{
  "id": "2010.07752",
  "version": "v1",
  "published": "2020-10-15T13:51:46.000Z",
  "updated": "2020-10-15T13:51:46.000Z",
  "title": "A density property for stochastic processes",
  "authors": [
    "Riccardo Passeggeri"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider a class of probability distributions which is dense in the space of all probability distributions on $\\mathbb{R}^{d}$ with respect to weak convergence, for every $d\\in\\mathbb{N}$. Then, we construct various explicit classes of continuous (c\\'{a}dl\\'{a}g) processes which are dense in the space of all continuous (c\\'{a}dl\\'{a}g) processes with respect to convergence in distribution. This is motivated by the recent result that quasi-infinitely divisible (QID) distributions are dense when $d=1$. If this result is extended to any $d\\in\\mathbb{N}$, then our result will imply that QID processes are dense in both spaces of continuous and c\\'{a}dl\\'{a}g processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-15T13:51:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic processes",
      "density property",
      "probability distributions",
      "qid processes",
      "weak convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}