  Theory of random processes provides an attractive mathematical tool to
describe the fluctuating signal from accreting sources, such as active galactic
nuclei and Galactic black holes observed in X-rays. These objects exhibit
featureless variability on different timescales, probably originating from an
accretion disc. We study the basic features of the power spectra in terms of a
general framework, which permits semi-analytical determination of the power
spectral density (PSD) of the resulting light curve. We consider the expected
signal generated by an ensemble of spots randomly created on the accretion disc
surface. Spot generation is governed by Poisson or by Hawkes processes. We
include general relativity effects shaping the signal on its propagation to a
distant observer. We analyse the PSD of a spotted disc light curve and show the
accuracy of our semi-analytical approach by comparing the obtained PSD with the
results of Monte Carlo simulations. The asymptotic slopes of PSD are 0 at low
frequencies and they drop to -2 at high frequencies, usually with a single
frequency break. More complex two-peak solutions also occur. The amplitude of
the peaks and their frequency difference depend on the inherent timescales of
the model. At intermediate frequencies, the intrinsic PSD is influenced by the
individual light curve profile as well as by the type of the underlying
process. However, even in cases when two Lorentzians seem to dominate the PSD,
it does not necessarily imply that two single oscillation mechanisms operate
simultaneously. Instead, it may well be the manifestation of the avalanche
mechanism. The main advantage of our approach is an insight in the model
functioning and the fast evaluation of the PSD.
