{
  "annotation_id": "a2694335-5632-4353-866f-6ae82ba16432",
  "date_created": "2026-02-17T05:53:20.213000Z",
  "date_modified": "2026-02-17T05:53:20.213000Z",
  "file_hash": "6beb0e7db83e84283569ec30a777d06b23c6c539d552eb248cf612e88c6355cf",
  "private": false,
  "record": {
    "abstract": "In this paper we extend the notion of $\\varphi$-mixing to set-valued random sequences that take values in the family of closed subsets of a Banach space. Several strong laws of large numbers for such $\\varphi$-mixing sequences are stated and proved. Illustrative examples show that the hypotheses of the theorems are both natural and sharp.",
    "arxiv_id": "2601.09197",
    "authors": [
      "Luc Tri Tuyen"
    ],
    "categories": [
      "math.PR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On strong law of large numbers for weakly stationary $\\varphi$-mixing set-valued random variable sequences",
    "url": "https://arxiv.org/abs/2601.09197",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "1894f058-1ce2-4a6a-95f3-cb20d8ff1599",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}