标题： 从随机序列中提取强测量噪声：对实证数据的应用 显示英文标题

标题： Extracting strong measurement noise from stochastic series: applications to empirical data

摘要： 在实验数据分析中，将不可避免的测量噪声与内在的动力学噪声区分开来是一个巨大的挑战。 在这里，我们提出了一种通用的操作方法，可以从随机时间序列中提取测量噪声，即使在测量噪声的幅度和未受污染信号的幅度处于同一数量级的情况下也是如此。 我们的方法基于一种最近开发的用于非参数重建朗之万过程的方法。 通过最小化一个适当的非负函数，该方法能够正确提取强测量噪声，并估计描述原始未受干扰信号演化的朗之万方程中的漂移和扩散系数。 该算法仅使用直接从随机序列中提取的两个前阶条件矩，因此适用于各种不同的信号。 为了展示该方法的强大功能，我们将该算法应用于合成数据以及气候测量数据，即每日北大西洋涛动指数，从而对其中潜在物理过程的本质讨论提供了新的见解。 显示英文摘要

摘要： It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time series, even in the case when the amplitudes of measurement noise and uncontaminated signal are of the same order of magnitude. Our approach is based on a recently developed method for a nonparametric reconstruction of Langevin processes. Minimizing a proper non-negative function the procedure is able to correctly extract strong measurement noise and to estimate drift and diffusion coefficients in the Langevin equation describing the evolution of the original uncorrupted signal. As input, the algorithm uses only the two first conditional moments extracted directly from the stochastic series and is therefore suitable for a broad panoply of different signals. To demonstrate the power of the method we apply the algorithm to synthetic as well as climatological measurement data, namely the daily North Atlantic Oscillation index, shedding new light on the discussion of the nature of its underlying physical processes.