{"paper":{"title":"Operator self-similar processes and functional central limit theorems","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":"2016-09-06T08:44:18Z","abstract_excerpt":"Let $\\{X_k:k\\ge1\\}$ be a linear process with values in the separable Hilbert space $L_2(\\mu)$ given by $X_k=\\sum_{j=0}^\\infty(j+1)^{-D}\\varepsilon_{k-j}$ for each $k\\ge1$, where $D$ is defined by $Df=\\{d(s)f(s):s\\in\\mathbb S\\}$ for each $f\\in L_2(\\mu)$ with $d:\\mathbb S\\to\\mathbb R$ and $\\{\\varepsilon_k:k\\in\\mathbb Z\\}$ are independent and identically distributed $L_2(\\mu)$-valued random elements with $\\operatorname E\\varepsilon_0=0$ and $\\operatorname E\\|\\varepsilon_0\\|^2<\\infty$. We establish sufficient conditions for the functional central limit theorem for $\\{X_k:k\\ge1\\}$ when the series o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01435","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"}