Exterior Differential Systems of stochastic Dynamic

Abstract

In article geometry of stochastic differential equations is considered. Based correlation relations for the mean of the Wiener process an extension of the Cartan distributions is proposed. In spite of features intertwining independent variables this distribution admits existence of Lie’s fields and their lifts. Geometric formulation of problem of the variations calculus involves the Cartan distributions as nonholonomic connection and introduction of a differential 1-form of momentum as the Lagrange multiplier. On the basis of this the Euler – Lagrange equation that realizing the Ito equation as an extremal of some functional was obtained in the work, as well as the system of Jacobi equations in Hamiltonian form.