Transformation of the probability structures of the random fields of sources in the nonlinearly parametric mapping process
V. I. Klyachkin · Acoustical Physics · 2008
The formation of the functional operator procedure for solving the problem of the propagation of random fields generated by extraneous sources in a statistically inhomogeneous continuous medium is considered. The solution is represented in the form of a probability density functional or a characteristic functional as the basis for analyzing the likelihood ratio. The structure of operators introduced in the calculations correlates with the statistical properties of both the fields of random sources and the parameters of the propagation medium. In the framework of Gaussian models of sources and propagation parameters, the solution is constructed in a closed form. Representations for the mean fields and their correlation functions are derived.