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英文文献：On non-standard limits of Brownian semi-stationary-关于布朗半平稳的非标准极限
英文文献作者：Kerstin G?rtner,Mark Podolskij
英文文献摘要：
In this paper we present some new asymptotic results for high frequency statistics of Brownian semi-stationary (BSS) processes. More precisely, we will show that singularities in the weight function, which is one of the ingredients of a BSS process, may lead to non-standard limits of the realised quadratic variation. In this case the limiting process is a convex combination of shifted integrals of the intermittency function. Furthermore, we will demonstrate the corresponding stable central limit theorem. Finally, we apply the probabilistic theory to study the asymptotic properties of the realized ratio statistics, which estimates the smoothness parameter of a BSS process.
本文给出了布朗半平稳(BSS)过程高频统计量的一些新的渐近结果。更准确地说，我们将说明权函数的奇异性，这是一个BSS过程的成分之一，可能导致实现的二次变差的非标准极限。在这种情况下，极限过程是间断函数的移位积分的凸组合。此外，我们将证明相应的稳定中心极限定理。最后，应用概率理论研究了估计BSS过程平滑参数的已实现比值统计量的渐近性质。
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