{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JZSTMSGVHIJQP6NJHMY4ATHIJT","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":"4186feda2781dc64096bc8539a325ced9afd6efb47c0150786a01008fc84b1a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-14T09:27:14Z","title_canon_sha256":"4e4ad47caa302c121e286d26b32a82fb1f140480450000622875f06ee09090de"},"schema_version":"1.0","source":{"id":"1212.3420","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3420","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3420v4","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3420","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"JZSTMSGVHIJQ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JZSTMSGVHIJQP6NJ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JZSTMSGV","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:4f5e54af05d7d34b3a70df5dc9c887684770618ec060c9dfe34a2990bbb2e357","target":"graph","created_at":"2026-05-18T01:20:50Z","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":"We consider the $L_2$-regularity of solutions to backward stochastic differential equations (BSDEs) with Lipschitz generators driven by a Brownian motion and a Poisson random measure associated with a L\\'{e}vy process $(X_t)_{t\\in[0,T]}$. The terminal condition may be a Borel function of finitely many increments of the L\\'{e}vy process which is not necessarily Lipschitz but only satisfies a fractional smoothness condition. The results are obtained by investigating how the special structure appearing in the chaos expansion of the terminal condition is inherited by the solution to the BSDE.","authors_text":"Alexander Steinicke, Christel Geiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-14T09:27:14Z","title":"$L_2$-variation of L\\'{e}vy driven BSDEs with non-smooth terminal conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3420","kind":"arxiv","version":4},"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":"sha256:15f489508103412070af0d3958fed37af64ac79e8a2e9de443e7fda222a6b222","target":"record","created_at":"2026-05-18T01:20:50Z","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":"4186feda2781dc64096bc8539a325ced9afd6efb47c0150786a01008fc84b1a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-14T09:27:14Z","title_canon_sha256":"4e4ad47caa302c121e286d26b32a82fb1f140480450000622875f06ee09090de"},"schema_version":"1.0","source":{"id":"1212.3420","kind":"arxiv","version":4}},"canonical_sha256":"4e653648d53a1307f9a93b31c04ce84cf7e1af2fe8b125bc71e17fb3c772068c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e653648d53a1307f9a93b31c04ce84cf7e1af2fe8b125bc71e17fb3c772068c","first_computed_at":"2026-05-18T01:20:50.879543Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:50.879543Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rrxZG5il6PPi4xNaPaqWVgrySPEHDzi9qAxnukYk1eGfDjB4Wx6Sd01XrpYhsPna0QxU8dcP8rSrJpZhcVMZBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:50.880224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3420","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15f489508103412070af0d3958fed37af64ac79e8a2e9de443e7fda222a6b222","sha256:4f5e54af05d7d34b3a70df5dc9c887684770618ec060c9dfe34a2990bbb2e357"],"state_sha256":"5f07862f1f9987b2897de169c2a62d2c4b54dfe06c092430bcf03a1a9627fbde"}