{"paper":{"title":"Functional limit theorems for the maxima of perturbed random walks and divergent perpetuities in the $M_1$-topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Iksanov, Andrey Pilipenko, Igor Samoilenko","submitted_at":"2016-10-20T07:50:17Z","abstract_excerpt":"Let $(\\xi_1,\\eta_1)$, $(\\xi_2,\\eta_2),\\ldots$ be a sequence of i.i.d. two-dimensional random vectors. In the earlier article Iksanov and Pilipenko (2014) weak convergence in the $J_1$-topology on the Skorokhod space of $n^{-1/2}\\underset{0\\leq k\\leq \\cdot}{\\max}\\,(\\xi_1+\\ldots+\\xi_k+\\eta_{k+1})$ was proved under the assumption that contributions of $\\underset{0\\leq k\\leq n}{\\max}\\,(\\xi_1+\\ldots+\\xi_k)$ and $\\underset{1\\leq k\\leq n}{\\max}\\,\\eta_k$ to the limit are comparable and that $n^{-1/2}(\\xi_1+\\ldots+\\xi_{[n\\cdot]})$ is attracted to a Brownian motion. In the present paper, we continue thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06312","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"}