Theory of Brownian motion in Bogolyubov's method of abbreviated description

On the basis of N. N. Bogoliubov's idea about the reduced description of dynamical systems, the brownian motion in the equilibriun medium on the kinetic and hydrodynamic stages of the evolution is considered. Integral equations are derived which make it possible to evaluate the nonequilibrium distribution function in the perturbation theory with respect to the small ratio $\mu$ of masses of particles of the medium and brownian particles or to the interaction between these particles. Corresponding kinetic equations are constructed, up to the terms of the order $\mu^3$, in the case $\mu\ll 1$. This makes it possible determine the correction to the Einstein expression for the diffusion coefficient, in the investigation of the process of diffusion of the brownian particle.