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 ...

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 ...

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 ...

We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass ...

The emerging diffusive dynamics in many complex systems shows a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a ...

The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such ...

We present a modelling approach for diffusion in a complex medium characterized by a random lengthscale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle ...