  This work uses the mathematical machinery of Renewal/Ruin (surplus risk)
theory to derive preliminary explicit estimations for the radiative properties
of dilute and disperse porous media otherwise only computable accurately with
Monte Carlo Ray Tracing (MCRT) simulations. Although random walk and Levy
processes have been extensively used for modeling diffuse processes in various
transport problems and porous media modeling, relevance to radiation heat
transfer is scarce, as opposed to other problems such as probe diffusion and
permeability modeling. Furthermore, closed form derivations that lead to
tangible variance reduction in MCRT are widely missing. The particular angle of
surplus risk theory provides a richer apparatus to derive directly related
quantities. To the best of the authors' knowledge, the current work is the only
work relating the surplus risk theory derivations to explicit computations of
ray tracing results in porous media. The paper contains mathematical
derivations of the radiation heat transfer estimates using the extracted
machinery along with proofs and numerical validation using MCRT.
