Perturbation method in the theory of kinetic equations

Including in the definitions of correlation functions singular corrections that describe “self-correlations”, it is possible to find a rigorous, almost trivial solution of the complete BBGKY hierarchy for a system of charged particles corresponding to motion of them in a self-consistent field. Study of the averaged small deviations from this motion makes it possible to construct a scheme of successive approximations. In this manner, an expansion is obtained for the single-particle distribution function which is equivalent to a generalization of Grad's moment method to the phase space. In the first order of perturbation theory, an approximate Lenard–Balescu equation that differs from the result of its direct linearization is obtained. The proposed approach makes possible a more consistent approximate treatment of statistical systems.