{
  "id": "1506.07659",
  "version": "v1",
  "published": "2015-06-25T08:14:11.000Z",
  "updated": "2015-06-25T08:14:11.000Z",
  "title": "Multiplicative ergodicity of Laplace transforms for additive functional of Markov chains",
  "authors": [
    "Loïc Hervé",
    "Françoise Pène"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We study properties of the Laplace transforms of non-negative additive func-tionals of Markov chains. We are namely interested in a multiplicative ergodicity property used in [16] to study bifurcating processes with ancestral dependence. We develop a general approach based on the use of the operator perturbation method. We apply our general results to two examples of Markov chains, including a linear autoregressive model. In these two examples the operator-type assumptions reduce to some expected finite moment conditions on the functional (no exponential moment conditions are assumed in this work).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-25T08:14:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "markov chains",
      "laplace transforms",
      "multiplicative ergodicity",
      "additive functional",
      "exponential moment conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150607659H"
    }
  }
}