Abstract
Stochastic variational expressions are derived for the statistical moments of the vector scattering amplitude for scatterers with arbitrary linear electric and magnetic properties. This requires determination of the adjoint of the dyadic differential operator that characterizes the scatterers. The adjoint operator is presented in explicit form and is discussed in some detail. This formulation extends the vector stochastic variational principle to include electromagnetic plane wave scattering from random objects and surfaces with generally inhomogeneous and anisotropic permeability, permittivity, and conductivity. These invariant formulations appear as ratios of averages of volume integrals involving the fields within the scatterers. They are inherently simpler to evaluate than direct averages of the deterministic variational expressions that involve averages of ratios of these integrals.
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