The parabolic or forward scattering approximation to the equation describing wave propagation in a random medium leads to a stochastic partial differential equation which has the form of a random Schrödinger equation. Existence, uniqueness and continuity of solutions to this equation are established. The resulting process is a Markov diffusion process on the unit sphere in complex Hilbert space. Using Markov methods a limiting Markov process is identified in the case of a narrow beam limit; this limiting process corresponds to a simple random translation of the beam known as "spot-dancing."

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Journal Applied Mathematics & Optimization
Dawson, D.A, & Papanicolaou, G.C. (1984). A random wave process. Applied Mathematics & Optimization, 12(1), 97–114. doi:10.1007/BF01449037