A Direct Method for the Langevin-Analysis of Multidimensional Stochastic Processes with Strong Correlated Measurement Noise
A Direct Method for the Langevin-Analysis of Multidimensional Stochastic Processes with Strong Correlated Measurement Noise
复制标题
强相关测量噪声多维随机过程朗之万分析的直接方法
DOI：
10.1007/978-3-319-28725-6_1
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
B. Lehle
中科院分区：
文献类型：
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作者：
T. Scholz;F. Raischel;P. Lind;M. Wächter;V. V. Lopes;V. V. Lopes;B. Lehle
本文解决了寻找一种直接运算方法来解开两个连续马尔可夫随机过程之和的问题，这是所谓的测量噪声概念的更一般情况，仅给出总和过程的测量时间序列。所提出的方法基于最近发布的在存在强相关测量噪声的情况下分析多维朗之万型随机过程的方法（Lehle, J Stat Phys 152(6):1145–1169, 2013）。该方法从噪声数据中提取对应于描述每个随机过程的 Itô-Langevin 方程的相应漂移和扩散系数。这里提出的方法既不施加约束，也不施加参数，而是直接从多维数据中提取所有系数。该方法被引入现有重建方法的框架内，然后应用于与 Ornstein-Uhlenbeck 过程卷积的二维随机过程的求和。
This paper addresses the problem of finding a direct operational method to disentangle the sum of two continuous Markovian stochastic processes, a more general case of the so-called measurement noise concept, given only a measured time series of the sum process. The presented method is based on a recently published approach for the analysis of multidimensional Langevin-type stochastic processes in the presence of strong correlated measurement noise (Lehle, J Stat Phys 152(6):1145–1169, 2013). The method extracts from noisy data the respective drift and diffusion coefficients corresponding to the Itô–Langevin equation describing each stochastic process. The method presented here imposes neither constraints nor parameters, but all coefficients are directly extracted from the multidimensional data. The method is introduced within the framework of existing reconstruction methods, and then applied to the sum of a two-dimensional stochastic process convoluted with an Ornstein–Uhlenbeck process.