Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland.
Phys Rev E. 2019 Jan;99(1-1):012143. doi: 10.1103/PhysRevE.99.012143.
Recent advances in experimental techniques for complex systems and the corresponding theoretical findings show that in many cases random parametrization of the diffusion coefficients gives adequate descriptions of the observed fractional dynamics. In this paper we introduce two statistical methods which can be effectively applied to analyze and estimate parameters of superstatistical fractional Brownian motion with random scale parameter. The first method is based on the analysis of the increments of the process, the second one takes advantage of the variation of the trajectories of the process. We prove the effectiveness of the methods using simulated data. Also, we apply it to the experimental data describing random motion of individual molecules inside the cell of E.coli. We show that fractional Brownian motion with Weibull-distributed diffusion coefficient gives adequate description of this experimental data.
最近在复杂系统的实验技术和相应的理论发现方面的进展表明，在许多情况下，扩散系数的随机参数化可以充分描述观察到的分数动力学。在本文中，我们介绍了两种统计方法，可有效地应用于分析和估计具有随机标度参数的超统计分数布朗运动的参数。第一种方法基于过程增量的分析，第二种方法利用过程轨迹的变化。我们使用模拟数据证明了该方法的有效性。此外，我们将其应用于描述大肠杆菌细胞内单个分子随机运动的实验数据。我们表明，具有 Weibull 分布扩散系数的分数布朗运动可以充分描述这些实验数据。
