{
  "id": "1201.5867",
  "version": "v1",
  "published": "2012-01-27T19:16:53.000Z",
  "updated": "2012-01-27T19:16:53.000Z",
  "title": "Wiener-Hopf factorization for a family of Levy processes related to theta functions",
  "authors": [
    "Alexey Kuznetsov"
  ],
  "comment": "12 pages, published online at http://projecteuclid.org/euclid.jap/1294170516",
  "journal": "J. Appl. Probab. Volume 47, Number 4 (2010), 1023-1033",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we study the Wiener-Hopf factorization for a class of L\\'evy processes with double-sided jumps, characterized by the fact that the density of the L\\'evy measure is given by an infinite series of exponential functions with positive coefficients. We express the Wiener-Hopf factors as infinite products over roots of a certain transcendental equation, and provide a series representation for the distribution of the supremum/infimum process evaluated at an independent exponential time. We also introduce five eight-parameter families of L\\'evy processes, defined by the fact that the density of the L\\'evy measure is a (fractional) derivative of the theta-function, and we show that these processes can have a wide range of behavior of small jumps. These families of processes are of particular interest for applications, since the characteristic exponent has a simple expression, which allows efficient numerical computation of the Wiener-Hopf factors and distributions of various functionals of the process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-01-27T19:16:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G51",
      "60E10"
    ],
    "keywords": [
      "wiener-hopf factorization",
      "levy processes",
      "theta functions",
      "levy measure",
      "wiener-hopf factors"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1201.5867K"
    }
  }
}