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Ergodicity testing for anomalous diffusion: Small sample statistics
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DOI：10.1063/1.4916912.png)
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摘要
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The analysis of trajectories recorded in experiments often requires calculating time averages instead of ensemble averages. According to the Boltzmann hypothesis, they are equivalent only under the assumption of ergodicity. In this paper, we implement tools that allow to study ergodic properties. This analysis is conducted in two classes of anomalous diffusion processes: fractional Brownian motion and subordinated Ornstein-Uhlenbeck process. We show that only first of them is ergodic. We demonstrate this by applying rigorous statistical methods: mean square displacement, confidence intervals, and dynamical functional test. Our methodology is universal and can be implemented for analysis of many experimental data not only if a large sample is available but also when there are only few trajectories recorded. (C) 2015 AIP Publishing LLC.
Keyword:
DYNAMICS
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期刊
IF:
3.1
论文数:
7.2W
被引数:
23.2W
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引用论文
The random walk's guide to anomalous diffusion: a fractional dynamics approach随机游走的异常扩散指南: 分数动力学方法
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BIOPHYSICAL JOURNALIF3.1
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