{
  "id": "1905.06111",
  "version": "v1",
  "published": "2019-05-15T12:09:51.000Z",
  "updated": "2019-05-15T12:09:51.000Z",
  "title": "Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices",
  "authors": [
    "Martin Friesen",
    "Peng Jin",
    "Jonas Kremer",
    "Barbara Rüdiger"
  ],
  "comment": "22 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "This article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite $d\\times d$-matrices. In particular, for conservative and subcritical affine processes on this cone we show that a finite $\\log$-moment of the state-independent jump measure is sufficient for the existence of a unique limit distribution. Moreover, we study the convergence rate of the underlying transition kernel to the limit distribution: firstly, in a specific metric induced by the Laplace transform and secondly, in the Wasserstein distance under a first moment assumption imposed on the state-independent jump measure and an additional condition on the diffusion parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-15T12:09:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "37A25",
      "60G10",
      "60J75"
    ],
    "keywords": [
      "symmetric positive semidefinite matrices",
      "state-independent jump measure",
      "ergodicity",
      "unique limit distribution",
      "first moment assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}