{
  "id": "1907.03725",
  "version": "v1",
  "published": "2019-07-08T17:09:05.000Z",
  "updated": "2019-07-08T17:09:05.000Z",
  "title": "Couplings via comparison principle and exponential ergodicity of SPDEs in the hypoelliptic setting",
  "authors": [
    "Oleg Butkovsky",
    "Michael Scheutzow"
  ],
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We develop a general framework for studying ergodicity of order-preserving Markov semigroups. We establish natural and in a certain sense optimal conditions for existence and uniqueness of the invariant measure and exponential convergence of transition probabilities of an order-preserving Markov process. As an application, we show exponential ergodicity and exponentially fast synchronization-by-noise of the stochastic reaction-diffusion equation in the hypoelliptic setting. This refines and complements corresponding results of Hairer, Mattingly (2011).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-08T17:09:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential ergodicity",
      "hypoelliptic setting",
      "comparison principle",
      "sense optimal conditions",
      "stochastic reaction-diffusion equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}