{
  "id": "2107.11974",
  "version": "v1",
  "published": "2021-07-26T06:02:16.000Z",
  "updated": "2021-07-26T06:02:16.000Z",
  "title": "For which functions are $f(X_t)-\\mathbb{E} f(X_t)$ and $g(X_t)/\\,\\mathbb{E} g(X_t)$ martingales?",
  "authors": [
    "Franziska Kühn",
    "René L. Schilling"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $X=(X_t)_{t\\geq 0}$ be a one-dimensional L\\'evy process such that each $X_t$ has a $C^1_b$-density w.r.t. Lebesgue measure and certain polynomial or exponential moments. We characterize all polynomially bounded functions $f:\\mathbb{R}\\to\\mathbb{R}$, and exponentially bounded functions $g:\\mathbb{R}\\to (0,\\infty)$, such that $f(X_t)-\\mathbb{E} f(X_t)$, resp. $g(X_t)/\\mathbb{E} g(X_t)$, are martingales.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-26T06:02:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G44",
      "60G51",
      "60J65",
      "39B22",
      "45E10"
    ],
    "keywords": [
      "martingales",
      "one-dimensional levy process",
      "lebesgue measure",
      "exponential moments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}