  We suggest a new derivation of a kinetic equation of Kolmogorov-Zakharov (KZ)
type for the spectrum of the weakly nonlinear Schr\"odinger equation with
stochastic forcing. The kynetic equation is obtained as a result of a double
limiting procedure. Firstly, we consider the equation on a finite box with
periodic boundary conditions and send the size of the nonlinearity and of the
forcing to zero, while the time is correspondingly rescaled; then, the size of
the box is sent to infinity (with a suitable rescaling of the solution). We
report here the results of the first limiting procedure, analyzed with full
rigour in arXiv:1311.6793, and show how the second limit leads to a kinetic
equation for the spectrum, if some further hypotheses (commonly employed in the
weak turbulence theory) are accepted. Finally we show how to derive from these
equations the KZ spectra.
