{
  "id": "1812.05174",
  "version": "v1",
  "published": "2018-12-12T22:06:11.000Z",
  "updated": "2018-12-12T22:06:11.000Z",
  "title": "Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities",
  "authors": [
    "Jeremiah Birrell",
    "Luc Rey-Bellet"
  ],
  "comment": "35 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e. robustness) bounds for quantities of interest in the presence of non-parametric model-form uncertainty. In this work, we combine such variational formulas with functional inequalities (Poincar\\'e, $\\log$-Sobolev, Liapunov functions) to derive explicit uncertainty quantification bounds applicable to both discrete and continuous-time Markov processes. These bounds are well-behaved in the infinite-time limit and apply to steady-states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-12T22:06:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47D07",
      "39B72",
      "60F10",
      "60J25"
    ],
    "keywords": [
      "functional inequalities",
      "variational principles",
      "derive explicit uncertainty quantification bounds",
      "explicit uncertainty quantification bounds applicable",
      "continuous-time markov processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}