{"paper":{"title":"Asymptotic analysis of average case approximation complexity of additive random fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. A. Khartov, M. Zani","submitted_at":"2017-10-30T11:00:43Z","abstract_excerpt":"We study approximation properties of sequences of centered additive random fields $Y_d$, $d\\in\\mathbb{N}$. The average case approximation complexity $n^{Y_d}(\\varepsilon)$ is defined as the minimal number of evaluations of arbitrary linear functionals that is needed to approximate $Y_d$ with relative $2$-average error not exceeding a given threshold $\\varepsilon\\in(0,1)$. We investigate the growth of $n^{Y_d}(\\varepsilon)$ for arbitrary fixed $\\varepsilon\\in(0,1)$ and $d\\to\\infty$. Under natural assumptions we obtain general results concerning asymptotics of $n^{Y_d}(\\varepsilon)$. We apply ou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10865","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"}