{"paper":{"title":"Central limit theorem under variance uncertainty","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dmitry B. Rokhlin","submitted_at":"2015-06-04T11:30:42Z","abstract_excerpt":"We prove the central limit theorem (CLT) for a sequence of independent zero-mean random variables $\\xi_j$, perturbed by predictable multiplicative factors $\\lambda_j$ with values in intervals $[\\underline\\lambda_j,\\overline\\lambda_j]$. It is assumed that the sequences $\\underline\\lambda_j$, $\\overline\\lambda_j$ are bounded and satisfy some stabilization condition. Under the classical Lindeberg condition we show that the CLT limit, corresponding to a \"worst\" sequence $\\lambda_j$, is described by the solution $v$ of one-dimensional $G$-heat equation. The main part of the proof follows Peng's app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01551","kind":"arxiv","version":2},"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"}