{
  "id": "0909.1331",
  "version": "v1",
  "published": "2009-09-07T20:13:00.000Z",
  "updated": "2009-09-07T20:13:00.000Z",
  "title": "Fluctuations of Multi-Dimensional Kingman-LÉvy Processes",
  "authors": [
    "Thu Nguyen"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In the recent paper \\cite{Ng5} we have introduced a method of studying the multi-dimensional Kingman convolutions and their associated stochastic processes by embedding them into some multi-dimensional ordinary convolutions which allows to study multi-dimensional Bessel processes in terms of the cooresponding Brownian motions. Our further aim in this paper is to introduce k-dimensional Kingman-L\\'evy (KL) processes and prove some of their fluctuation properties which are analoguous to that of k-symmetric L\\'evy processes. In particular, the L\\'evy-It\\^o decomposition and the series representation of Rosi\\'nski type for k-dimensional KL-processes are obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-07T20:13:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B07",
      "60B11",
      "60B15",
      "60K99"
    ],
    "keywords": [
      "multi-dimensional kingman-lévy processes",
      "fluctuation",
      "study multi-dimensional bessel processes",
      "k-symmetric levy processes",
      "multi-dimensional kingman convolutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.1331N"
    }
  }
}