{
  "id": "2109.07126",
  "version": "v1",
  "published": "2021-09-15T07:18:54.000Z",
  "updated": "2021-09-15T07:18:54.000Z",
  "title": "Limit theorems for Hawkes processes including inhibition",
  "authors": [
    "Patrick Cattiaux",
    "Laetitia Colombani",
    "Manon Costa"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we consider some non linear Hawkes processes with signed reproduction function (or memory kernel) thus exhibiting both self-excitation and inhibition. We provide a Law of Large Numbers, a Central Limit Theorem and large deviation results, as time growths to infinity. The proofs lie on a renewal structure for these processes introduced in Costa et al. (2020) which leads to a comparison with cumulative processes. Explicit computations are made on some examples. Similar results have been obtained in the literature for self-exciting Hawkes processes only.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-15T07:18:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G55",
      "60F05",
      "60K15"
    ],
    "keywords": [
      "inhibition",
      "non linear hawkes processes",
      "large deviation results",
      "central limit theorem",
      "explicit computations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}