{
  "id": "math/0511519",
  "version": "v2",
  "published": "2005-11-21T14:04:50.000Z",
  "updated": "2007-04-26T13:53:50.000Z",
  "title": "Exponential functionals of Brownian motion, II: Some related diffusion processes",
  "authors": [
    "Hiroyuki Matsumoto",
    "Marc Yor"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/154957805100000168 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Probability Surveys 2005, Vol. 2, 348-384",
  "doi": "10.1214/154957805100000168",
  "categories": [
    "math.PR"
  ],
  "abstract": "This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have been discussed in the first part. Pricing formula for call options for the Asian options, explicit expressions for the heat kernels on hyperbolic spaces, diffusion processes in random environments and extensions of L\\'{e}vy's and Pitman's theorems are discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-04-26T13:53:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60J60",
      "60H30"
    ],
    "keywords": [
      "exponential functionals",
      "related diffusion processes",
      "brownian motion",
      "first part",
      "pitmans theorems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11519M"
    }
  }
}