{
  "id": "1009.1039",
  "version": "v1",
  "published": "2010-09-06T12:27:38.000Z",
  "updated": "2010-09-06T12:27:38.000Z",
  "title": "Filtering of continuous-time Markov chains with noise-free observation and applications",
  "authors": [
    "Fulvia Confortola",
    "Marco Fuhrman"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Let X be a continuous-time Markov chain in a finite set I, let h be a mapping of I onto another set, and let Y be defined by Y_t=h(X_t), (for t nonnegative). We address the filtering problem for X in terms of the observation Y, which is not directly affected by noise. We write down explicit equations for the filtering process and show that this is a Markov process with the Feller property. We also prove that it is a piecewise-deterministic Markov process in the sense of Davis, and we identify its characteristics explicitly. We finally solve an optimal stopping problem for X with partial observation, i.e. where the moment of stopping is required to be a stopping time with respect to the natural filtration of Y.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-09-06T12:27:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E11",
      "60J27",
      "60G40",
      "60G35"
    ],
    "keywords": [
      "continuous-time markov chain",
      "noise-free observation",
      "applications",
      "piecewise-deterministic markov process",
      "explicit equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.1039C"
    }
  }
}