Wave propagation in a random medium: a complete set of the moment equations with different wavenumbers

Propagation of waves in a random medium is studied under the ``quasioptics'' and the ``Markov random process'' approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of the moment equations with different transverse coordinates and different wavenumbers is then obtained from the Fokker-Planck equation of the characteristic functional. The applications of our results to the pulse smearing of the pulsar signal and the frequency correlation function of the wave intensity in interstellar scintillation are briefly discussed.