Abstract
We investigate the stochastic behavior of the single-trajectory spectral density of several Gaussian stochastic processes, i.e., Brownian motion, the Ornstein–Uhlenbeck process, the Brownian gyrator model and fractional Brownian motion, as a function of the frequency ω and the observation time . We evaluate in particular the variance and the frequency–frequency correlation of for different values of ω. We show that these properties exhibit different behaviors for different physical cases and can therefore be used as a sensitive probe discriminating between different kinds of random motion. These results may prove quite useful in the analysis of experimental and numerical data.
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