{
  "id": "2206.03901",
  "version": "v1",
  "published": "2022-06-08T13:53:34.000Z",
  "updated": "2022-06-08T13:53:34.000Z",
  "title": "Wasserstein Convergence for Empirical Measures of Subordinated Dirichlet Diffusions on Riemannian Manifolds",
  "authors": [
    "Huaiqian Li",
    "Bingyao Wu"
  ],
  "comment": "Comments welcome!",
  "categories": [
    "math.PR"
  ],
  "abstract": "We investigate long-time behaviors of empirical measures associated with subordinated Dirichlet diffusion processes on a compact Riemannian manifold $M$ with boundary $\\partial M$ to some reference measure, under the quadratic Wasserstein distance. For any initial distribution not concentrated on $\\partial M$, we obtain the rate of convergence and even the precise limit for the conditional expectation of the quadratic Wasserstein distance conditioned on the process killed upon exiting $M\\setminus\\partial M$. In particular, the results coincide with the recent ones proved by F.-Y. Wang in \\cite{eW2} for Dirichlet diffusion processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-08T13:53:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "empirical measures",
      "wasserstein convergence",
      "quadratic wasserstein distance",
      "compact riemannian manifold",
      "subordinated dirichlet diffusion processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}