  We examine the applicability of the stochastic electron acceleration to two
high synchrotron peaked blazars, Mrk 421 and Mrk 501, assuming synchrotron
self-Compton emission of gamma-rays. Our model considers an emitting region
moving at relativistic speed, where non-thermal electrons are accelerated and
attain a steady-state energy spectrum together with the photons they emit. The
kinetic equations of the electrons and photons are solved numerically, given a
stationary wave number spectrum of the magnetohydrodynamic (MHD) disturbances,
which are responsible for the electron acceleration and escape. Our simple
formulation appears to reproduce the two well-sampled, long-term averaged
photon spectra. In order to fit the model to the emission component from the
radio to the X-ray bands, we need both a steeper wave spectral index than the
Kolmogorov spectrum and efficient particle escape. Although the model provides
a natural explanation for the high-energy cutoff of the electron energy
distribution, the derived physical parameters raise a problem with an energy
budget if the MHD waves with the Alfv{\'e}n velocity are assumed to be the
acceleration agent.
