{"paper":{"title":"Approximation of stable law in Wasserstein-1 distance by Stein's method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lihu Xu","submitted_at":"2017-09-04T04:00:18Z","abstract_excerpt":"Let $n \\in \\mathbb N$, let $\\zeta_{n,1},...,\\zeta_{n,n}$ be a sequence of independent random variables with $\\mathbb E \\zeta_{n,i}=0$ and $\\mathbb E |\\zeta_{n,i}|<\\infty$ for each $i$, and let $\\mu$ be an $\\alpha$-stable distribution having characteristic function $e^{-|\\lambda|^{\\alpha}}$ with $\\alpha\\in (1,2)$. Denote $S_{n}=\\zeta_{n,1}+...+\\zeta_{n,n}$ and its distribution by $\\mathcal L(S_n)$, we bound the Wasserstein distance of $\\mathcal L(S_{n})$ and $\\mu$ essentially by an $L^{1}$ discrepancy between two kernels, this bound can be interpreted as a generalization of the Stein discrepanc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00805","kind":"arxiv","version":4},"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"}