  Hot spots residing on the surface of an accretion disc have been considered
as a model of short-term variability of active galactic nuclei. In this paper
we apply the theory of random point processes to model the observed signal from
an ensemble of randomly generated spots. The influence of general relativistic
effects near a black hole is taken into account and it is shown that typical
features of power spectral density can be reproduced. Connection among spots is
also discussed in terms of Hawkes' process, which produces more power at low
frequencies. We derive a semi-analytical way to approximate the resulting
power-spectral density.
