{
  "id": "1209.4217",
  "version": "v2",
  "published": "2012-09-19T12:00:45.000Z",
  "updated": "2013-05-21T13:32:29.000Z",
  "title": "A Generalised Gangolli-Levy-Khintchine Formula for Infinitely Divisible Measures and Levy Processes on Semi-Simple Lie Groups and Symmetric Spaces",
  "authors": [
    "David Applebaum",
    "Anthony Dooley"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In 1964 R.Gangolli published a L\\'{e}vy-Khintchine type formula which characterised $K$ bi-invariant infinitely divisible probability measures on a symmetric space $G/K$. His main tool was Harish-Chandra's spherical functions which he used to construct a generalisation of the Fourier transform of a measure. In this paper we use generalised spherical functions (or Eisenstein integrals) and extensions of these which we construct using representation theory to obtain such a characterisation for arbitrary infinitely divisible probability measures on a non-compact symmetric space. We consider the example of hyperbolic space in some detail.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-21T13:32:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinitely divisible probability measures",
      "symmetric space",
      "semi-simple lie groups",
      "generalised gangolli-levy-khintchine formula",
      "infinitely divisible measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}