Stability of solutions of systems of linear Itô difference equations with aftereffect with respect to the initial data
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.
scientific article; zbMATH DE number 6493782