Parabolic and Gaussian white noise approximation for wave propagation in random media

The parabolic or forward scattering approximation has been used extensively in the study of wave propagation This approximation is combined with a Gaussian white noise approximation for waves propagating in a random medium. The validity of this approximation is proved for stratified weakly fluctuating random media in the high-frequencies regime. The limiting distribution of the wave field is characterized as the unique solution of a random Schrodinger equation studied by Dawson and Papanicolaou [Appl. Math. Optim., 12 (1984), pp. 97-114]. The proofs are based on various generalizations of the perturbed test function method developed by Kushner [Approximation and Weak Convergence Methods for Random Processes, MIT Press, 1984].