The European Physical Journal B ( IF 1.6 ) Pub Date : 2021-07-21 , DOI: 10.1140/epjb/s10051-021-00149-0 Clemens Willers 1 , Oliver Kamps 1
|
Abstract
Langevin models are widely used to model various stochastic processes in different fields of natural and social sciences. They are adapted to measured data by estimation techniques such as maximum likelihood estimation, Markov chain Monte Carlo methods, or the non-parametric direct estimation method introduced by Friedrich et al. (Phys Lett A 271(3):217, 2000). The latter has the distinction of being very effective in the context of large data sets. Due to their \(\delta \)-correlated noise, standard Langevin models are limited to Markovian dynamics. A non-Markovian Langevin model can be formulated by introducing a hidden component that realizes correlated noise. For the estimation of such a partially observed diffusion a different version of the direct estimation method was introduced by Lehle et al. (Phys Rev E 97(1):012113, 2018). However, this procedure requests that the correlation length of the noise component is small compared to that of the measured component. In this work, we propose a direct estimation method without this restriction. This allows one to effectively deal with large data sets from a wide range of examples. We discuss the abilities of the proposed procedure using several synthetic examples.
Graphic Abstract
中文翻译：
相关噪声驱动的朗之万模型的非参数估计
摘要
Langevin 模型被广泛用于模拟自然科学和社会科学不同领域的各种随机过程。它们适用于通过估计技术（例如最大似然估计、马尔可夫链蒙特卡罗方法或Friedrich 等人引入的非参数直接估计方法）测量的数据。(Phys Lett A 271(3):217, 2000)。后者的特点是在大数据集的上下文中非常有效。由于他们的\(\delta \)- 相关噪声，标准 Langevin 模型仅限于马尔可夫动力学。可以通过引入实现相关噪声的隐藏组件来制定非马尔可夫朗之万模型。为了估计这种部分观察到的扩散，Lehle 等人引入了不同版本的直接估计方法。(Phys Rev E 97(1):012113, 2018)。然而，该过程要求噪声分量的相关长度与被测分量的相关长度相比较小。在这项工作中，我们提出了一种没有这种限制的直接估计方法。这允许人们有效地处理来自广泛示例的大型数据集。我们使用几个综合示例讨论了所提出程序的能力。
京公网安备 11010802027423号