{
  "id": "2005.10730",
  "version": "v1",
  "published": "2020-05-21T15:38:29.000Z",
  "updated": "2020-05-21T15:38:29.000Z",
  "title": "On Strong Feller Property, Exponential Ergodicity and Large Deviations Principle for Stochastic Damping Hamiltonian Systems with State-Dependent Switching",
  "authors": [
    "Fubao Xi",
    "Chao Zhu",
    "Fuke Wu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This work focuses on a class of stochastic damping Hamiltonian systems with state-dependent switching, where the switching process has a countably infinite state space. After establishing the existence and uniqueness of a global weak solution via the martingale approach under very mild conditions, the paper next proves the strong Feller property for regime-switching stochastic damping Hamiltonian systems by the killing technique together with some resolvent and transition probability identities. The commonly used continuity assumption for the switching rates $q_{kl}(\\cdot)$ in the literature is relaxed to measurability in this paper. Finally the paper provides sufficient conditions for exponential ergodicity and large deviations principle for regime-switching stochastic damping Hamiltonian systems. Several examples on regime-switching van der Pol and (overdamped) Langevin systems are studied in detail for illustration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-21T15:38:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J27",
      "34D25"
    ],
    "keywords": [
      "large deviations principle",
      "strong feller property",
      "exponential ergodicity",
      "state-dependent switching",
      "regime-switching stochastic damping hamiltonian systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}