Probability distributions of scattered signals in a random multilayer

摘要

This is a review paper on the study of the randomly scattered signals in a random multilayer based upon a stochastic and asymptotic formulation under strong mixing condition. This formulation generalizes the dominant Ito's formulation. The existence of a turning point of the random wave requires several type stochastic differential equations and the relevant limit theorems. The probability distributions of the randomly scattered signals have been obtained in the form of the Kolmogorov PDEs along the line of Khasminskii's limit theorem. This article demonstrates the step-by-step development of the relevant generators which contain the ultimate information for the probability distributions of the random signals.