The intensity and the time correlation function of radiation transmitted through a layer of a randomly inhomogeneous medium are determined by numerical simulation of the Bethe-Salpeter equation for scalar and electromagnetic fields. The results of simulation agree well with the available experimental data. The domain of validity is determined numerically for the hypothesis of the diffusion approximation on the replacement of the extinction length by the transport length as a characteristic spatial scale for systems with the anisotropic scattering cross section. The polarized and depolarized components of the time correlation function of the transmitted light are calculated for the first time for different anisotropy parameters. It is shown that, to describe the residual polarization of transmitted light taking into account anisotropy, it is insufficient to perform the scale replacement of the extinction length by the transport length. © 2008 Pleiades Publishing, Ltd.