{
  "id": "2301.07585",
  "version": "v1",
  "published": "2023-01-18T15:02:24.000Z",
  "updated": "2023-01-18T15:02:24.000Z",
  "title": "Large deviations for the mean-field limit of Hawkes processes",
  "authors": [
    "Fuqing Gao",
    "Lingjiong Zhu"
  ],
  "comment": "34 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Hawkes processes are a class of simple point processes whose intensity depends on the past history, and is in general non-Markovian. Limit theorems for Hawkes processes in various asymptotic regimes have been studied in the literature. In this paper, we study a multidimensional nonlinear Hawkes process in the asymptotic regime when the dimension goes to infinity, whose mean-field limit is a time-inhomogeneous Poisson process, and our main result is a large deviation principle for the mean-field limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-18T15:02:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean-field limit",
      "multidimensional nonlinear hawkes process",
      "asymptotic regime",
      "simple point processes",
      "large deviation principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}