Appleby, John A.D. and Lawless, Emmet (2024) Mean square asymptotic stability characterisation of perturbed linear stochastic functional differential equations. Applied Numerical Mathematics, 200 . pp. 80-109. ISSN 1873-5460
Abstract
In this paper we investigate the mean square asymptotic stability of a perturbed scalar linear stochastic functional differential equation. Specifically, we are able to give necessary and sufficient conditions on the forcing terms for convergence of the mean square, exponential convergence of the mean square, and integrability of the mean square of solutions. It is also essential that the underlying unperturbed SFDE is mean–square asymptotically stable for these results to hold.
Metadata
| Item Type: | Article (Published) |
|---|---|
| Refereed: | Yes |
| Uncontrolled Keywords: | Perturbed stochastic functional differential equation; Mean-square asymptotic stability; Mean square exponential asymptotic stability; Asymptotic behaviour; Stochastic functional differential equation; Volterra equations |
| Subjects: | Mathematics Mathematics > Mathematical analysis |
| DCU Faculties and Centres: | DCU Faculties and Schools > Faculty of Science and Health DCU Faculties and Schools > Faculty of Science and Health > School of Mathematical Sciences |
| Publisher: | Elsevier BV * North-Holland |
| Official URL: | https://www.sciencedirect.com/science/article/pii/... |
| Copyright Information: | Authors |
| ID Code: | 31261 |
| Deposited On: | 17 Jul 2025 11:02 by Vidatum Academic . Last Modified 17 Jul 2025 11:02 |
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