The W-transform in stability analysis for stochastic linear functional difference equations

We apply the method of integral transforms to study stability properties of rather general linear functional difference equations of Itô-type. This approach called “the W-method” is based on integral transforms coming from auxiliary equations that already possess the desired asymptotic properties. Some sufficient conditions for different kinds of stability are found in this way. A general framework is offered as well that can be used to study asymptotic properties of other classes of stochastic difference equations.