Statistics of Stokes variables for correlated Gaussian fields

The joint and marginal probability distribution functions of the Stokes variables are derived for correlated Gaussian fields [an extension of D. Eliyahu, Phys. Rev. E 47, 2881 (1993)]. The statistics depend only on the first moment (averaged) Stokes variables and have a universal form for ${\mathit{S}}_1$, ${\mathit{S}}_2$, and ${\mathit{S}}_3$. The statistics of the variables describing the Cartesian coordinates of the Poincaré sphere are given also.