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A sharp asymptotics of the tail of X =(X _1,X_2) is obtained. We show that under \"so called\" Kesten-Goldie conditions P (X_2>t)\\sim t^{-a} and P (X_1>t )\\sim t^{-a}(\\log t)^b, where b =a or a\\2."},"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":"1806.08985","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-23T15:36:06Z","cross_cats_sorted":[],"title_canon_sha256":"9e7bc0720ee153681a25162941b6c64fd324a131a3aa76369e40cb3c4f13d339","abstract_canon_sha256":"94f3fa02788a8fc73999cb719bf1141714da4a07ee492585ddc039ddf950daf0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:30.679637Z","signature_b64":"AHHymAC0FT3MiGKtlF4bg4Z9tIgtGvGoVgDtjdlb1VE6Kv7ceqZMViEseL88pGtuR+wM46wCVY9boLybe5tHCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b3d5c41f82308bc94d6d25e7627a2e47d082a73a99c3e1605c661bc7c992c95","last_reissued_at":"2026-05-18T00:12:30.679082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:30.679082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Affine stochastic equation with triangular matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ewa Damek, Jacek Zienkiewicz","submitted_at":"2018-06-23T15:36:06Z","abstract_excerpt":"We study solution X of the stochastic equation X = AX +B, where A is a random matrix and B,X are random vectors, the law of (A,B) is given and X is independent of (A,B). 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