Abstract
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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Communicated by H. H. Kuo
Research supported by the Natural Sciences and Engineering Research Council of Canada.
Research supported by the Air Force Office of Scientific Research under Grant number AFOSR-80-0228.
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Dawson, D.A., Papanicolaou, G.C. A random wave process. Appl Math Optim 12, 97–114 (1984). https://doi.org/10.1007/BF01449037
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DOI: https://doi.org/10.1007/BF01449037