{
  "id": "1312.1624",
  "version": "v3",
  "published": "2013-12-05T17:26:07.000Z",
  "updated": "2014-07-07T07:40:26.000Z",
  "title": "Measurability of Semimartingale Characteristics with Respect to the Probability Law",
  "authors": [
    "Ariel Neufeld",
    "Marcel Nutz"
  ],
  "comment": "37 pages; forthcoming in 'Stochastic Processes and their Applications'",
  "categories": [
    "math.PR",
    "math.OC"
  ],
  "abstract": "Given a c\\`adl\\`ag process $X$ on a filtered measurable space, we construct a version of its semimartingale characteristics which is measurable with respect to the underlying probability law. More precisely, let $\\mathfrak{P}_{sem}$ be the set of all probability measures $P$ under which $X$ is a semimartingale. We construct processes $(B^P,C,\\nu^P)$ which are jointly measurable in time, space, and the probability law $P$, and are versions of the semimartingale characteristics of $X$ under $P$ for each $P\\in\\mathfrak{P}_{sem}$. This result gives a general and unifying answer to measurability questions that arise in the context of quasi-sure analysis and stochastic control under the weak formulation.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-07T07:40:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G44",
      "93E20"
    ],
    "keywords": [
      "semimartingale characteristics",
      "weak formulation",
      "stochastic control",
      "quasi-sure analysis",
      "measurability questions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.1624N"
    }
  }
}