{
  "id": "1710.01042",
  "version": "v1",
  "published": "2017-10-03T09:19:29.000Z",
  "updated": "2017-10-03T09:19:29.000Z",
  "title": "Asymptotic Log-Harnack Inequality and Applications for Stochastic Systems of Infinite Memory",
  "authors": [
    "Jianhai Bao",
    "Feng-Yu Wang",
    "Chenggui Yuan"
  ],
  "comment": "20 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The asymptotic log-Harnack inequality is established for several different models of stochastic differential systems with infinite memory: non-degenerate SDEs, Neutral SDEs, semi-linear SPDEs, and stochastic Hamiltonian systems. As applications, the following properties are derived for the associated segment Markov semigroups: asymptotic heat kernel estimate; uniqueness of the invariant probability measure; asymptotic gradient estimate and hence, asymptotically strong Feller property; and asymptotic irreducibilty.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-03T09:19:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H10",
      "47G20"
    ],
    "keywords": [
      "asymptotic log-harnack inequality",
      "infinite memory",
      "stochastic systems",
      "applications",
      "asymptotic heat kernel estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}