{"paper":{"title":"Weak law of large numbers for linear processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alfredas Ra\\v{c}kauskas, Vaidotas Characiejus","submitted_at":"2016-02-01T10:22:33Z","abstract_excerpt":"We establish sufficient conditions for the Marcinkiewicz-Zygmund type weak law of large numbers for a linear process $\\{X_k:k\\in\\mathbb Z\\}$ defined by $X_k=\\sum_{j=0}^\\infty\\psi_j\\varepsilon_{k-j}$ for $k\\in\\mathbb Z$, where $\\{\\psi_j:j\\in\\mathbb Z\\}\\subset\\mathbb R$ and $\\{\\varepsilon_k:k\\in\\mathbb Z\\}$ are independent and identically distributed random variables such that $x^p\\Pr\\{|\\varepsilon_0|>x\\}\\to0$ as $x\\to\\infty$ with $1<p<2$ and $\\operatorname E\\varepsilon_0=0$. We use an abstract norming sequence that does not grow faster than $n^{1/p}$ if $\\sum|\\psi_j|<\\infty$. If $\\sum|\\psi_j|=\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00461","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"}