论文标题
噪声污染的预先计算过程，并应用于湍流
Pre-averaging fractional processes contaminated by noise, with an application to turbulence
论文作者
论文摘要
在本文中，我们考虑了基于嘈杂的高频数据估算分数过程的问题。通过证明相关变化功能的大量定律，我们将预定预先计算的想法概括为分数设置。与Semimartingale设置相反，预平均的最佳窗口大小取决于基础过程的未知粗糙度参数。我们在仿真研究中评估了估计器的性能，并使用它们来验证Kolmogorov的2/3-Law在受仪器噪声污染的湍流数据中。
In this article, we consider the problem of estimating fractional processes based on noisy high-frequency data. Generalizing the idea of pre-averaging to a fractional setting, we exhibit a sequence of consistent estimators for the unknown parameters of interest by proving a law of large numbers for associated variation functionals. In contrast to the semimartingale setting, the optimal window size for pre-averaging depends on the unknown roughness parameter of the underlying process. We evaluate the performance of our estimators in a simulation study and use them to empirically verify Kolmogorov's 2/3-law in turbulence data contaminated by instrument noise.
