Codifference can detect ergodicity breaking and non-Gaussianity
arXiv:1903.11905 · doi:10.1088/1367-2630/ab13f3
Abstract
We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a non-linear analogue of the mean squared displacement.
39 pages, 5 figures, IOP LaTeX
References in corpus (10)
- Anomalous transport in the crowded world of biological cells
- Lévy walks
- Random Time-Scale Invariant Diffusion and Transport Coefficients
- "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
- Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins
- Diffusion-limited reactions in dynamic heterogeneous media
- Spectral content of a single non-Brownian trajectory
- Codifference as a practical tool to measure interdependence
- Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
- Moment ratios for the pair contact process with diffusion