Solution of the stochastic transport equation of neutral particles with anisotropic scattering using RVT technique

Much of the literatures are directed toward the development of a mathematical formalism for a rigorous estimation of the ensemble average of the solution process of a stochastic differential equation (SDE). The Random Variable Transformation technique (RVT) is a powerful technique to get the complete solution for the SDE represented by the probability-density function of the solution process. In this paper, the RVT technique together with a simple integral transformation to the input stochastic process are implemented to get the complete solution of the one-speed transport equation for neutral particles in a semi-infinite stochastic medium with linear anisotropic scattering. The extinction function of the medium (input stochastic process) is assumed to be a continuous random function of position. The probability-density function and hence, the higher order statistical moments of the solution process are presented. Numerical results are given for different distributions of the input stochastic process.