title: Ergodicity testing for anomalous diffusion: small sample statistics.
abstract: 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.
authors: Hugo Steinhaus Center, Faculty of Fundamental Problems of Technology, Wrocław University of Technology, 50-370 Wrocław, Poland.
authors: Joanna
authors: J
authors: Janczura
authors: Hugo Steinhaus Center, Faculty of Fundamental Problems of Technology, Wrocław University of Technology, 50-370 Wrocław, Poland.
authors: Aleksander
authors: A
authors: Weron
mesh_terms: D004058:Diffusion; D009038:Motion; D013223:Statistics as Topic