The Nn Bogolyubov Method Of Averaging For Stochastic Differential Equations

The author formulates a theorem substantiating the use of the averaging method to determine to a first approximation the mathematical expectations for the solution of equations in a standard form with right-hand parts represented by random functions of time. The statement and proof of the theorem are analogous to those of the theorem of N.N. Bogolyubov which estimates the error of a first approximation derived with the aid of asymptotic methods for a finite interval of time. (Author).