A study of turbulent diffusion has led to a stochastic process stationary in time, but spatially variable, which is defined only by local specific rates of generation of zeroth, first and second moments. An analysis, based on appropriate integrations by parts, establishes the connection between the local specific rates of generation of various moments and the (spatially variable) coefficients of an associated trial partial differential equation. It is thus shown that the given process is correctly modeled by a spatially variable Fokker-Planck equation. The analysis is simply extended to yield the general result that a process defined by local specific rates of generation of zeroth to nth moments can be correctly modeled by an equation of first order in time and nth order in the space variables.