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Gaussian processes in complex media: new vistas on anomalous diffusion
Normal or Brownian diffusion is historically identified by the linear growth in time of the variance and by a Gaussian shape of the displacement distribution. Processes departing from the at least one of the above conditions ...
Single-trajectory spectral analysis of scaled Brownian motion
A standard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the ...
Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
Fractional Brownian motion (FBM) is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically FBM confined to a finite ...
Finite-energy Lévy-type motion through heterogeneous ensemble of Brownian particles
Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling $x \sim t^\delta$ with $\delta \neq 1/2$ in the probability density function (PDF). Anomalous diffusion can emerge jointly ...
Stochastic processes for anomalous diffusion
Anomalous diffusion is a diffusion process which Mean Square Displacement (MSD) is not a linear funtion of time, what is known as normal diffusion. When the relation is faster than linear, it is called superdiffusion and ...