{
  "id": "math/0510208",
  "version": "v2",
  "published": "2005-10-11T01:35:36.000Z",
  "updated": "2008-04-21T11:13:32.000Z",
  "title": "The bi-Poisson process: a quadratic harness",
  "authors": [
    "Włodzimierz Bryc",
    "Wojciech Matysiak",
    "Jacek Wesołowski"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/009117907000000268 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2008, Vol. 36, No. 2, 623-646",
  "doi": "10.1214/009117907000000268",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper is a continuation of our previous research on quadratic harnesses, that is, processes with linear regressions and quadratic conditional variances. Our main result is a construction of a Markov process from given orthogonal and martingale polynomials. The construction uses a two-parameter extension of the Al-Salam--Chihara polynomials and a relation between these polynomials for different values of parameters.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-21T11:13:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25"
    ],
    "keywords": [
      "bi-poisson process",
      "quadratic conditional variances",
      "al-salam-chihara polynomials",
      "quadratic harnesses",
      "linear regressions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10208B"
    }
  }
}