{"paper":{"title":"Functional Convergence of Linear Sequences in a non-Skorokhod Topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Adam Jakubowski, Raluca Balan, Sana Louhichi","submitted_at":"2012-09-06T00:09:10Z","abstract_excerpt":"In this article, we prove a new functional limit theorem for the partial sum sequence $S_{[nt]}=\\sum_{i=1}^{[nt]}X_i$ corresponding to a linear sequence of the form $X_i=\\sum_{j \\in \\bZ}c_j \\xi_{i-j}$ with i.i.d. innovations $(\\xi_i)_{i \\in \\bZ}$ and real-valued coefficients $(c_j)_{j \\in \\bZ}$. This weak convergence result is obtained in space $\\bD[0,1]$ endowed with the $S$-topology introduced in Jakubowski (1992), and the limit process is a linear fractional stable motion (LFSM). One of our result provides an extension of the results of Avram and Taqqu (1992) to the case when the coefficien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1147","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"}