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The W-transform in stability analysis for stochastic linear functional difference equations. (English) Zbl 1248.93168
Summary: 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.

93E15 Stochastic stability in control theory
93C05 Linear systems in control theory
39A06 Linear difference equations
Full Text: DOI
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