Moment Equations for Waves Propagated in Random Media*

We show that the partial differential equations obtained by Tatarski, Beran, and Ho for the first, second, and fourth statistical moments of a wave propagating in a random medium are special cases of a general partial differential equation satisfied by the mth moment when the refractive-index inhomogeneities are sufficiently weak. In addition, we derive moment equations that apply regardless of the strength of the inhomogeneities. The results obtained in this case are in the form of difference relations satisfied for the moments.