  The discrete self-trapping equation (DST) represents an useful model for
several properties of one-dimensional nonlinear molecular crystals. The
modulational instability of DST equation is discussed from a statistical point
of view, considering the oscillator amplitude as a random variable. A kinetic
equation for the two-point correlation function is written down, and its linear
stability is studied. Both a Gaussian and a Lorentzian form for the initial
unperturbed wave spectrum are discussed. Comparison with the continuum limit
(NLS equation) is done.
