  In this work we investigate the nature of multi-wavelength variability of
blazars from a purely numerical approach. We use a time-dependent one-zone
leptonic blazar emission model to simulate multi-wavelength variability by
introducing stochastic parameter variations in the emission region. These
stochastic parameter variations are generated by Monte Carlo methods and have a
characteristic power law index of $\alpha=-2$ in their power spectral
densities. We include representative blazar test cases for a flat spectrum
radio quasar and a high synchrotron peaked BL Lacertae object for which the
high energy component of the Spectral Energy Distribution is dominated by
external Compton and synchrotron self-Compton emission, respectively. The
simulated variability is analyzed in order to characterise the distinctions
between the two blazar cases and the physical parameters driving the
variability. We show that the variability's power spectrum is closely related
to underlying stochastic parameter variations for both cases. Distinct
differences between the different progenitor variations are present in the
multi-wavelength cross-correlation functions.
