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We study the asymptotics for $\\mathbf P(M_\\tau>x),$ as $x\\to\\infty$."},"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":"1907.08920","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-21T06:21:24Z","cross_cats_sorted":[],"title_canon_sha256":"405768265e5252b2deac277c3cc2a9b5e0c18e9919f7c1793fdabba4a5a20ed4","abstract_canon_sha256":"dcd32c0eb645646d276670c6423dd6c2a6b2a524b72cc11a7975941f1c8000be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:02.723337Z","signature_b64":"f38/WH1BGj8qtXx56i603eUpd6kDSxDfcRlW5RSav7Z0BHgbJNPb9hFntslmMvo7e09fj7S/xl6277xMaef2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"593c776d663d10711a808516e5b7d423ea31d1d71475deb0b4e8186f8a70d4b7","last_reissued_at":"2026-05-17T23:40:02.722861Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:02.722861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $M_\\tau=\\max_{0\\le i\\le \\tau} S_i$. 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