{"paper":{"title":"First-passage times over moving boundaries for asymptotically stable walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Sakhanenko, Denis Denisov, Vitali Wachtel","submitted_at":"2018-01-12T11:34:49Z","abstract_excerpt":"Let $\\{S_n, n\\geq1\\}$ be a random walk wih independent and identically distributed increments and let $\\{g_n,n\\geq1\\}$ be a sequence of real numbers. Let $T_g$ denote the first time when $S_n$ leaves $(g_n,\\infty)$. Assume that the random walk is oscillating and asymptotically stable, that is, there exists a sequence $\\{c_n,n\\geq1\\}$ such that $S_n/c_n$ converges to a stable law. In this paper we determine the tail behaviour of $T_g$ for all oscillating asymptotically stable walks and all boundary sequences satisfying $g_n=o(c_n)$. Furthermore, we prove that the rescaled random walk conditione"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04136","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"}