{
  "id": "2010.08284",
  "version": "v1",
  "published": "2020-10-16T10:21:17.000Z",
  "updated": "2020-10-16T10:21:17.000Z",
  "title": "On non-negative solutions of SDDEs with an application to CARMA processes",
  "authors": [
    "Mikkel Slot Nielsen",
    "Victor Rohde"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This note provides a simple sufficient condition ensuring that solutions of stochastic delay differential equations (SDDEs) driven by subordinators are non-negative. While, to the best of our knowledge, no simple non-negativity conditions are available in the context of SDDEs, we compare our result to the literature within the subclass of invertible continuous-time ARMA (CARMA) processes. In particular, we analyze why our condition cannot be necessary for CARMA($p,q$) processes when $p=2$, and we show that there are various situations where our condition applies while existing results do not as soon as $p\\geq 3$. Finally, we extend the result to a multidimensional setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-16T10:21:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G10",
      "60G17",
      "60H05",
      "60H10"
    ],
    "keywords": [
      "carma processes",
      "non-negative solutions",
      "application",
      "stochastic delay differential equations",
      "simple non-negativity conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}