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VOL. 53 | 2009 On asymptotic stability of linear stochastic Volterra difference equations with respect to a fading perturbation
John A. D. Appleby, Markus Riedle, Alexandra Rodkina

Editor(s) Saber Elaydi, Kazuo Nishimura, Mitsuhiro Shishikura, Nobuyuki Tose


The paper concerns necessary and sufficient conditions on the fading intensity of a state–independent stochastic perturbation for the asymptotic stability of a linear stochastic Volterra difference equation. In broad terms, it is shown here that the results obtained in the deterministic case are robust to fading stochastic perturbations which are independent of the state, once it is known that these perturbations fade more rapidly than an identifiable critical rate.


Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1179.39025
MathSciNet: MR2582424

Digital Object Identifier: 10.2969/aspm/05310271

Keywords: Almost sure asymptotic stability , resolvent , Stochastic Volterra difference equation , Volterra difference equation

Rights: Copyright © 2009 Mathematical Society of Japan


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