{
  "id": "2009.11688",
  "version": "v1",
  "published": "2020-09-24T13:45:56.000Z",
  "updated": "2020-09-24T13:45:56.000Z",
  "title": "Fractional Ornstein-Uhlenbeck process with stochastic forcing and its applications",
  "authors": [
    "Giacomo Ascione",
    "Yuliya Mishura",
    "Enrica Pirozzi"
  ],
  "comment": "29 pages, 14 figures",
  "journal": "Methodol Comput Appl Probab (2019)",
  "doi": "10.1007/s11009-019-09748-y",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a fractional Ornstein-Uhlenbeck process involving a stochastic forcing term in the drift, as a solution of a linear stochastic differential equation driven by a fractional Brownian motion. For such process we specify mean and covariance functions, concentrating on their asymptotic behavior. This gives us a sort of short- or long-range dependence, under specified hypotheses on the covariance of the forcing process. Applications of this process in neuronal modeling are discussed, providing an example of a stochastic forcing term as a linear combination of Heaviside functions with random center. Simulation algorithms for the sample path of this process are finally given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-24T13:45:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G22",
      "60G15",
      "68U20"
    ],
    "keywords": [
      "fractional ornstein-uhlenbeck process",
      "linear stochastic differential equation driven",
      "applications",
      "stochastic forcing term",
      "fractional brownian motion"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}