{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OHG5O5VCXKQ3LHVVBO6JUHVQBK","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":"52f2a22faa5b48a95ffff38f71e6d6ce20de64be94b2ea6e7781defbde79710b","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-01T16:54:41Z","title_canon_sha256":"115da04a9a5159ae865c31ab369c28a735675d0a644248acbad4721fa229af88"},"schema_version":"1.0","source":{"id":"1310.0392","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0392","created_at":"2026-05-18T03:11:35Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0392v2","created_at":"2026-05-18T03:11:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0392","created_at":"2026-05-18T03:11:35Z"},{"alias_kind":"pith_short_12","alias_value":"OHG5O5VCXKQ3","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OHG5O5VCXKQ3LHVV","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OHG5O5VC","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:48c48c7e999a05c10732ffb53af1ddb31710a850f9b51d5a58c5c6c9f4cb36bb","target":"graph","created_at":"2026-05-18T03:11:35Z","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":"We discuss numerical approximation methods for Random Time Change equations which possess a deterministic drift part and jump with state-dependent rates. It is first established that solutions to such equations are versions of certain Piecewise Deterministic Markov Processes. Then we present a convergence theorem establishing strong convergence (convergence in the mean) for semi-implicit Maruyama-type one step methods based on a local error analysis. The family of $\\Theta$--Maruyama methods is analysed in detail where the local error is analysed in terms of It{\\^o}-Taylor expansions of the exa","authors_text":"Girolama Notarangelo, Martin G. Riedler","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-01T16:54:41Z","title":"Strong Error Analysis of the $\\Theta$-Method for Stochastic Hybrid Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0392","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":"sha256:9424d7bcec2a7f885d404fe9d39134074a92166b7db944cf23a625763dd5f606","target":"record","created_at":"2026-05-18T03:11:35Z","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":"52f2a22faa5b48a95ffff38f71e6d6ce20de64be94b2ea6e7781defbde79710b","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-01T16:54:41Z","title_canon_sha256":"115da04a9a5159ae865c31ab369c28a735675d0a644248acbad4721fa229af88"},"schema_version":"1.0","source":{"id":"1310.0392","kind":"arxiv","version":2}},"canonical_sha256":"71cdd776a2baa1b59eb50bbc9a1eb00abfb68ff3434994b503422f873d6d7395","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71cdd776a2baa1b59eb50bbc9a1eb00abfb68ff3434994b503422f873d6d7395","first_computed_at":"2026-05-18T03:11:35.218985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:35.218985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8MwD0/f7ae/hwGgv07VmrENg9VmO1W95cQH5ju/sHnNIb+7cHl/1vBCQXdubnhhkyDItXBn54Q0ius73VuOUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:35.219524Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0392","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9424d7bcec2a7f885d404fe9d39134074a92166b7db944cf23a625763dd5f606","sha256:48c48c7e999a05c10732ffb53af1ddb31710a850f9b51d5a58c5c6c9f4cb36bb"],"state_sha256":"0d4d71348492d6119e71711fe236360e3ac0f07656b077904405fdfe37b5a01d"}