{
  "id": "1906.01208",
  "version": "v1",
  "published": "2019-06-04T05:55:52.000Z",
  "updated": "2019-06-04T05:55:52.000Z",
  "title": "Martingale Representation in the Enlargement of the Filtration Generated by a Point Process",
  "authors": [
    "Paolo Di Tella",
    "Monique Jeanblanc"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $X$ be a point process and let $\\mathbb{X}$ denote the filtration generated by $X$. In this paper we study the martingale representation in the filtration $\\mathbb{G}$ obtained as an initial and progressive enlargement of the filtration $\\mathbb{X}$. In particular, the progressive enlargement is done by means of a whole point process $H$. We work here in full generality, without requiring any further assumption on the point process $H$ and we recover the special case in which $\\mathbb{X}$ is enlarged progressively by a random time $\\tau$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-04T05:55:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "point process",
      "martingale representation",
      "filtration",
      "progressive enlargement",
      "full generality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}