{
  "id": "1701.06630",
  "version": "v1",
  "published": "2017-01-23T21:03:28.000Z",
  "updated": "2017-01-23T21:03:28.000Z",
  "title": "Lévy Processes and Infinitely Divisible Measures in the Dual of a Nuclear Space",
  "authors": [
    "C. A. Fonseca-Mora"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let $\\Phi$ be a nuclear space and let $\\Phi'_{\\beta}$ denote its strong dual. In this work we establish the one-to-one correspondence between infinitely divisible measures on $\\Phi'_{\\beta}$ and L\\'{e}vy processes taking values in $\\Phi'_{\\beta}$. Moreover, we prove the L\\'{e}vy-It\\^{o} decomposition, the L\\'{e}vy-Khintchine formula and the existence of c\\`{a}dl\\`{a}g versions for $\\Phi'_{\\beta}$-valued L\\'{e}vy processes. A characterization for L\\'{e}vy measures on $\\Phi'_{\\beta}$ is also established. Finally, we prove the L\\'{e}vy-Khintchine formula for infinitely divisible measures on $\\Phi'_{\\beta}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-23T21:03:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinitely divisible measures",
      "nuclear space",
      "lévy processes",
      "strong dual",
      "one-to-one correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}