{
  "id": "2110.10193",
  "version": "v2",
  "published": "2021-10-19T18:20:53.000Z",
  "updated": "2022-05-29T12:42:40.000Z",
  "title": "On the local limit theorems for lower psi-mixing Markov chains",
  "authors": [
    "Florence Merlevède",
    "Magda Peligrad",
    "Costel Peligrad"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we investigate the local limit theorem for additive functionals of nonstationary Markov chains that converge in distribution. We consider both the lattice and the non-lattice cases. The results are also new in the stationary setting and lead to local limit theorems linked to convergence to stable distributions. The conditions are imposed to individual summands and are expressed in terms of lower psi-mixing coefficients.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-05-29T12:42:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local limit theorem",
      "lower psi-mixing markov chains",
      "nonstationary markov chains",
      "individual summands",
      "non-lattice cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}