  We present a new model for the propagation of polarized light in a random
birefringent medium. This model is based on a decomposition of the higher order
statistics of the reduced Stokes parameters along the irreducible
representations of the rotation group. We show how this model allows a detailed
description of the propagation, giving analytical expressions for the
probability densities of the Mueller matrix and the Stokes vector throughout
the propagation. It also allows an exact description of the evolution of
averaged quantities, such as the degree of polarization. We will also discuss
how this model allows a generalization of the concepts of reduced Stokes
parameters and degree of polarization to higher order statistics. We give some
notes on how it can be extended to more general random media.
