  We derive from first principles a one-way radiative transfer equation for the
wave intensity resolved over directions (Wigner transform of the wave field) in
random media. It is an initial value problem with excitation from a source
which emits waves in a preferred, forward direction. The equation is derived in
a regime with small random fluctuations of the wave speed but long distances of
propagation with respect to the wavelength, so that cumulative scattering is
significant. The correlation length of the medium and the scale of the support
of the source are slightly larger than the wavelength, and the waves propagate
in a wide cone with opening angle less than $180^o$, so that the backward and
evanescent waves are negligible. The scattering regime is a bridge between that
of radiative transfer, where the waves propagate in all directions and the
paraxial regime, where the waves propagate in a narrow angular cone. We connect
the one-way radiative transport equation with the equations satisfied by the
Wigner transform of the wave field in these regimes.
