{
  "id": "2106.07711",
  "version": "v1",
  "published": "2021-06-14T19:04:16.000Z",
  "updated": "2021-06-14T19:04:16.000Z",
  "title": "Central limit theorem for bifurcating Markov chains under $L^{2}$-ergodic conditions",
  "authors": [
    "S. Valère Bitseki Penda",
    "Jean-François Delmas"
  ],
  "comment": "39 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:2012.04741",
  "categories": [
    "math.PR"
  ],
  "abstract": "Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for additive functionals of BMC under $L^2$-ergodic conditions with three different regimes. This completes the pointwise approach developed in a previous work. As application, we study the elementary case of symmetric bifurcating autoregressive process, which justify the non-trivial hypothesis considered on the kernel transition of the BMC. We illustrate in this example the phase transition observed in the fluctuations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-14T19:04:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J05",
      "60F05",
      "60J80"
    ],
    "keywords": [
      "central limit theorem",
      "bifurcating markov chains",
      "ergodic conditions",
      "full binary tree representing",
      "phase transition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}