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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.

MSC:
93E15 Stochastic stability in control theory
93C05 Linear systems in control theory
39A06 Linear difference equations
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