Honisch Christoph, Friedrich Rudolf, Hörner Florian, Denz Cornelia
Institute for Theoretical Physics, University of Muenster, D-48149 Muenster, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Aug;86(2 Pt 2):026702. doi: 10.1103/PhysRevE.86.026702. Epub 2012 Aug 1.
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 the computation of error estimates for estimated parameters using a Monte Carlo error propagation technique. Finally, the extended method is applied to a data set of an optical trapping experiment yielding estimations of the forces acting on a Brownian particle trapped by optical tweezers. We find an increased Markov-Einstein time scale of the order of the relaxation time of the process, which can be traced back to memory effects caused by the interaction of the particle and the fluid. Above the Markov-Einstein time scale, the process can be very well described by the classical overdamped Markov model for Brownian motion.
克拉默斯-莫亚尔分析是一种用于分析复杂系统随机时间序列的成熟方法。如果测量时间序列的采样间隔过低，分析结果中会出现系统误差。在文献中，这些误差被标记为有限时间效应。在本文中，我们给出了关于这些效应的一些新见解，并讨论了在存在有限时间效应的情况下，一种先前发表的估计克拉默斯-莫亚尔系数方法的局限性。为了提高该方法的可靠性并避免误解，我们使用蒙特卡罗误差传播技术通过计算估计参数的误差估计来对其进行扩展。最后，将扩展后的方法应用于一个光学捕获实验的数据集，得到了作用在被光镊捕获的布朗粒子上的力的估计值。我们发现马尔可夫-爱因斯坦时间尺度增加到了该过程弛豫时间的量级，这可以追溯到粒子与流体相互作用引起的记忆效应。在马尔可夫-爱因斯坦时间尺度之上，该过程可以用经典的过阻尼布朗运动马尔可夫模型很好地描述。
