On asymptotic stability of linear stochastic Volterra difference equations with respect to a fading perturbation

Abstract

The paper concerns necessary and sufficient conditions on the fading intensity of a state–independent stochastic perturbation for the asymptotic stability of a linear stochastic Volterra difference equation. In broad terms, it is shown here that the results obtained in the deterministic case are robust to fading stochastic perturbations which are independent of the state, once it is known that these perturbations fade more rapidly than an identifiable critical rate.