{
  "id": "2303.11576",
  "version": "v1",
  "published": "2023-03-21T03:49:42.000Z",
  "updated": "2023-03-21T03:49:42.000Z",
  "title": "On the Existence and Uniqueness of Stationary Distributions for Some Class of Piecewise Deterministic Markov Processes With State-Dependent Jump Intensity",
  "authors": [
    "Dawid Czapla"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we are concerned with a class of piecewise deterministic Markov processes that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate, between which, at any time, the trajectory is driven by one of the given semiflows, randomly drawn right after the jump. We prove that there is a one-to-one correspondence between stationary distributions of such processes and those of the discrete-time Markov chains given by their post-jump locations. Further, we apply this result to provide a criterion guaranteeing the existence and uniqueness of the stationary distribution in a particular case, where the post-jump locations result from the action of an iterated function system with place-dependent probabilities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-21T03:49:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60J05",
      "60J35",
      "37A30"
    ],
    "keywords": [
      "piecewise deterministic markov processes",
      "stationary distribution",
      "state-dependent jump intensity",
      "uniqueness",
      "discrete-time markov chains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}