{
  "id": "1612.00498",
  "version": "v1",
  "published": "2016-12-01T22:21:27.000Z",
  "updated": "2016-12-01T22:21:27.000Z",
  "title": "Pathwise Stieltjes integrals of discontinuously evaluated stochastic processes",
  "authors": [
    "Zhe Chen",
    "Lasse Leskelä",
    "Lauri Viitasaari"
  ],
  "comment": "35 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this article we study the existence of pathwise Stieltjes integrals of the form $\\int f(X_t)\\, dY_t$ for nonrandom, possibly discontinuous, evaluation functions $f$ and H\\\"older continuous random processes $X$ and $Y$. We discuss a notion of sufficient variability for the process $X$ which ensures that the paths of the composite process $t \\mapsto f(X_t)$ are almost surely regular enough to be integrable. We show that the pathwise integral can be defined as a limit of Riemann-Stieltjes sums for a large class of discontinuous evaluation functions of locally finite variation, and provide new estimates on the accuracy of numerical approximations of such integrals, together with a change of variables formula for integrals of the form $\\int f(X_t) \\, dX_t$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-01T22:21:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H05",
      "60G22",
      "26A33",
      "60G07",
      "60G15"
    ],
    "keywords": [
      "discontinuously evaluated stochastic processes",
      "pathwise stieltjes integrals",
      "continuous random processes",
      "sufficient variability",
      "variables formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}