{"paper":{"title":"Regularity of solutions of the Stein equation and rates in the multivariate central limit theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Guillaume Mijoule, Thomas Gallou\\\"et (MOKAPLAN), Yvik Swan","submitted_at":"2018-05-04T11:45:23Z","abstract_excerpt":"Consider the multivariate Stein equation $\\Delta f - x\\cdot \\nabla f = h(x) - E h(Z)$, where $Z$ is a standard $d$-dimensional Gaussian random vector, and let $f\\_h$ be the solution given by Barbour's generator approach. We prove that, when $h$ is $\\alpha$-H\\\"older ($0<\\alpha\\leq1$), all derivatives of order $2$ of $f\\_h$ are $\\alpha$-H\\\"older {\\it up to a $\\log$ factor}; in particular they are $\\beta$-H\\\"older for all $\\beta \\in (0, \\alpha)$, hereby improving existing regularity results on the solution of the multivariate Gaussian Stein equation. For $\\alpha=1$, the regularity we obtain is op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01720","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"}