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

摘要

We apply the method of integral transforms to study stability properties of rather general linear functional difference equations of It?-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.