{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:FMY6FCJYGYKDV2KWDCDTKMBOOI","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":"1ab452dfee64a869e9c6e190f7331783409bc62605a361245f28ffc79f7d58e0","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-12-10T12:03:07Z","title_canon_sha256":"8442c14ad1ef982453304de0072ed4aabcea84e4f999a4002f5427ca497b69b8"},"schema_version":"1.0","source":{"id":"0912.1968","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.1968","created_at":"2026-06-03T23:06:31Z"},{"alias_kind":"arxiv_version","alias_value":"0912.1968v2","created_at":"2026-06-03T23:06:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.1968","created_at":"2026-06-03T23:06:31Z"},{"alias_kind":"pith_short_12","alias_value":"FMY6FCJYGYKD","created_at":"2026-06-03T23:06:31Z"},{"alias_kind":"pith_short_16","alias_value":"FMY6FCJYGYKDV2KW","created_at":"2026-06-03T23:06:31Z"},{"alias_kind":"pith_short_8","alias_value":"FMY6FCJY","created_at":"2026-06-03T23:06:31Z"}],"graph_snapshots":[{"event_id":"sha256:52bff64459e5c4bc8a72d7794d082c922647b2f69ef50c786dc5aa7febd1fbeb","target":"graph","created_at":"2026-06-03T23:06:31Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0912.1968/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article we compare the mean-square stability properties of the Theta-Maruyama and Theta-Milstein method that are used to solve stochastic differential equations. For the linear stability analysis, we propose an extension of the standard geometric Brownian motion as a test equation and consider a scalar linear test equation with several multiplicative noise terms. This test equation allows to begin investigating the influence of multi-dimensional noise on the stability behaviour of the methods while the analysis is still tractable. Our findings include: (i) the stability condition for t","authors_text":"Evelyn Buckwar, Thorsten Sickenberger","cross_cats":["cs.NA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-12-10T12:03:07Z","title":"A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1968","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":"sha256:238ff8cc18d321783f98a970a3156a15c2cf356d3289fe3a64bafd0573aea0e6","target":"record","created_at":"2026-06-03T23:06:31Z","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":"1ab452dfee64a869e9c6e190f7331783409bc62605a361245f28ffc79f7d58e0","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2009-12-10T12:03:07Z","title_canon_sha256":"8442c14ad1ef982453304de0072ed4aabcea84e4f999a4002f5427ca497b69b8"},"schema_version":"1.0","source":{"id":"0912.1968","kind":"arxiv","version":2}},"canonical_sha256":"2b31e2893836143ae956188735302e722aed1e91661bac2f7464b2e920eb4789","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b31e2893836143ae956188735302e722aed1e91661bac2f7464b2e920eb4789","first_computed_at":"2026-06-03T23:06:31.271693Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:06:31.271693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZwXO7Fpt4bpCL9bPiTWygzbgR7cYwKTN3Y9qhkXL/xYE6Pat/0Nb7C3vz5hweB8NEqDT/WHl2L8WjYgWXTIBAw==","signature_status":"signed_v1","signed_at":"2026-06-03T23:06:31.272172Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.1968","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:238ff8cc18d321783f98a970a3156a15c2cf356d3289fe3a64bafd0573aea0e6","sha256:52bff64459e5c4bc8a72d7794d082c922647b2f69ef50c786dc5aa7febd1fbeb"],"state_sha256":"c74503c6dcd32c643c86105a3d4ace68be2d353aa12231b63304f1b3026039cd"}