2002/05/13 by Guillaume Bal, Bal, Guillaume, George Papanicolaou +3
Engineering · Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Geophysical Methods and Applications #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0205025
arxiv created 2002/05/13 · openalex publication_date 2002/05/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows us to construct an approximate martingale for the phase space Wigner transform of two wave fields. Using a priori L2-bounds available in the time-reversal setting, we prove that the Wigner transform in the high frequency limit converges in probability to its deterministic limit, which is the solution of a transport equation.