{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:K5LYNISPQDMMEJX32PLLHQGQLX","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8fac8c9a9ac63eabc3fe4b6cb94b18d2a9491d2a8c3e968a509bb88297188bdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-01T21:28:20Z","title_canon_sha256":"9a272e11d7e7bab9047bf3495315b10fe3e2289fdaa9bf7f7241babf6245d741"},"schema_version":"1.0","source":{"id":"1102.0301","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0301","created_at":"2026-05-18T03:57:50Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0301v3","created_at":"2026-05-18T03:57:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0301","created_at":"2026-05-18T03:57:50Z"},{"alias_kind":"pith_short_12","alias_value":"K5LYNISPQDMM","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"K5LYNISPQDMMEJX3","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"K5LYNISP","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:02a3a4632c6ea499f400348480aea8dd24021d3af8643f9e2b68d702c399456a","target":"graph","created_at":"2026-05-18T03:57:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $\\{X_i\\}$ be a sequence of independent identically distributed random variables with an intermediate regularly varying (IR) right tail $\\bar{F}$. Let $(N, C_1, ..., C_N)$ be a nonnegative random vector independent of the $\\{X_i\\}$ with $N \\in \\mathbb{N} \\cup \\{\\infty\\}$. We study the weighted random sum $S_N = \\sum_{i=1}^N C_i X_i$, and its maximum, $M_N = \\sup_{1 \\leq k < N+1} \\sum_{i=1}^k C_i X_i$. These type of sums appear in the analysis of stochastic recursions, including weighted branching processes and autoregressive processes. In particular, we derive conditions under which $$P(M_N","authors_text":"Mariana Olvera-Cravioto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-01T21:28:20Z","title":"Asymptotics for Weighted Random Sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0301","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3df71f6b4c9f4656d395d8ef209bf5293a0c3a081b98c12aaf37d9bf053d08a6","target":"record","created_at":"2026-05-18T03:57:50Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8fac8c9a9ac63eabc3fe4b6cb94b18d2a9491d2a8c3e968a509bb88297188bdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-01T21:28:20Z","title_canon_sha256":"9a272e11d7e7bab9047bf3495315b10fe3e2289fdaa9bf7f7241babf6245d741"},"schema_version":"1.0","source":{"id":"1102.0301","kind":"arxiv","version":3}},"canonical_sha256":"575786a24f80d8c226fbd3d6b3c0d05df4e45d058cbe785a8293aa84da7d0823","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"575786a24f80d8c226fbd3d6b3c0d05df4e45d058cbe785a8293aa84da7d0823","first_computed_at":"2026-05-18T03:57:50.620111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:50.620111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"20I3RgaD1XdLaBix3uzbSyKVtNyVBSqrICe1M5gF9EqWHn5ENv+e+ILApx3wPCgr5l7H5w+tNC6EWcwMg/+HCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:50.620746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0301","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3df71f6b4c9f4656d395d8ef209bf5293a0c3a081b98c12aaf37d9bf053d08a6","sha256:02a3a4632c6ea499f400348480aea8dd24021d3af8643f9e2b68d702c399456a"],"state_sha256":"6883dd1bf509ea6ba5c3decd076d4e6bc432d549ccb533d5bb34d38ef5ce0940"}