  Starting with the Wigner distribution formulation for beam wave propagation
in H\"{o}lder continuous non-Gaussian random refractive index fields we show
that the wave beam regime naturally leads to the white-noise scaling limit and
converges to a Gaussian white-noise model which is characterized by the
martingale problem associated to a stochastic differential-integral equation of
the It\^o type. In the simultaneous geometrical optics the convergence to the
Gaussian white-noise model for the Liouville equation is also established if
the ultraviolet cutoff or the Fresnel number vanishes sufficiently slowly. The
advantage of the Gaussian white-noise model is that its $n$-point correlation
functions are governed by closed form equations.
