{"paper":{"title":"Hitting time of a half-line by a two-dimensional nonsymmetric random walk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yasunari Fukai","submitted_at":"2012-12-12T06:07:47Z","abstract_excerpt":"We consider the probability that a two-dimensional random walk starting from the origin never returns to the half-line $ (- \\infty,0] \\times {0}$ before time $n$. Let $X^{(1)}=(X_{1},X_{2})$ be the increment of the two-dimensional random walk. For an aperiodic random walk with moment conditions ($E[X_{2}]=0 $ and $ E[|X_{1}|^{\\delta}]<\\infty, E[|X_{2}|^{2+ \\delta}]< \\infty $ for some $ \\delta \\in (0,1)$), we obtain an asymptotic estimate (as $n \\rightarrow \\infty $) of this probability by assuming the behavior of the characteristic function of $X_{1}$ near zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2714","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"}