Geometric and projection effects in Kramers-Moyal analysis

Finite sampling interval effects in Kramers-Moyal analysis

Large sampling intervals can affect reconstruction of Kramers-Moyal coefficients from data. A new method, which is direct, non-stochastic and exact up to numerical accuracy, can estimate these finite-time effects. For the first time, exact finite-time effects are described analytically for special cases; biologically inspired numerical examples are also worked through numerically. The approach developed here will permit better evaluation of Langevin or Fokker-Planck based models from data with large sampling intervals. It can also be used to predict the sampling intervals for which finite-time…

Estimation of Kramers-Moyal coefficients at low sampling rates

A new optimization procedure for the estimation of Kramers-Moyal coefficients from stationary, one-dimensional, Markovian time series data is presented. The method takes advantage of a recently reported approach that allows to calculate exact finite sampling interval effects by solving the adjoint Fokker-Planck equation. Therefore it is well suited for the analysis of sparsely sampled time series. The optimization can be performed either making a parametric ansatz for drift and diffusion functions or also parameter free. We demonstrate the power of the method in several numerical examples with…

Kramers-Moyal analysis of interplanetary magnetic field fluctuations at sub-ion scales

In the framework of statistical time series analysis of complex dynamics we present a multiscale characterization of solar wind turbulence in the near-Earth environment. The data analysis, based on the Markov-process theory, is meant to estimate the Kramers-Moyal coefficients associated with the measured magnetic field fluctuations. In fact, when the scale-to-scale dynamics can be successfully described as a Markov process, first- and second-order Kramers-Moyal coefficients provide a complete description of the dynamics in terms of Langevin stochastic process. The analysis is carried out by us…

局部统计矩用于捕捉 Kramers-Moyal 系数

Local statistical moments to capture Kramers-Moyal coefficients

本研究提出一种局部统计矩方法估计 Kramers-Moyal 系数，结合非参数灵活性与参数可解释性，适用于平稳与非平稳时间序列及风力涡轮机等实际复杂系统。

Extended Kramers-Moyal analysis applied to optical trapping

The Kramers-Moyal analysis is a well established approach to analyze stochastic time series from complex systems. If the sampling interval of a measured time series is too low, systematic errors occur in the analysis results. These errors are labeled as finite time effects in the literature. In the present article, we present some new insights about these effects and discuss the limitations of a previously published method to estimate Kramers-Moyal coefficients at the presence of finite time effects. To increase the reliability of this method and to avoid misinterpretations, we extend it by th…

Markov property of the Super-MAG Auroral Electrojet Indices

The dynamics of the Earth's magnetosphere exhibits strongly fluctuating patterns as well as non-stationary and non-linear interactions, more pronounced during magnetospheric substorms and magnetic storms. This complex dynamics comprises both stochastic and deterministic features occurring at different time scales. Here we investigate the stochastic nature of the magnetospheric substorm dynamics by analysing the Markovian character of SuperMAG SME and SML geomagnetic indices. By performing the Chapman-Kolmogorov test, the SME/SML dynamics appears to satisfy the Markov condition at scales below …