{
  "id": "1403.2214",
  "version": "v1",
  "published": "2014-03-10T11:40:09.000Z",
  "updated": "2014-03-10T11:40:09.000Z",
  "title": "Integrability of solutions of the Skorokhod Embedding Problem for Diffusions",
  "authors": [
    "David Hobson"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Suppose $X$ is a time-homogeneous diffusion on an interval $I^X \\subseteq \\mathbb R$ and let $\\mu$ be a probability measure on $I^X$. Then $\\tau$ is a solution of the Skorokhod embedding problem (SEP) for $\\mu$ in $X$ if $\\tau$ is a stopping time and $X_\\tau \\sim \\mu$. There are well-known conditions which determine whether there exists a solution of the SEP for $\\mu$ in $X$. We give necessary and sufficient conditions for there to exist an integrable solution. Further, if there exists a solution of the SEP then there exists a minimal solution. We show that every minimal solution of the SEP has the same first moment. When $X$ is Brownian motion, every integrable embedding of $\\mu$ is minimal. However, for a general diffusion there may be integrable embeddings which are not minimal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-10T11:40:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G40",
      "60G44",
      "60J60"
    ],
    "keywords": [
      "skorokhod embedding problem",
      "minimal solution",
      "integrability",
      "probability measure",
      "sufficient conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1403.2214H"
    }
  }
}