{"paper":{"title":"Aggregation of autoregressive random fields and anisotropic long-range dependence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Donata Puplinskait\\.e, Donatas Surgailis","submitted_at":"2013-03-09T13:40:53Z","abstract_excerpt":"We introduce the notions of scaling transition and distributional long-range dependence for stationary random fields $Y$ on $\\mathbb {Z}^2$ whose normalized partial sums on rectangles with sides growing at rates $O(n)$ and $O(n^{\\gamma})$ tend to an operator scaling random field $V_{\\gamma}$ on $\\mathbb {R}^2$, for any $\\gamma>0$. The scaling transition is characterized by the fact that there exists a unique $\\gamma_0>0$ such that the scaling limits $V_{\\gamma}$ are different and do not depend on $\\gamma$ for $\\gamma>\\gamma_0$ and $\\gamma<\\gamma_0$. The existence of scaling transition together"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2209","kind":"arxiv","version":4},"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"}