The power spectral density (PSD) of the X-ray emission variability from the accretion disc-corona region of black hole X-ray binaries and active galactic nuclei has a broken power law shape with a characteristic break time-scale. If the disc and the jet are connected, the jet variability may also contain a characteristic time-scale related to that of the disc-corona. Recent observations of the blazar Mrk 421 have confirmed the broken power law shape of the PSD of its jet X-ray variability. We model the time variability of a blazar, in which emitting particles are assumed to be accelerated by successive shock waves flowing down the jet with a varying inter-shock time-scale. We investigate the possible relation between the characteristic time-scales in the disc and jet variability based on the above model, along with mathematically and physically simulated disc variability. We find that both the PSD of the jet and disc variability may have a broken power law shape but the break time-scales are not related in general except only in systems with a small range of BH mass. The break in the jet and the disc PSD are connected to the interval between large amplitude outbursts in the jet (inter-shock time-scale) and to the viscous time-scale in the disc, respectively. In frequency bands where multiple emission processes are involved or emission is from lower energy particles, the break in the PSD may not be prominent enough for detection.
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