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BL Lac objects undergo strong flux variations involving considerable changesin their spectral shapes. We specifically investigate the X-ray spectralevolution of Mrk 421 over a time span of about nine years. We aim atstatistically describing and physically understanding the large spectralchanges in X rays observed in Mrk 421 over this time span. We perform ahomogeneous spectral analysis of a wide data set including archivedobservations with ASCA, BeppoSax, RXTE, as well as published and unpublishedXMM-Newton data. The presence of uncertainties is taken into account in ourcorrelation analysis. The significance of the correlations found and possiblespurious effects are studied with Monte Carlo simulations. We find that theMrk421 spectral energy distribution (SED) has a lower peak at energies thatvary 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 positivecorrelation 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 peakenergy. We show that these relations between the spectral parameters areconsistent with statistical or stochastic acceleration of the emittingparticles, and provide insight into the physical processes occurring in BL Lacnuclei.Comment: 11 pages, 5 fiures, Accepted for publication in A&

Signatures of synchrotron emission and of electron acceleration in the X-ray spectra of Mrk 421