Generalized solutions of Gibbs type for the Bogolyubov–Strel'tsova diffusion hierarchy

A generalized solution is constructed for the hierarchy of coupled diffusion equations for the sequence of correlation functions of interacting particles diffusing in a fluid. At the initial time, this solution is identical to Gibbs correlation functions. The solution is obtained in the form of a series in powers of the activity, and the series converges uniformly over a finite time interval.