Partial Stability of Systems of Itô Linear Delay Differential Equations

Abstract

We study the moment stability of solutions in part of the variables with respect to the initial data for systems of Itô linear delay differential equations using a modified regularization method based on the choice of an auxiliary equation and an application of the theory of nonnegatively invertible matrices. For these systems, sufficient stability conditions are obtained in terms of nonnegative invertibility of matrices constructed from the parameters of these systems. The satisfiability of these conditions is verified for specific classes of systems of Itô linear equations with delay.