  BL Lac objects undergo strong flux variations involving considerable changes
in their spectral shapes. We specifically investigate the X-ray spectral
evolution of Mrk 421 over a time span of about nine years. We aim at
statistically describing and physically understanding the large spectral
changes in X rays observed in Mrk 421 over this time span. We perform a
homogeneous spectral analysis of a wide data set including archived
observations with ASCA, BeppoSax, RXTE, as well as published and unpublished
XMM-Newton data. The presence of uncertainties is taken into account in our
correlation analysis. The significance of the correlations found and possible
spurious effects are studied with Monte Carlo simulations. We find that the
Mrk421 spectral energy distribution (SED) has a lower peak at energies that
vary in the range, 0.1-10 keV while its X-ray spectrum is definitely curved.
Parameterizing the X-ray spectra with a log-parabolic model, we find a positive
correlation between the position and the height of the SED peak. In addition,
we find a negative trend of the spectral curvature parameter vs. the SED peak
energy. We show that these relations between the spectral parameters are
consistent with statistical or stochastic acceleration of the emitting
particles, and provide insight into the physical processes occurring in BL Lac
nuclei.
