Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift

Abstract

The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the traping phase) in a disordered medium is considered in the presence of an external drift. In particular, we consider trapping events whose times follow a scale-free distribution with diverging mean trapping time. We construct this process in terms of fractional Brownian motion (FBM) with constant forcing in which the trapping effect is introduced by the subordination technique, connecting "operational time" with observable "real time". We derive the statistical properties of this process such as non-Gaussianity and non-ergodicity, for both ensemble and single-trajectory (time) averages. We demonstrate nice agreement with extensive simulations for the probability density function, skewness, kurtosis, as well as ensemble and time-averaged mean squared displacements. We pay specific emphasis on the comparisons between the cases with and without drift.

References in corpus (32)

• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Ergodic Properties of Fractional Brownian-Langevin Motion
• Langevin equations for continuous time Lévy flights
• Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Machine learning method for single trajectory characterization
• Spectral content of a single non-Brownian trajectory
• Exact and explicit probability densities for one-sided Levy stable distributions
• Inequivalence of time and ensemble averages in ergodic systems: exponential versus power-law relaxation in confinement
• Measurement of Anomalous Diffusion Using Recurrent Neural Networks
• Bayesian deep learning for error estimation in the analysis of anomalous diffusion
• Fractional kinetics emerging from ergodicity breaking in random media
• Classification of particle trajectories in living cells: machine learning versus statistical testing hypothesis for fractional anomalous diffusion
• Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion
• Diffusion coefficient of a Brownian particle in equilibrium and nonequilibrium: Einstein model and beyond
• Molecular motors transporting cargos in viscoelastic cytosol: how to beat subdiffusion with a power stroke?
• Fokker-Planck-Kolmogorov equations associated with SDEs driven by time-changed fractional Brownian motion
• Fractional Brownian motion with random Hurst exponent: accelerating diffusion and persistence transitions
• Aging power spectrum of membrane protein transport and other subordinated random walks
• On relation between generalized diffusion equations and subordination schemes
• Boosting the performance of anomalous diffusion classifiers with the proper choice of features
• Superstatistical modelling of protein diffusion dynamics in bacteria
• Moses, Noah and Joseph Effects in Coupled Lévy Processes
• Fractional Brownian motion time-changed by gamma and inverse gamma process
• Bayesian inference with information content model check for Langevin equations
• Alternative numerical computation of one-sided Levy and Mittag-Leffler distributions
• Anomalous diffusion originated by two Markovian hopping-trap mechanisms
• Ergodic property of random diffusivity system with trapping events
• On the properties of Laplace transform originating from one-sided Lévy stable laws
• Trapped by the drift
• Theory of relativistic heat polynomials and one-sided Lévy distributions