| 张世斌,林正炎.时间变换稳定Levy过程幂变差的极限定理[J].数学年刊A辑,2013,34(4):385~400 |
| 时间变换稳定Levy过程幂变差的极限定理 |
| Limit Theorems of Power Variation for Time-Changed Stable L\'{e}vy Processes |
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| DOI： |
| 中文关键词: 时间变换Levy过程, 稳定过程, 幂变差, 中心极限定理 |
| 英文关键词:Time-Changed L′evy process, Stable process, Power variation,
Central limit theorem |
| 基金项目:国家自然科学基金 (No. 10901100, No. 11171303) |
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| 中文摘要: |
| 研究时间变换α-稳定Levy过程已实现幂变差的极限行为. 证明了规范化之后的已实现幂变差一致依概率收敛的大数定律, 并给出了除幂次$\frac \alpha 2$之外其它各幂次已实现幂变差的中心极限定理. |
| 英文摘要: |
| This paper is concerned with the asymptotic behavior of the realized power variation for time-changed
$\alpha$-stable L\'{e}vy processes.
The authors prove a law of large numbers, which is the uniform convergence in probability of
the realized power variation after normalization. The authors also exhibit the central
limit theorems of the realized power variation in all the orders except $\frac \alpha 2$. |
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