A preliminary account is given of an approximation method useful in the calculation of the ensemble mean value of a field subject to perturbation by, or interaction with, a stochastic field, where the stochastic field is characterized by its two-point (bilocal) autocorrelation function. The method consists of treating the perturbed field and quadratic terms in the perturbing field as statistically independent when they occur in a certain integral expression. This is called the hypothesis of local independence, and it amounts to regarding the stochastic field as having a negligible local effect on the perturbed field. Use of the method, according to a certain prescription given, results in an integrodifferential equation for the ensemble mean value of the randomly perturbed field. Dispersion relations are obtained with great facility through use of the method described.A diagrammatic representation is introduced which permits the visualization of the underlying processes of generalized scattering and which helps clarify the limitations of the hypothesis of local independence. Two examples are given: wave propagation in a medium with random scalar inhomogeneities, and turbulent diffusion.