{"paper":{"title":"A note on linear processes with tapered innovations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Vygantas Paulauskas","submitted_at":"2019-05-06T09:12:51Z","abstract_excerpt":"In the paper we consider the partial sum process $\\sum_{k=1}^{[nt]}X_k^{(n)}$, where $\\{X_k^{(n)}, \\ k\\in Z\\},\\ n\\ge 1,$ is a series of linear processes with innovations having heavy-tailed tapered distributions with tapering parameter $b_n$ depending on $n$. It is shown that, depending on the properties of a filter of a linear process under consideration and on the parameter $b_n$ defining if the tapering is hard or soft, the limit process for such partial sum process can be fractional Brownian motion or linear fractional stable motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01891","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"}