A boundary-value problem for the polarized-radiation transfer equation with Fresnel interface conditions for a layered medium

A boundary-value problem for the polarized-radiation transfer equation for a layered medium with Fresnel matching conditions at the boundaries of the medium partition is examined. The theorems of solvability of the boundary-value problem are proved, and the continuity properties for its solution are examined. A numerical algorithm based on the Monte Carlo method for solving the boundary-value problem is proposed and proved.