{
  "id": "1901.11125",
  "version": "v1",
  "published": "2019-01-30T22:26:56.000Z",
  "updated": "2019-01-30T22:26:56.000Z",
  "title": "Exponential ergodicity for SDEs and McKean-Vlasov processes with Lévy noise",
  "authors": [
    "Mingjie Liang",
    "Mateusz B. Majka",
    "Jian Wang"
  ],
  "comment": "36 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study stochastic differential equations (SDEs) of McKean-Vlasov type with distribution dependent drifts and driven by pure jump L\\'{e}vy processes. We prove a uniform in time propagation of chaos result, providing quantitative bounds on convergence rate of interacting particle systems with L\\'{e}vy noise to the corresponding McKean-Vlasov SDE. By applying techniques that combine couplings, appropriately constructed $L^1$-Wasserstein distances and Lyapunov functions, we show exponential convergence of solutions of such SDEs to their stationary distributions. Our methods allow us to obtain results that are novel even for a broad class of L\\'{e}vy-driven SDEs with distribution independent coefficients.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-30T22:26:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential ergodicity",
      "mckean-vlasov processes",
      "lévy noise",
      "study stochastic differential equations",
      "distribution independent coefficients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}