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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 ...
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 ...