit theorems for the realized power variation of processes of the form $X_t=\int_0^t\phi_s {\rm d}G_s +\xi_t$ observed at
high frequency. Here $G$ is a Gaussian process with stationary increments, $\xi$ is a non-Gaussian L\'{e}vy process, and $G,\xi$
are mutually independent. The integral is a pathwise Riemann-Stieltjes integral. Under some assumptions, the authors prove the convergence in probability for properly
normalized realized power variation and some associated stable central limit theorems. The results provide new statistical tools to
analyse the long memory processes with jumps. |
| View Full Text View/Add Comment Download reader |
| Close |
|
|
|
|
|
