{
  "id": "2304.08161",
  "version": "v1",
  "published": "2023-04-17T11:19:19.000Z",
  "updated": "2023-04-17T11:19:19.000Z",
  "title": "Mean square asymptotic stability characterisation of perturbed linear stochastic functional differential equations",
  "authors": [
    "John Appleby",
    "Emmet Lawless"
  ],
  "comment": "To be published in Applied Numerical Mathematics as part of the conference proceedings for FAATNA (Functional Analysis, Approximation Theory and Numerical Analysis), Matera Italy, July 2022",
  "categories": [
    "math.PR",
    "math.DS"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-17T11:19:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H20",
      "60H10",
      "34K50",
      "34K20",
      "34K27"
    ],
    "keywords": [
      "linear stochastic functional differential equation",
      "mean square asymptotic stability characterisation",
      "perturbed linear stochastic functional differential"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}