Abstract
We consider a stochastic bilinear system model for laser propagation in atmospheric turbulence. The model consists of a random Schrödinger equation in which the white noise input is multiplied by the state. We consider approximate product form solutions of the Trotter-Kato type, and use these product forms to relate the Hilbert space-valued white noise model and the Itô equation model. We also consider white noise as the limit of a sequence Ornstein-Uhlenbeck processes. Finally, we consider approximate solutions using the Feynman-Itô equation, and an approximate calculation of the mean field without using the Markov approximation.
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Leland, R.P. White noise in atmospheric optics. Acta Appl Math 35, 103–130 (1994). https://doi.org/10.1007/BF00994913
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DOI: https://doi.org/10.1007/BF00994913