{
  "id": "1710.05612",
  "version": "v1",
  "published": "2017-10-16T10:44:50.000Z",
  "updated": "2017-10-16T10:44:50.000Z",
  "title": "Ergodicity and Kolmogorov equations for dissipative SPDEs with singular drift: a variational approach",
  "authors": [
    "Carlo Marinelli",
    "Luca Scarpa"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We prove existence of invariant measures for the Markovian semigroup generated by the solution to a parabolic semilinear stochastic PDE whose nonlinear drift term satisfies only a kind of symmetry condition on its behavior at infinity, but no restriction on its growth rate is imposed. Thanks to strong integrability properties of invariant measures $\\mu$, solvability of the associated Kolmogorov equation in $L^1(\\mu)$ is then established, and the infinitesimal generator of the transition semigroup is identified as the closure of the Kolmogorov operator. A key role is played by a generalized variational setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-16T10:44:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kolmogorov equation",
      "variational approach",
      "singular drift",
      "dissipative spdes",
      "invariant measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}