Conditional probability calculations for the nonlinear Schrödinger equation with additive noise

Abstract: The method for computation of conditional probability density function for the nonlinear Schr\"odinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of a small noise and analytically derive it in a weakly nonlinear case. The general theory results are illustrated using fibre-optic communications as a particular, albeit practically very important, example.