{"paper":{"title":"An optimal approximation of Rosenblatt sheet by multiple Wiener integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guangjun Shen, Qian Yu","submitted_at":"2015-05-13T02:59:37Z","abstract_excerpt":"Let $Z^{\\alpha,\\beta}$ be the Rosenblatt sheet with the representation $$ Z^{\\alpha,\\beta}(t,s)=\\int^t_0\\int^s_0\\int^t_0\\int^s_0Q^\\alpha(t,y_1,y_2)Q^\\beta(s,u_1,u_2)B(dy_1,du_1)B(dy_2,du_2) $$ where $B$ is a Brownian sheet, $\\frac12<\\alpha,\\beta<1$, $Q^\\alpha$ and $Q^\\beta$ are the given kernel. In this paper, we contruct multiple Wiener integrals of the form \\begin{align*} \\int^t_0\\int^s_0\\int^t_0\\int^s_0&[k_1(y_1,y_2)^{-\\frac12\\alpha}(u_1,u_2)^{-\\frac12\\beta}+k_2(y_1\\vee y_2)^{\\frac12\\alpha}(y_1\\wedge y_2)^{-\\frac12\\alpha}|y_1-y_2|^{\\alpha-1}\\\\ &\\cdot(u_1\\vee u_2)^{\\frac12\\beta}(u_1\\wedge u_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03225","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"}