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.
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