Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Advances in Discrete Dynamical Systems, S. Elaydi, K. Nishimura, M. Shishikura and N. Tose, eds. (Tokyo: Mathematical Society of Japan, 2009), 271 - 282
On asymptotic stability of linear stochastic Volterra difference equations with respect to a fading perturbation
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.
Received: 12 October 2007
First available in Project Euclid: 28 November 2018
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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