  Kinetic equations are often appropriate to model the energy density of high
frequency waves propagating in highly heterogeneous media. The limitations of
the kinetic model are quantified by the statistical instability of the wave
energy density, i.e., by its sensitivity to changes in the realization of the
underlying heterogeneous medium modeled as a random medium. In the simplified
It\^o-Schr\"odinger regime of wave propagation, we obtain optimal estimates for
the statistical instability of the wave energy density for different
configurations of the source terms and the domains over which the energy
density is measured. We show that the energy density is asymptotically
statistically stable (self-averaging) in many configurations. In the case of
highly localized source terms, we obtain an explicit asymptotic expression for
the scintillation function in the high frequency limit.
