{
  "id": "2009.14672",
  "version": "v1",
  "published": "2020-09-30T13:52:22.000Z",
  "updated": "2020-09-30T13:52:22.000Z",
  "title": "A generalisation of the Burkholder-Davis-Gundy inequalities",
  "authors": [
    "Saul Jacka",
    "Ma. Elena Hérnandez-Hérnandez"
  ],
  "comment": "6 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider a c\\'adl\\'ag local martingale $M$ with square brackets $[M]$. In this paper, we provide lower and upper bounds for expectations of the type $E [M]^{q/2}_{\\tau}$, for any stopping time $\\tau$ and $q\\ge 2$. This result is a Burkholder-Davis-Gundy-type inequality as it relates the expectation of the running maximum $|M^*|^q$ to the expectation of the dual previsible projections of the relevant powers of the associated jumps of $M$. The case of convex moderate functions is also treated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-30T13:52:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G07",
      "60H05"
    ],
    "keywords": [
      "burkholder-davis-gundy inequalities",
      "generalisation",
      "cadlag local martingale",
      "convex moderate functions",
      "expectation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}