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Stochastic processes described by evolution equations in the universalityclass of the FKPP equation may be approximately factorized into a linearstochastic part and a nonlinear deterministic part. We prove this factorizationon a model with no spatial dimensions and we illustrate it numerically on aone-dimensional toy model that possesses some of the main features of highenergy QCD evolution. We explain how this procedure may be applied to QCDamplitudes, by combining Salam's Monte-Carlo implementation of the dipole modeland a numerical solution of the Balitsky-Kovchegov equation.Comment: 9 pages. v2: Eq.(4) corrected, numerics improved, various clarifying  comments added. Conclusions unchanged. v3: comments and references added,  many misprints fixe

Dense-dilute factorization for a class of stochastic processes and for high energy QCD