{"paper":{"title":"Anisotropic scaling limits of long-range dependent linear random fields on ${\\mathbb {Z}}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Donatas Surgailis","submitted_at":"2018-05-09T15:00:32Z","abstract_excerpt":"We provide a complete description of anisotropic scaling limits of stationary linear random field on ${\\mathbb {Z}}^3$ with long-range dependence and moving average coefficients decaying as $O(|t_i|^{-q_i})$ in the $i$th direction, $i=1,2,3.$ The scaling limits are taken over rectangles in ${\\mathbb {Z}}^3$ whose sides increase as $O(\\lambda^{\\gamma_i}), i=1,2,3$ when $\\lambda \\to \\infty$, for any fixed $\\gamma_i >0, i=1,2,3 $. We prove that all these limits are Gaussian RFs whose covariance structure essentially is determined by the fulfillment or violation of the balance conditions $\\gamma_i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03570","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"}