{"paper":{"title":"Variance of partial sums of stationary sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"George Deligiannidis, Sergey Utev","submitted_at":"2012-05-18T15:07:26Z","abstract_excerpt":"Let $X_1,X_2,\\ldots$ be a centred sequence of weakly stationary random variables with spectral measure $F$ and partial sums $S_n=X_1+\\cdots+X_n$. We show that $\\operatorname {var}(S_n)$ is regularly varying of index $\\gamma$ at infinity, if and only if $G(x):=\\int_{-x}^xF(\\mathrm {d}x)$ is regularly varying of index $2-\\gamma$ at the origin ($0<\\gamma<2$)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4172","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"}