Advanced Studies in Pure Mathematics

On asymptotic stability of linear stochastic Volterra difference equations with respect to a fading perturbation

John A. D. Appleby, Markus Riedle, and Alexandra Rodkina

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Abstract

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.

Article information

Source
Advances in Discrete Dynamical Systems, S. Elaydi, K. Nishimura, M. Shishikura and N. Tose, eds. (Tokyo: Mathematical Society of Japan, 2009), 271-282

Dates
Received: 12 October 2007
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543447660

Digital Object Identifier
doi:10.2969/aspm/05310271

Mathematical Reviews number (MathSciNet)
MR2582424

Zentralblatt MATH identifier
1179.39025

Keywords
Volterra difference equation stochastic Volterra difference equation resolvent almost sure asymptotic stability

Citation

Appleby, John A. D.; Riedle, Markus; Rodkina, Alexandra. On asymptotic stability of linear stochastic Volterra difference equations with respect to a fading perturbation. Advances in Discrete Dynamical Systems, 271--282, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05310271. https://projecteuclid.org/euclid.aspm/1543447660


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