带跳分数维积分过程幂变差的渐近行为

数学物理学报 ›› 2014, Vol. 34 ›› Issue (4): 925-937.

带跳分数维积分过程幂变差的渐近行为

刘广应|唐加山|张新生

南京审计学院数学与统计学院南京 210029；南京邮电大学理学院南京 210046；复旦大学管理学院统计学系上海 204330

收稿日期:2012-08-24 修回日期:2013-04-24 出版日期:2014-08-25 发布日期:2014-08-25
基金资助:
国家自然科学基金(11071045, 11226201)、江苏省自然科学基金(BK20131340)、教育部人文社会科学基金(12YJCZH128)、江苏高校优势学科建设工程资助项目(审计科学与技术)和江苏省高校“青蓝工程”优秀青年骨干教师基金资助.

Asymptotic Properties for Power Variations of Fractional Integral Processes with Jumps

LIU Guang-Ying, TANG Jia-Shan, ZHANG Xin-Sheng

Department of Mathematics and Statistics, Nanjing Audit University, Nanjing 210029； College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210046； Department of Statistics, School of Management, Fudan University, Shanghai 204330

Received:2012-08-24 Revised:2013-04-24 Online:2014-08-25 Published:2014-08-25
Supported by:
国家自然科学基金(11071045, 11226201)、江苏省自然科学基金(BK20131340)、教育部人文社会科学基金(12YJCZH128)、江苏高校优势学科建设工程资助项目(审计科学与技术)和江苏省高校“青蓝工程”优秀青年骨干教师基金资助.

摘要/Abstract

摘要：

研究X_t=∫^t₀Φ_sdB^H_s+ξ_t现实幂变差渐近行为, B^H为Hurst指数H∈ (0,1)分数维Brown运动, Φ为具有有限q次变差的随机过程且
q<1/(1-H), ξ为独立于B^H不含Gauss项的L\'{e}vy过程, 建立现实幂变差幂次为1/H的中心极限定理, 得到现实截断幂变差大数定律和中心极限定理.

关键词: 现实幂变差, 现实截断幂变差, 高频数据, 长期记忆性, 中心极限定理

Abstract:

In this paper, we investigate asymptotic properties for realized power variations of a process given by =∫^t₀Φ_sdB^H_s+ξ_t, where B^H is a fractional Brownian motion with Hurst parameter H∈ (0,1), Φ is a process having finite q-th variation with q<1/(1-H), and ξ is a purely non-Gaussian L\'{e}vy process and is independent of B^H. We present some central limit theorems (CLT) for the realized power variations in the situation that the exponent is 1/H. Some limit theorems on the law of large numbers and the CLTs for the realized threshold power variations are obtained as well.

Key words: Realized power variation, Realized threshold power variation, High-frequency data, Long memory, Central limit theorem

中图分类号:

60F17

刘广应, 唐加山, 张新生. 带跳分数维积分过程幂变差的渐近行为[J]. 数学物理学报, 2014, 34(4): 925-937.

LIU Guang-Ying, TANG Jia-Shan, ZHANG Xin-Sheng. Asymptotic Properties for Power Variations of Fractional Integral Processes with Jumps[J]. Acta mathematica scientia,Series A, 2014, 34(4): 925-937.

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