  We present exact analytical results for the statistics of nonlinear coupled
oscillators under the influence of additive white noise. We suggest a
perturbative approach for analysing the statistics of such systems under the
action of a deterministic perturbation, based on the exact expressions for
probability density functions for noise-driven oscillators. Using our
perturbation technique we show that our results can be applied to studying the
optical signal propagation in noisy fibres at (nearly) zero dispersion as well
as to weakly nonlinear lattice models with additive noise. The approach
proposed can account for a wide spectrum of physically meaningful perturbations
and is applicable to the case of large noise strength.
