Stability of solutions of systems of linear Itô difference equations with aftereffect with respect to the initial data (Q745260)

The paper deals with the vector linear Itô difference equation with aftereffect \[ x(s+1)=x(s) + \sum_{-\infty}^sA_1(s,j)x(j)h + \sum_{i=2}^m \sum_{j=-\infty}^sA_i(s,j)x(j)(B_i((s+1)h)-B_i(sh)),\;s\in \mathbb N_{+} \] \[ x(j) = \varphi (j),\;j<0. \] Sufficient conditions are given for the \(p\)- and \(2p\)-stability, asymptotic stability and exponential stability of the aforementioned system.