英文文献：Limit theorems for non-degenerate U-statistics of continuous semimartingales-连续半鞅非退化u -统计量的极限定理
英文文献作者：Mark Podolskij,Christian Schmidt,Johanna Fasciati Ziegel
英文文献摘要：
This paper presents the asymptotic theory for non-degenerate U-statistics of high frequency observations of continuous It? semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.

本文给出了连续伊托半鞅高频观测值非退化u -统计量的渐近理论。证明了标准化u统计量在概率上的一致收敛，并给出了一个泛函稳定中心极限定理。中心极限定理中的极限过程证明是均值为零的条件高斯分布。最后，我们指出我们的概率结果的潜在统计应用。