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

*(English)*Zbl 1248.93168Summary: 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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\textit{R. Kadiev} and \textit{A. Ponosov}, J. Math. Anal. Appl. 389, No. 2, 1239--1250 (2012; Zbl 1248.93168)

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