{
  "id": "1211.4039",
  "version": "v3",
  "published": "2012-11-16T21:16:13.000Z",
  "updated": "2015-02-26T00:40:58.000Z",
  "title": "Limit Theorems for Marked Hawkes Processes with Application to a Risk Model",
  "authors": [
    "Dmytro Karabash",
    "Lingjiong Zhu"
  ],
  "comment": "14 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper focuses on limit theorems for linear Hawkes processes with random marks. We prove a large deviation principle, which answers the question raised by Bordenave and Torrisi. A central limit theorem is also obtained. We conclude with an example of application in finance.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-26T01:54:15.000Z",
      "comment": "15 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-02-26T00:40:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G55",
      "60F10",
      "60F05"
    ],
    "keywords": [
      "marked hawkes processes",
      "risk model",
      "application",
      "linear hawkes processes",
      "large deviation principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.4039K"
    }
  }
}