Asymptotic Moment Stability of Solutions to Systems of Nonlinear Differential Itô Equations with Aftereffect

The paper studies the global moment stability of systems of nonlinear Itô differential equations with delays. The analysis is done by a modified regularization method, known as the W-method, and based on the use of some auxiliary equation with subsequent application of the theory of positively invertible matrices. Sufficient conditions for the global asymptotic moment stability for both sufficiently general and specific systems of Itô equations formulated in terms of parameters of these systems are given. Connections between this stability and the properties of the delay functions are established.