{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EUJA5BCQUBC5YPRYHT4DA4WHR4","short_pith_number":"pith:EUJA5BCQ","canonical_record":{"source":{"id":"1301.0442","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-03T12:52:04Z","cross_cats_sorted":[],"title_canon_sha256":"9fadba527815f7edaa2bb023a90b45538cb4fb0d811e9b043ccad5eddd96271a","abstract_canon_sha256":"464efb305ecdac7fb0154fab97ea16e17ac19e39c6ccbb1c44baa3bfb04124d8"},"schema_version":"1.0"},"canonical_sha256":"25120e8450a045dc3e383cf83072c78f11c9e620d6bed31db28871976b28887f","source":{"kind":"arxiv","id":"1301.0442","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0442","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0442v2","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0442","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"EUJA5BCQUBC5","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EUJA5BCQUBC5YPRY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EUJA5BCQ","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EUJA5BCQUBC5YPRYHT4DA4WHR4","target":"record","payload":{"canonical_record":{"source":{"id":"1301.0442","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-03T12:52:04Z","cross_cats_sorted":[],"title_canon_sha256":"9fadba527815f7edaa2bb023a90b45538cb4fb0d811e9b043ccad5eddd96271a","abstract_canon_sha256":"464efb305ecdac7fb0154fab97ea16e17ac19e39c6ccbb1c44baa3bfb04124d8"},"schema_version":"1.0"},"canonical_sha256":"25120e8450a045dc3e383cf83072c78f11c9e620d6bed31db28871976b28887f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:45.427805Z","signature_b64":"7Na36DIHKxzu87JgkUCIz9UyLpvjIC6uIjT7uHGJns9GFim09CwRkbfuw6Fd5ZC5eoHOEaXaKT+oWjli0laLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25120e8450a045dc3e383cf83072c78f11c9e620d6bed31db28871976b28887f","last_reissued_at":"2026-05-18T01:21:45.427170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:45.427170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.0442","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e7bklusKly+TydFEKOD351CFbYy4ekhPnmDO2j3909V4ju1KwdLGPvwW5zHBXCsnEekCRSflhJ89ReC4MJgkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:11:26.843068Z"},"content_sha256":"437bc501c45ed43633f97e412c06b215b0baeff41825a3d519950cde6c348a90","schema_version":"1.0","event_id":"sha256:437bc501c45ed43633f97e412c06b215b0baeff41825a3d519950cde6c348a90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EUJA5BCQUBC5YPRYHT4DA4WHR4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Delay Differential Equations with Jump Reflection: Invariant Measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chenggui Yuan, Lijun Bo","submitted_at":"2013-01-03T12:52:04Z","abstract_excerpt":"In this paper, we consider a class of multi-dimensional stochastic delay differential equations with jump reflection. Based on existence and uniqueness of the strong solution to the equation, we prove that the Markov semigroup generated by the segment process corresponding to the solution admits a unique invariant measure on the Skorohod space when the coefficients of equation satisfy a class of monotone conditions. Finally, we establish a relationship between the regulator and the local time of the solution and discuss a local time property at large time under the stationary setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0442","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xK5Rx/ZHKj8rn4EicA5KRRAQ2unEYgl6fJ2YJCdqZX1FFZqtpojs1ob9t9WfiMwdcrXWtlgWQptzcpKlGR3/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:11:26.843767Z"},"content_sha256":"93ab2860178e071b85f893999bd704c49cbd1170aaba618bff2e6ffdc9069f53","schema_version":"1.0","event_id":"sha256:93ab2860178e071b85f893999bd704c49cbd1170aaba618bff2e6ffdc9069f53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EUJA5BCQUBC5YPRYHT4DA4WHR4/bundle.json","state_url":"https://pith.science/pith/EUJA5BCQUBC5YPRYHT4DA4WHR4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EUJA5BCQUBC5YPRYHT4DA4WHR4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T17:11:26Z","links":{"resolver":"https://pith.science/pith/EUJA5BCQUBC5YPRYHT4DA4WHR4","bundle":"https://pith.science/pith/EUJA5BCQUBC5YPRYHT4DA4WHR4/bundle.json","state":"https://pith.science/pith/EUJA5BCQUBC5YPRYHT4DA4WHR4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EUJA5BCQUBC5YPRYHT4DA4WHR4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EUJA5BCQUBC5YPRYHT4DA4WHR4","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":"464efb305ecdac7fb0154fab97ea16e17ac19e39c6ccbb1c44baa3bfb04124d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-03T12:52:04Z","title_canon_sha256":"9fadba527815f7edaa2bb023a90b45538cb4fb0d811e9b043ccad5eddd96271a"},"schema_version":"1.0","source":{"id":"1301.0442","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0442","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0442v2","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0442","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"EUJA5BCQUBC5","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EUJA5BCQUBC5YPRY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EUJA5BCQ","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:93ab2860178e071b85f893999bd704c49cbd1170aaba618bff2e6ffdc9069f53","target":"graph","created_at":"2026-05-18T01:21:45Z","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 this paper, we consider a class of multi-dimensional stochastic delay differential equations with jump reflection. Based on existence and uniqueness of the strong solution to the equation, we prove that the Markov semigroup generated by the segment process corresponding to the solution admits a unique invariant measure on the Skorohod space when the coefficients of equation satisfy a class of monotone conditions. Finally, we establish a relationship between the regulator and the local time of the solution and discuss a local time property at large time under the stationary setting.","authors_text":"Chenggui Yuan, Lijun Bo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-03T12:52:04Z","title":"Stochastic Delay Differential Equations with Jump Reflection: Invariant Measure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0442","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":"sha256:437bc501c45ed43633f97e412c06b215b0baeff41825a3d519950cde6c348a90","target":"record","created_at":"2026-05-18T01:21:45Z","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":"464efb305ecdac7fb0154fab97ea16e17ac19e39c6ccbb1c44baa3bfb04124d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-03T12:52:04Z","title_canon_sha256":"9fadba527815f7edaa2bb023a90b45538cb4fb0d811e9b043ccad5eddd96271a"},"schema_version":"1.0","source":{"id":"1301.0442","kind":"arxiv","version":2}},"canonical_sha256":"25120e8450a045dc3e383cf83072c78f11c9e620d6bed31db28871976b28887f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25120e8450a045dc3e383cf83072c78f11c9e620d6bed31db28871976b28887f","first_computed_at":"2026-05-18T01:21:45.427170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:45.427170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Na36DIHKxzu87JgkUCIz9UyLpvjIC6uIjT7uHGJns9GFim09CwRkbfuw6Fd5ZC5eoHOEaXaKT+oWjli0laLDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:45.427805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0442","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:437bc501c45ed43633f97e412c06b215b0baeff41825a3d519950cde6c348a90","sha256:93ab2860178e071b85f893999bd704c49cbd1170aaba618bff2e6ffdc9069f53"],"state_sha256":"c997d9abbae668236d730af0ee1620c61e0b80dbe07a2feb72b076aa00f73eee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"veiwiVyHmlCMZnZlxBbUbF8/5yxCMkxYMNsj5x6MQpOnHN960Tsd72mogoh15zRQWNyecXdEZYX9EFpjsJKACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T17:11:26.849185Z","bundle_sha256":"f94be3202defef707f76bf5ea309af07bc2e51b7efe9063f90da61987d47db44"}}