{
  "id": "2502.06983",
  "version": "v1",
  "published": "2025-02-10T19:22:25.000Z",
  "updated": "2025-02-10T19:22:25.000Z",
  "title": "Riemann-Skorohod and Stratonovich integrals for Gaussian processes",
  "authors": [
    "Yanghui Liu"
  ],
  "comment": "25",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we consider Skorohod and Stratonovich-type integrals in a general setting of Gaussian processes. We show that a conversion formula holds when the covariance functions of the Gaussian process are of finite $\\rho$-variation for $\\rho\\geq 1$ and that the diagonals of covariance functions are of finite $\\rho'$-variation for $\\rho'\\geq 1$ such that $\\frac{1}{\\rho'}+\\frac{1}{2\\rho}>1$. The difference between the two types of integrals is identified with a Young integral. We also show that the Skorohod integral is the limit of a $[\\rho]$-th order Skorohod-Riemann sum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-02-10T19:22:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H07",
      "60L20"
    ],
    "keywords": [
      "gaussian process",
      "stratonovich integrals",
      "riemann-skorohod",
      "covariance functions",
      "th order skorohod-riemann sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}