英文文献：Limit theorems for functionals of higher order differences of Brownian semi-stationary processes-布朗半平稳过程高阶差分泛函的极限定理
英文文献作者：Ole E. Barndorff-Nielsen,José Manuel Corcuera,Mark Podolskij
英文文献摘要：
We present some new asymptotic results for functionals of higher order differences of Brownian semi-stationary processes. In an earlier work [4] we have derived a similar asymptotic theory for first order differences. However, the central limit theorems were valid only for certain values of the smoothness parameter of a Brownian semistationary process, and the parameter values which appear in typical applications, e.g. in modeling turbulent flows in physics, were excluded. The main goal of the current paper is the derivation of the asymptotic theory for the whole range of the smoothness parameter by means of using second order differences. We present the law of large numbers for the multipower variation of the second order differences of Brownian semi-stationary processes and show the associated central limit theorem. Finally, we demonstrate some estimation methods for the smoothness parameter of a Brownian semi-stationary process as an application of our probabilistic results.

摘要给出了布朗半平稳过程高阶差分泛函的一些新的渐近结果。在较早的工作[4]中，我们已经推导出一阶差分相似的渐近理论。然而，中心极限定理仅对布朗半静态过程的平滑参数的某些值有效，而在典型应用中出现的参数值，例如在物理中模拟湍流，被排除在外。本文的主要目的是利用二阶差分推导光滑参数全范围的渐近理论。摘要给出了布朗半平稳过程二阶差分多幂变分的大数定律，并给出了相应的中心极限定理。最后，作为概率结果的应用，我们给出了布朗半平稳过程光滑参数的一些估计方法。