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We consider mostly the case where $\\tau$ is independent of the summands; also, in a particular situation, we deal with a stopping time.\n  Also we consider the case where $E\\xi>0$ and where the tail of $\\tau$ is compar"},"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":"0808.3697","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-08-27T13:04:56Z","cross_cats_sorted":[],"title_canon_sha256":"65e7890b78e32b1f8448e81e00ea6271013a1f8d83cdb555d22d96e3314d2d50","abstract_canon_sha256":"8d633522b30f2b182191141fd5773e0c1db3f07fcaa534655b606e9acd5bc9c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:41.000298Z","signature_b64":"OMH30FoNS0LwTCDL3NLX7YL8j0UsnvQGOCNiHv23UECPTDYoC3xeXC5+MI0AobCrBL7sys5LzJyGAxEhe0EbAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5802b90c536f2538213b0a5201ca23e17d9fca910edf12e1c64bc1c23a8c108d","last_reissued_at":"2026-05-18T04:07:40.999621Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:40.999621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of randomly stopped sums in the presence of heavy tails","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Denis Denisov, Dmitry Korshunov, Sergey Foss","submitted_at":"2008-08-27T13:04:56Z","abstract_excerpt":"We study conditions under which $P(S_\\tau>x)\\sim P(M_\\tau>x)\\sim E\\tau P(\\xi_1>x)$ as $x\\to\\infty$, where $S_\\tau$ is a sum $\\xi_1+...+\\xi_\\tau$ of random size $\\tau$ and $M_\\tau$ is a maximum of partial sums $M_\\tau=\\max_{n\\le\\tau}S_n$. 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