  The carrier spin and impurity spin densities in diluted magnetic
semiconductors are considered using a semiclassical approach. Equations of
motions for the spin densities and the carrier spin current density in the
paramagnetic phase are derived, exhibiting their coupled diffusive dynamics.
The dynamical spin susceptibilities are obtained from these equations. The
theory holds for p-type and n-type semiconductors doped with magnetic ions of
arbitrary spin quantum number. Spin-orbit coupling in the valence band is shown
to lead to anisotropic spin diffusion and to a suppression of the Curie
temperature in p-type materials. As an application we derive the Hall-voltage
noise in the paramagnetic phase. This quantity is critically enhanced close to
the Curie temperature due to the contribution from the anomalous Hall effect.
