  We investigate the electron energy distributions (EEDs) and the acceleration
processes in the jet of Mrk 421 through fitting the spectral energy
distributions (SEDs) in different active states in the frame of a one-zone
synchrotron self-Compton (SSC) model. After assuming two possible EEDs formed
in different acceleration models: the shock accelerated power-law with
exponential cut-off (PLC) EED and the stochastic turbulence accelerated
log-parabolic (LP) EED, we fit the observed SEDs of Mrk 421 in both low and
giant flare states by using the Markov Chain Monte Carlo (MCMC) method which
constrains the model parameters in a more efficient way. Our calculating
results indicate that (1) the PLC and LP models give comparably good fits for
the SED in low state, but the variations of model parameters from low state to
flaring can be reasonably explained only in the case of the PLC in low state;
and (2) the LP model gives better fits compared to the PLC model for the SED in
flare state, and the intra-day/night variability observed at GeV-TeV bands can
be accommodated only in the LP model. The giant flare may be attributed to the
stochastic turbulence re-acceleration of the shock accelerated electrons in low
state. Therefore, we may conclude that shock acceleration is dominant in low
state, while stochastic turbulence acceleration is dominant in flare state.
Moreover, our result shows that the extrapolated TeV spectra from the best-fit
SEDs from optical through GeV with the two EEDs are different. It should be
considered in caution when such extrapolated TeV spectra are used to constrain
extragalactic background light (EBL) models.
