Alexandrova O. The symmetry analysis of the Ito stochastic system.

The dissertation is devoted to applications of methods for symmetry analysis of the systems of Ito stochastic differential equations. In the dissertation the concept of one-parameter group of transformations on the system of Ito SDEs is generalized. Conditions on the coefficients of the CDS Ito, in which this system is invariant with respect to a given group of transformations are formulated. The governing equations to calculate the symmetry of the system of Ito SDEs and a theorem on the invariance of the CDS with respect to the Ito transformation are obtained. Conditions for the existence of the first integral for a system of Ito SDEs are proved.