White-noise Limit of Wigner and Liouville Equations for Wave Beams in Turbulent Media

Starting with the Wigner function formulation for beam wave propagation in Hölder 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 Markovian model which is characterized the martingale problem associated to a stochastic differential-integral equation of the Ito type. In the geometric optics approximation a similar convergence result also holds for the corresponding Liouville equation if the ultraviolet cutoff is present. The advantage of the Gaussian Markovian model is that its n-point correlation function is governed by a closed form equation.