英文文献：Edgeworth expansion for functionals of continuous diffusion processes-连续扩散过程泛函的埃奇沃思展开式
英文文献作者：Mark Podolskij,Nakahiro Yoshida
英文文献摘要：
This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion processes. Our methodology relies on martingale embedding, Malliavin calculus and stable central limit theorems for semimartingales. Finally, we demonstrate the density expansion for studentized statistics of power variations.

本文给出了连续扩散过程高频泛函的埃奇沃思展开的新结果。我们推导了布朗运动加权泛函的渐近展开式，并应用它们给出了扩散过程幂次变化的边值展开式。我们的方法依赖于鞅嵌入、Malliavin演算和半鞅的稳定中心极限定理。最后，我们演示了用于研究功率变化统计的密度膨胀。