{"paper":{"title":"Asymptotic of spectral covariance for linear random fields with infinite variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Julius Damarackas, Vygantas Paulauskas","submitted_at":"2016-01-15T13:29:07Z","abstract_excerpt":"In the paper we continue to investigate measures of dependence for random variables with infinite variance. The asymptotic of spectral covariance $\\rho (X_{(0,0)}, X_{(k_1,k_2)})$ for linear random field $X_{k,l}=\\sum_{i,j=0}^\\infty c_{i,j}\\epsilon_{k-i, l-j}, \\ (k, l)\\in \\mathbb{Z}^2,$ with special form of filter $\\{c_{i,j}\\}$ and with innovations $\\{ \\epsilon_{i, j}\\}$ having infinite second moment is investigated. Different behavior of $\\rho (X_{(0,0)}, X_{(k_1,k_2)})$ is obtained in the cases $n\\to \\infty, \\ m\\to \\infty$ and $n\\to \\infty, \\ m\\to -\\infty$, the latter case being much more co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03911","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"}