  Compton scattering is a key process shaping spectra formation and accretion
flow dynamics in accreting strongly magnetized neutron stars. A strong magnetic
field affects the scattering cross section and makes it dependent on photon
energy, momentum, and polarization state. Using Monte Carlo simulations, we
investigate statistical features of Compton scattering of polarized X-ray
radiation in a strong magnetic field. Our analysis is focused on photon gas
behaviour well inside the scattering region. We take into account the resonant
scattering at the fundamental cyclotron frequency, thermal distribution of
electrons at the ground Landau level, and bulk velocity of the electron gas. We
show that (i) the photons scattered around the cyclotron energy by the electron
gas at rest tend to acquire the final energy close to the cyclotron one with a
very small dispersion measure; (ii) the redistribution of photons within the
Doppler core of cyclotron resonance differs significantly from the complete
redistribution; (iii) the efficiency of momentum transfer from photons to the
electron gas is affected by the temperature of electron gas both for photons at
cyclotron energy and below it; (iv) the momentum transfer from photons to the
electron gas of non-zero bulk velocity is more efficient in the case of
magnetic scattering.
