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 Levy Processes

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α/2之外其它各幂次已实现幂变差的中心极限定理.

This paper is concerned with the asymptotic behavior of the realized power variation for time-changed α-stable Levy 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 α/2.