{
  "id": "1011.2331",
  "version": "v4",
  "published": "2010-11-10T10:06:46.000Z",
  "updated": "2013-12-11T07:12:25.000Z",
  "title": "Intertwining and commutation relations for birth-death processes",
  "authors": [
    "Djalil Chafaï",
    "Aldéric Joulin"
  ],
  "comment": "Published in at http://dx.doi.org/10.3150/12-BEJ433 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)",
  "journal": "Bernoulli 2013, Vol. 19, No. 5A, 1855-1879",
  "doi": "10.3150/12-BEJ433",
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Given a birth-death process on $\\mathbb {N}$ with semigroup $(P_t)_{t\\geq0}$ and a discrete gradient ${\\partial}_u$ depending on a positive weight $u$, we establish intertwining relations of the form ${\\partial}_uP_t=Q_t\\,{\\partial}_u$, where $(Q_t)_{t\\geq0}$ is the Feynman-Kac semigroup with potential $V_u$ of another birth-death process. We provide applications when $V_u$ is nonnegative and uniformly bounded from below, including Lipschitz contraction and Wasserstein curvature, various functional inequalities, and stochastic orderings. Our analysis is naturally connected to the previous works of Caputo-Dai Pra-Posta and of Chen on birth-death processes. The proofs are remarkably simple and rely on interpolation, commutation, and convexity.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-12-11T07:12:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "birth-death processes",
      "commutation relations",
      "intertwining",
      "caputo-dai pra-posta",
      "discrete gradient"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.2331C"
    }
  }
}