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

Conditional probability calculations for the nonlinear Schr\"odinger equation with additive noise