  We analyze X-ray light curves of the blazars Mrk 421, PKS 2155-304, and 3C
273 using observations by the Soft X-ray Telescope on board AstroSat and
archival XMM-Newton data. We use light curves of length 30-90 ks each from 3-4
epochs for all three blazars. We apply the autoregressive integrated moving
average (ARIMA) model which indicates the variability is consistent with short
memory processes for most of the epochs. We show that the power spectral
density (PSD) of the X-ray variability of the individual blazars are consistent
within uncertainties across the epochs. This implies that the construction of
broadband PSD using light curves from different epochs is accurate. However,
using certain properties of the variance of the light curves and its segments,
we show that the blazars exhibit hints of non-stationarity beyond that due to
their characteristic red noise nature in some of those observations. We find a
linear relationship between the root-mean-squared amplitude of variability at
shorter timescales and the mean flux level at longer timescales for light
curves of Mrk 421 across epochs separated by decades as well as light curves
spanning 5 days and $\sim$10 yr. The presence of flux-rms relation over very
different timescales may imply that, similar to the X-ray binaries and Seyfert
galaxies, longer and shorter timescale variability are connected in blazars.
