Mean square asymptotic stability characterisation of perturbed linear stochastic functional differential equations
Probability
2023-06-19 v3 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2304.08161,
title = {Mean square asymptotic stability characterisation of perturbed linear stochastic functional differential equations},
author = {John Appleby and Emmet Lawless},
journal= {arXiv preprint arXiv:2304.08161},
year = {2023}
}
Comments
36 pages, to appear in Applied Numerical Mathematics as part of the conference proceedings for FAATNA (Functional Analysis, Approximation Theory and Numerical Analysis), Matera Italy, July 2022