By using the method of Lyapunov functions, we establish sufficient conditions of stability and asymptotic stability in
probability for the integral manifold of the Itˆo differential equations in the presence of random perturbations from the class
of processes with independent increments. Theorems on the stochastic stability of the analytically given integral manifold
of differential equations are proved in the first approximation and under the permanent action of small (in the mean) random
Citation Example:Tleubergenov M. I., Vasilina G. K. On the solution of the problem of stochastic stability of the integral manifold by the Lyapunov’s second method // Ukr. Mat. Zh. - 2016. - 68, № 1. - pp. 14-27.