2003/04/15 by Albert Fannjiang, Albert C. Fannjiang, Fannjiang, Albert C.
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Ocean Waves and Remote Sensing #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0304024
openalex publication_date 2003/04/15 · arxiv created 2004/03/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Starting with the Wigner distribution 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 white-noise model which is characterized by the martingale problem associated to a stochastic differential-integral equation of the Itô 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.