{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QZNOSSAVPWPV2J5OFD4PZ7WNTP","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":"399d276dc4f25ab272e4d091fea391b282d5fa86fcfd806d22898fc02d8e9c86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-28T19:51:19Z","title_canon_sha256":"1fdf1790ad408cc97f24d076e4173f76bdf34faee1f7795c01cddad29c042c8a"},"schema_version":"1.0","source":{"id":"1304.7510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7510","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7510v2","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7510","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"QZNOSSAVPWPV","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QZNOSSAVPWPV2J5O","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QZNOSSAV","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:4902e5884976b536313d28d4a574a002a0695224f11fb2aa4fd382cae131aa33","target":"graph","created_at":"2026-05-18T02:43:09Z","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":"In the paper Sato (2006) there are introduced two families of improper random integrals and the corresponding two convolution semigroups of infinitely divisible laws on $\\Rset^d$. Theorem 3.1 gives a relation (a factorization property) between those two integrals. Here, using \\emph{the random integral mappings} $I^{h,r}_{(a,b]}$ (cf. the survey article Jurek (2011)), we give a simpler proof that is also valid for measures on Banach spaces. Furthermore, using our technique we establish yet other relations between those two families of improper stochastic integrals.","authors_text":"Zbigniew J. Jurek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-28T19:51:19Z","title":"Remarks on factorization property of some stochastic integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7510","kind":"arxiv","version":2},"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":"sha256:8b38d3d7a7d1b45a020f87906e240d50f5d99adba0440f62b999e8a2b5f1e3b4","target":"record","created_at":"2026-05-18T02:43:09Z","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":"399d276dc4f25ab272e4d091fea391b282d5fa86fcfd806d22898fc02d8e9c86","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-28T19:51:19Z","title_canon_sha256":"1fdf1790ad408cc97f24d076e4173f76bdf34faee1f7795c01cddad29c042c8a"},"schema_version":"1.0","source":{"id":"1304.7510","kind":"arxiv","version":2}},"canonical_sha256":"865ae948157d9f5d27ae28f8fcfecd9bc9c5bbdea88328de19b521e78089698b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"865ae948157d9f5d27ae28f8fcfecd9bc9c5bbdea88328de19b521e78089698b","first_computed_at":"2026-05-18T02:43:09.448142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:09.448142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FxMv+b2yj3eevX7PMK6ZCjDMCzP5bUTugd05voOF8CqNARp9deCiS6qw30TUMmbWdmUkyMWVYqxSuE0J6Bp0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:09.448634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b38d3d7a7d1b45a020f87906e240d50f5d99adba0440f62b999e8a2b5f1e3b4","sha256:4902e5884976b536313d28d4a574a002a0695224f11fb2aa4fd382cae131aa33"],"state_sha256":"7514ec1356ee82bc3d8a36062f5116e98d0eaf0a53f236e3401567d44ab8928f"}