{
  "id": "1412.3771",
  "version": "v1",
  "published": "2014-12-11T19:32:41.000Z",
  "updated": "2014-12-11T19:32:41.000Z",
  "title": "Asymptotics for a Class of Self-Exciting Point Processes",
  "authors": [
    "Tzu-Wei Yang",
    "Lingjiong Zhu"
  ],
  "comment": "35 pages, 9 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study a class of self-exciting point processes. The intensity of the point process has a nonlinear dependence on the past history and time. When a new jump occurs, the intensity increases and we expect more jumps to come. Otherwise, the intensity decays. The model is a marriage between stochasticity and dynamical system. In the short-term, stochasticity plays a major role and in the long-term, dynamical system governs the limiting behavior of the system. We study the law of large numbers, central limit theorem, large deviations and asymptotics for the tail probabilities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-11T19:32:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-exciting point processes",
      "asymptotics",
      "central limit theorem",
      "jump occurs",
      "intensity increases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.3771Y"
    }
  }
}