{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:XN55T4DRICVQJIPKL3V5WFUVS3","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":"2efdb741e5ec72e3dcdc1048618bc9c702e8a110d066cf6d30c0593df9e993b9","cross_cats_sorted":["cs.NA","math.PR"],"license":"","primary_cat":"math.NA","submitted_at":"2006-09-06T19:47:44Z","title_canon_sha256":"13d466d0f000d51b54460017b088a14a98f5b8fb4831a7e4c6f78e719d7ed0e3"},"schema_version":"1.0","source":{"id":"math/0609186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609186","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609186v1","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609186","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"XN55T4DRICVQ","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"pith_short_16","alias_value":"XN55T4DRICVQJIPK","created_at":"2026-06-03T22:06:20Z"},{"alias_kind":"pith_short_8","alias_value":"XN55T4DR","created_at":"2026-06-03T22:06:20Z"}],"graph_snapshots":[{"event_id":"sha256:dc58626e9ea8cfa00810c0f8cfd17227ce158f9bc97ac7643a00e8b712f186c1","target":"graph","created_at":"2026-06-03T22:06:20Z","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/math/0609186/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational error, with computable leading order term in a posteriori form, based on stochastic flows and discrete dual backward problems which extends the results in [STZ]. These expansions lead to efficient and accurate computation of error estimates. Adaptive algorithms for either stochastic time steps or quasi-deterministic time steps are described. Numerical examples ","authors_text":"A. Szepessy, E. Mordecki, G. E. Zouraris, R. Tempone","cross_cats":["cs.NA","math.PR"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2006-09-06T19:47:44Z","title":"Adaptive Weak Approximation of Diffusions with Jumps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609186","kind":"arxiv","version":1},"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":"sha256:93a128c2c70d243b630df8437071ce316ba692e3bf3d6ed1f7df48544c847844","target":"record","created_at":"2026-06-03T22:06:20Z","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":"2efdb741e5ec72e3dcdc1048618bc9c702e8a110d066cf6d30c0593df9e993b9","cross_cats_sorted":["cs.NA","math.PR"],"license":"","primary_cat":"math.NA","submitted_at":"2006-09-06T19:47:44Z","title_canon_sha256":"13d466d0f000d51b54460017b088a14a98f5b8fb4831a7e4c6f78e719d7ed0e3"},"schema_version":"1.0","source":{"id":"math/0609186","kind":"arxiv","version":1}},"canonical_sha256":"bb7bd9f07140ab04a1ea5eebdb169596e4375ae2af51a315f9a0516db91a5113","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb7bd9f07140ab04a1ea5eebdb169596e4375ae2af51a315f9a0516db91a5113","first_computed_at":"2026-06-03T22:06:20.509320Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:20.509320Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gvvE59OjRJDOgLbkgH27sKZQ4rosyvcFeyjpRhIBfs/MY8AKI6Mc452GrLP92Z1F5Bs4nnh7Yas6cIyKLBkiAg==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:20.509721Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0609186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:93a128c2c70d243b630df8437071ce316ba692e3bf3d6ed1f7df48544c847844","sha256:dc58626e9ea8cfa00810c0f8cfd17227ce158f9bc97ac7643a00e8b712f186c1"],"state_sha256":"0ff623a2954ce97f737154167cc7fc0993b900e5c0c847e86d1049a1dbea43e6"}