{
  "id": "2009.10698",
  "version": "v1",
  "published": "2020-09-22T17:17:47.000Z",
  "updated": "2020-09-22T17:17:47.000Z",
  "title": "Limit Theorems for Trawl Processes",
  "authors": [
    "Mikko S. Pakkanen",
    "Riccardo Passeggeri",
    "Orimar Sauri",
    "Almut E. D. Veraart"
  ],
  "comment": "35 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this work we derive limit theorems for trawl processes. First,we study the asymptotic behaviour of the partial sums of the discretized trawl process $(X_{i\\Delta_{n}})_{i=0}^{\\lfloor nt\\rfloor-1}$, under the assumption that as $n\\uparrow\\infty$, $\\Delta_{n}\\downarrow0$ and $n\\Delta_{n}\\rightarrow\\mu\\in[0,+\\infty]$. Second, we derive a functional limit theorem for trawl processes as the L\\'{e}vy measure of the trawl seed grows to infinity and show that the limiting process has a Gaussian moving average representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-22T17:17:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional limit theorem",
      "gaussian moving average representation",
      "derive limit theorems",
      "discretized trawl process",
      "asymptotic behaviour"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}