Construction of an analytic solution for one class of Langevin-type equations with orthogonal random actions

Abstract

We find an analytic representation of a solution of the Itô-Langevin equations in R ³ with orthogonal random actions with respect to the vector of the solution. We construct a stochastic process to which the integral of the solution weakly converges as a small positive parameter with the derivative in the equation tends to zero.