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We are interested in the tail behaviour of this distribution in the case when $\\Psi_0(t) \\approx A_0t+B_0$. We will show that under subexponential assumptions on the random variable $\\log^+(A_0\\vee B_0)$ the tail asymptotic in question can be described using the integrated tail function of $\\l"},"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":"1408.1658","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-07T17:21:07Z","cross_cats_sorted":[],"title_canon_sha256":"79499fc60b117f0564d91a22d1a1e4c239ba4d8e5f628ae503f336fc0994c833","abstract_canon_sha256":"dd3b64d1ceca64f6c62bc06839f98e96fd9fce8c52394c28140cddf3712d3650"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:23.741373Z","signature_b64":"70M9hOBCziMsMaLPSCzAWOkysjQnpxRwD7hjQdnwZbIhOEBcsiCL4MwAp0tFjGYv5eHbGBLxFTaWsMP7edePCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abd39fe98ce739b8da3eea0ee509d1836742c076ce6268ed5453148185a36203","last_reissued_at":"2026-05-18T02:18:23.739519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:23.739519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Iterated Random Functions and Slowly Varying Tails","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Piotr Dyszewski","submitted_at":"2014-08-07T17:21:07Z","abstract_excerpt":"Consider a sequence of i.i.d. random Lipschitz functions $\\{\\Psi_n\\}_{n \\geq 0}$. 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