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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1212.2714","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-12T06:07:47Z","cross_cats_sorted":[],"title_canon_sha256":"ed1ddd06415a48e53e6d753aa2a2e0650c78181158ef569378da22e021db038b","abstract_canon_sha256":"4ba7d6f8e281cad89be7e81f93a002487a84b9d42f496ca68b75ade64f23722c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:35.621426Z","signature_b64":"+WeNvdZhXYs2+9FCP9mIqQffMG6QZPnOsTF8KBqjLP8GpsoiiUKZRpXNIQ4IeAZnXarco8CwFvSukuFSLDHgDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f554d246115dec44f00f0de2f06b0ba4d3e2b7c1c5d9d54d0a59eaa125cf616","last_reissued_at":"2026-05-18T03:38:35.620889Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:35.620889Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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