{"paper":{"title":"Limit theorems for functionals of long memory linear processes with infinite variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fangjun Xu, Hui Liu, Yudan Xiong","submitted_at":"2023-04-05T15:49:21Z","abstract_excerpt":"Let $X=\\{X_n: n\\in\\mathbb{N}\\}$ be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an $\\alpha$-stable law with $\\alpha\\in (0, 2)$. Then, for any integrable and square integrable function $K$ on $\\mathbb{R}$, under certain mild conditions, we establish the asymptotic behavior of the partial sum process \\[ \\left\\{\\sum\\limits_{n=1}^{[Nt]}\\big[K(X_n)-\\E K(X_n)\\big]:\\; t\\geq 0\\right\\} \\] as $N$ tends to infinity, where $[Nt]$ is the integer part of $Nt$ for $t\\geq 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.02528","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.02528/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}