**abstract:**
Time-dependent processes are often analyzed using the power spectral density (PSD), which is calculated by making an appropriate Fourier transform of individual trajectories and finding the ensemble-averaged value. In some cases, however, one cannot create a statistical sample of a big enough size and hence it is of a great conceptual and practical importance to understand to which extent a relevant information can be gained from the PSD of a single trajectory, S(f,T). Here we focus on the behaviour of S(f,T), which is a random, realization-dependent variable, for a broad family of anomalous diffusion processes – the so-called fractional Brownian motion with Hurst-index H, and derive exactly its probability-density-function. We show that S(f,T) is proportional - up to a random numerical-factor with universal distribution which we determine - to the ensemble-averaged PSD. For subdiffusion (H<1*2) we find that S(f,T) ∼ A*f^{{2H+1}} with random-amplitude A. In sharp contrast, for superdiffusion (H>1*2) S(f,T) ∼ B T ^{{2H}-1}*f

Wed 19 Sep, 10:15 - 11:00, Aula Dini

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