Problems with the Gaussian statistics in stochastic theories of the radiative transfer

We present a stochastic non-perturbative analysis of the 'rod model' of thr theory of radiative transfer treating the 'rods' of lengths L as random media. The cross-section function σ(χ) (per unit length) is defined as a Gaussian random function with the mean value σ-bar. Since X > 0 for physical reasons, we define the probability density of X as a Gaussian only for X > 0; if X < 0, we define it as zero. (We show that if such a cut off were not considered and if the Gaussian distribution were extrapolated on the negative semiaxis of X, the stochastic analysis of the albedo problem would bear non-physical divergencies.) With this probability density, we carry out (both analytical and numerical) calculations of the first-order and second-order statistical moments of Τ and Ρ, as well as of the variances of Τ and Ρ as functions of the parameter β. We calculate also the correlation function between the stochastic values of Τ and the stochastic values of Ρ (Authors)