{"paper":{"title":"Maximum on a random time interval of a random walk with infinite mean","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Denis Denisov","submitted_at":"2019-07-21T06:21:24Z","abstract_excerpt":"Let $\\xi_1,\\xi_2,\\ldots$ be independent, identically distributed random variables with infinite mean $\\mathbf E[|\\xi_1|]=\\infty.$ Consider a random walk $S_n=\\xi_1+\\cdots+\\xi_n$, a stopping time $\\tau=\\min\\{n\\ge 1: S_n\\le 0\\}$ and let $M_\\tau=\\max_{0\\le i\\le \\tau} S_i$. We study the asymptotics for $\\mathbf P(M_\\tau>x),$ as $x\\to\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08920","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"}