{
  "id": "1909.05396",
  "version": "v1",
  "published": "2019-09-11T22:23:45.000Z",
  "updated": "2019-09-11T22:23:45.000Z",
  "title": "Continuous dependence of an invariant measure on the jump rate of a piecewise-deterministic Markov process",
  "authors": [
    "Dawid Czapla",
    "Sander C. Hille",
    "Katarzyna Horbacz",
    "Hanna Wojewódka-Ściążko"
  ],
  "comment": "15 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly selected continuous transformation. It is assumed that the jumps appear at random moments, which coincide with the jump times of a Poisson process with intensity $\\lambda$. The model of this type, although in a more general version, was examined in our previous papers, where we have shown, among others, that the Markov process under consideration possesses a unique invariant probability measure, say $\\nu_{\\lambda}^*$. The aim of this paper is to prove that the map $\\lambda\\mapsto\\nu_{\\lambda}^*$ is continuous (in the topology of weak convergence of probability measures). The studied dynamical system is inspired by certain stochastic models for cell division and gene expression.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-11T22:23:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J05",
      "60J25",
      "37A30",
      "37A25"
    ],
    "keywords": [
      "piecewise-deterministic markov process",
      "invariant measure",
      "jump rate",
      "continuous dependence",
      "unique invariant probability measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}