{
  "id": "2408.09079",
  "version": "v1",
  "published": "2024-08-17T02:52:05.000Z",
  "updated": "2024-08-17T02:52:05.000Z",
  "title": "Catalan Numbers, Riccati Equations and Convergence",
  "authors": [
    "Yicheng Feng",
    "Jean-Pierre Fouque",
    "Tomoyuki Ichiba"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CA",
    "math.PR"
  ],
  "abstract": "We analyze both finite and infinite systems of Riccati equations derived from stochastic differential games on infinite networks. We discuss a connection to the Catalan numbers and the convergence of the Catalan functions by Fourier transforms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-17T02:52:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34D05",
      "91A15",
      "60H30",
      "11B83"
    ],
    "keywords": [
      "riccati equations",
      "catalan numbers",
      "convergence",
      "stochastic differential games",
      "catalan functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}