{"paper":{"title":"Density convergence in the Breuer-Major theorem for Gaussian stationary sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Fangjun Xu, Samy Tindel, Yaozhong Hu","submitted_at":"2014-03-13T20:04:38Z","abstract_excerpt":"Consider a Gaussian stationary sequence with unit variance $X=\\{X_k;k\\in {\\mathbb{N}}\\cup\\{0\\}\\}$. Assume that the central limit theorem holds for a weighted sum of the form $V_n=n^{-1/2}\\sum^{n-1}_{k=0}f(X_k)$, where $f$ designates a finite sum of Hermite polynomials. Then we prove that the uniform convergence of the density of $V_n$ towards the standard Gaussian density also holds true, under a mild additional assumption involving the causal representation of $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3413","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"}