Methods for Solution of Stochastic Initial and Boundary Value Problems.
Final technical rept. Dec 72-Dec 73,
TEL-AVIV UNIV (ISRAEL) DEPT OF MATHEMATICAL SCIENCES
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Wave propagation in a one-dimensional random medium whose index of refraction is characterized randomly and is assumed to have small fluctuations about the mean was studied. The appropriate stochastic boundary value problem for the scattering region is transformed into a Cauchy type initial value problem for the boundary values of the random Greens function. The stochastic differential equation derived is a first order, nonlinear equation of the Riccati type. The initial value problem is solved in two ways 1 by conventional power series perturbation expansion, and 2 by quasilinearization. In both cases the refracting medium are considered to be characterized by a general stationary process in the broad sense, and for such a process, general expressions for the statistical properties of the reflected and transmitted amplitude waves are derived.
- Statistics and Probability