{"paper":{"title":"Generalized stationary random fields with linear regressions - an operator approach","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pawe{\\l} J. Szab{\\l}owski, Wojciech Matysiak","submitted_at":"2005-07-16T12:26:57Z","abstract_excerpt":"Existence, $L^2$-stationarity and linearity of conditional expectations $\\wwo{X_k}{...,X_{k-2},X_{k-1}}$ of square integrable random sequences $\\mathbf{X}=(X_{k})_{k\\in\\mathbb{Z}}$ satisfying \\[ \\wwo{X_k}{...,X_{k-2},X_{k-1},X_{k+1},X_{k+2},...}=\\sum_{j=1}^\\infty b_j(X_{k-j}+X_{k+j}) \\] for a real sequence $(b_n)_{n\\in\\nat}$, is examined. The analysis is reliant upon the use of Laurent and Toeplitz operator techniques."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0507332","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"}