{
  "abstract": "In this paper, we study the existence of invariant sublinear expectations of Markovian semigroups on sublinear expectation spaces. To achieve this, we establish a complete metric space of sublinear expectations, on which we extend Harris' method to the nonlinear setting on the convergence of sublinear semigroups. We then explore two cases of $G\\text{-}$diffusions by studying the Lyapunov function and the local Doeblin condition. One is the $G\\text{-}$Brownian motion on the unit circle which is the case studied in Feng and Zhao(2021), but with the new method. Another is the multidimensional $G\\text{-}$SDEs on the whole space $\\mathbb{R}^d$. We establish, for the first time in the literature, the existence of the invariant sublinear expectation for $G\\text{-}$SDEs under the non-degenerate and weakly dissipative assumption. For this, we prove that for a class of $G\\text{-}$SDEs, the $G\\text{-}$expectation can be represented as the supremum of the semigroup of a family of SDEs, of which the regularity is obtained by considering { oscillations and coupling of the nonlinear Markovian semigroup,} and the Denis-Hu-Peng representation for the distribution of $G\\text{-}$Brownian motions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.15203",
  "author_total": 2,
  "authors": [
    {
      "name": "Danyang Zhao"
    },
    {
      "name": "Huaizhong Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1ywsnn0t2fdaw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.15203",
  "fulltext_url": null,
  "id": "1ywsnn0t2fdaw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.15203",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7164883047",
  "pdf_url": "https://arxiv.org/pdf/2606.15203",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1ywsnn0t2fdaw.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2606.15203",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.15203"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The existence of invariant sublinear expectations for $G$-SDEs",
  "title_text": "The existence of invariant sublinear expectations for G-SDEs",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/1ywsnn0t2fdaw",
  "venue": "arXiv",
  "versions": []
}