{
  "id": "1606.03186",
  "version": "v1",
  "published": "2016-06-10T05:43:42.000Z",
  "updated": "2016-06-10T05:43:42.000Z",
  "title": "Projecting the distribution of planar Browian motion at a stopping time through an analytic function",
  "authors": [
    "Greg Markowsky"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "A method is given of deriving the distribution of planar Brownian motion evaluated at certain stopping times using analytic functions. This method relies upon a generalization of the standard conformal invariance of harmonic measure. A number of examples are given, including several in which the stopping time in question is not the exit time of a domain. It is also shown how appropriate choices of domains and stopping times can lead to new proofs of identities, including Euler's Basel sum and the Fourier transform for cosecant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-10T05:43:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "30A99"
    ],
    "keywords": [
      "stopping time",
      "planar browian motion",
      "analytic function",
      "distribution",
      "planar brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}