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

Kadiev, Ramazan; Ponosov, Arcady

J. Math. Anal. Appl. 389, No. 2, 1239-1250 (2012).

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

Keywords:

stochastic difference equations; stability; admissibility

References:

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