{
  "id": "math/0501014",
  "version": "v1",
  "published": "2005-01-02T07:43:13.000Z",
  "updated": "2005-01-02T07:43:13.000Z",
  "title": "Stability Properties of Constrained Jump-Diffusion Processes",
  "authors": [
    "Rami Atar",
    "Amarjit Budhiraja"
  ],
  "journal": "Electronic Journal of Probability, Vol. 7, paper 22, p. 1-31 (2002)",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a class of jump-diffusion processes, constrained to a polyhedral cone $G\\subset\\R^n$, where the constraint vector field is constant on each face of the boundary. The constraining mechanism corrects for ``attempts'' of the process to jump outside the domain. Under Lipschitz continuity of the Skorohod map \\Gamma, it is known that there is a cone \\mathcalC such that the image \\Gamma\\phi of a deterministic linear trajectory \\phi remains bounded if and only if \\dot\\phi\\in\\mathcalC. Denoting the generator of a corresponding unconstrained jump-diffusion by \\cll, we show that a key condition for the process to admit an invariant probability measure is that for x\\in G, \\cll \\id(x) belongs to a compact subset of \\mathcalC^o.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-02T07:43:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J75",
      "34D20",
      "60K25"
    ],
    "keywords": [
      "constrained jump-diffusion processes",
      "stability properties",
      "constraint vector field",
      "deterministic linear trajectory",
      "invariant probability measure"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}