英文文献：Multipower Variation for Brownian Semistationary Processes-布朗半静态过程的多幂变异
英文文献作者：Ole E. Barndorff-Nielsen,José Manuel Corcuera,Mark Podolskij
英文文献摘要：
In this paper we study the asymptotic behaviour of power and multipower variations of stochastic processes. Processes of the type considered serve in particular, to analyse data of velocity increments of a fluid in a turbulence regime with spot intermittency sigma. The purpose of the present paper is to determine the probabilistic limit behaviour of the (multi)power variations of Y, as a basis for studying properties of the intermittency process. Notably the processes Y are in general not of the semimartingale kind and the established theory of multipower variation for semimartingales does not suffice for deriving the limit properties. As a key tool for the results a general central limit theorem for triangular Gaussian schemes is formulated and proved. Examples and an application to realised variance ratio are given.

本文研究了随机过程的幂次变化和多次变化的渐近性态。所考虑的这类过程特别用于分析带有局部间断sigma的湍流状态下流体的速度增量数据。本文的目的是确定Y的(多)次幂变化的概率极限行为，作为研究间歇过程性质的基础。值得注意的是，这些过程一般不属于半鞅类，并且所建立的半鞅多幂变分理论还不能充分地导出极限性质。作为得到结果的关键工具，给出并证明了三角高斯格式的一般中心极限定理。给出了实现方差比的实例和应用。