An equation of the Kolmogorov–Feller type in a factorized probability space

Calculations of probabilities are considered in the products of separable probability spaces, factored with respect to the permutation group of factors, by means of the trace operation with respect to the symmetric and antisymmetric orthonormal bases. A nonlinear Kolmogorov–Feller type equation is deduced which is the image of the forward linear Kolmogorov–Feller equation under factorization of the initial probability space with respect to the permutation group with certain rules of superselection.