Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique

摘要

This paper considers the solution of the radiative transfer equation in a semi-infinite continuous stochastic medium with Rayleigh scattering. The available solutions – in literature – for this stochastic integro–differential equation (SIDE) are represented only by the ensemble-averaged solutions. Here, the deterministic solution of the problem is obtained at first. Then, the random variable transformation (RVT) technique together with an integral transformation to the input stochastic process is implemented to get the complete stochastic solution of the problem. This solution is represented by the probability density function of the solution process. Moreover, the nth statistical moment of the solution is derived. Numerical results are given for exponential and Gaussian distributions of the input stochastic process. Also, these results are given for different boundary conditions.