{
  "id": "2207.08422",
  "version": "v1",
  "published": "2022-07-18T08:13:41.000Z",
  "updated": "2022-07-18T08:13:41.000Z",
  "title": "On the Wiener Chaos Expansion of the Signature of a Gaussian Process",
  "authors": [
    "Emilio Rossi Ferrucci",
    "Thomas Cass"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We compute the Wiener chaos decomposition of the signature for a class of Gaussian processes, which contains fractional Brownian motion (fBm) with Hurst parameter H in (1/4, 1). At level 0, our result yields an expression for the expected signature of such processes, which determine their law [CL16]. In particular, this formula simultaneously extends both the one for 1/2 < H-fBm [BC07] and the one for Brownian motion (H = 1/2) [Faw03], to the general case H > 1/4, thereby resolving an established open problem. Other processes studied include continuous and centred Gaussian semimartingales.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-18T08:13:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60L10",
      "60H07"
    ],
    "keywords": [
      "wiener chaos expansion",
      "gaussian process",
      "contains fractional brownian motion",
      "wiener chaos decomposition",
      "result yields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}