Codifference can detect ergodicity breaking and non-Gaussianity

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 (24)

• Anomalous transport in the crowded world of biological cells
• Superstatistics
• Lévy walks
• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Fractional Langevin equation
• Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities
• "Diffusing diffusivity": A model for anomalous and "anomalous yet Brownian" diffusion
• Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
• On the strong anomalous diffusion
• Quantitative analysis of single particle trajectories: mean maximal excursion method
• Stochastic modeling in nanoscale biophysics: Subdiffusion within proteins
• Diffusion-limited reactions in dynamic heterogeneous media
• Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion
• Spectral content of a single non-Brownian trajectory
• Anomalous diffusion in correlated continuous time random walks
• Noisy continuous time random walks
• Power spectral density of a single Brownian trajectory: What one can and cannot learn from it
• Codifference as a practical tool to measure interdependence
• Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
• Exact Results on Sinai's Diffusion
• Correlated continuous-time random walks: combining scale-invariance with long-range memory for spatial and temporal dynamics
• Moment ratios for the pair contact process with diffusion
• Grey Brownian motion local time: Existence and weak-approximation

Cited by in corpus (10)

• Bayesian deep learning for error estimation in the analysis of anomalous diffusion
• Brownian motion and beyond: first-passage, power spectrum, non-Gaussianity, and anomalous diffusion
• Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories
• Universal spectral features of different classes of random diffusivity processes
• Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems
• Fractional Brownian motion in superharmonic potentials and non-Boltzmann stationary distributions
• Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories
• Objective comparison of methods to decode anomalous diffusion
• Change-point detection in anomalous-diffusion trajectories utilising machine-learning-based uncertainty estimates
• Asymptotic theory for the detection of mixing in anomalous diffusion