Pereguda O. Qualitative analysis of the stochastic differential equations

In the dissertation the string of the conditions of a locally invariant set is determined. The conditions of existence and functional independence a locally first integrals of stochastic differential equations are established. The qualitative analysis for the homogeneous stochastic differential equations of the phase picture in the two-dimensional case is realized. The methods of construction of a classes of stochastic differential equations for which a given surface is a locally invariant set are produced. The behavior of the solutions of a classes stochastic differential equations for invariant surfaces are investigated.