{"paper":{"title":"Stein Type Characterization for $G$-normal Distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mingshang Hu, Shige Peng, Yongsheng Song","submitted_at":"2016-03-15T09:29:39Z","abstract_excerpt":"In this article, we provide a Stein type characterization for $G$-normal distributions: Let $\\mathcal{N}[\\varphi]=\\max_{\\mu\\in\\Theta}\\mu[\\varphi],\\ \\varphi\\in C_{b,Lip}(\\mathbb{R}),$ be a sublinear expectation. $\\mathcal{N}$ is $G$-normal if and only if for any $\\varphi\\in C_b^2(\\mathbb{R})$, we have \\[\\int_\\mathbb{R}[\\frac{x}{2}\\varphi'(x)-G(\\varphi\"(x))]\\mu^\\varphi(dx)=0,\\] where $\\mu^\\varphi$ is a realization of $\\varphi$ associated with $\\mathcal{N}$, i.e., $\\mu^\\varphi\\in \\Theta$ and $\\mu^\\varphi[\\varphi]=\\mathcal{N}[\\varphi]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04611","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}